Financing Risky R&D Projects under Asymmetric

Information

Research Thesis

Submitted in Partial Fulfillment of the Requirements for the

Degree of Master of Science in Economics

Submitted to the Senate of the Technion

Israel Institute of Technology

University of Haifa – The Graduate School

Tevet 5777 Haifa January 2007

Financing Risky R&D Projects under Asymmetric

Information

Research Thesis

Submitted in Partial Fulfillment of the Requirements for the

Degree of Master of Science in Economics

Lev Noppe

Submitted to the Senate of the Technion

Israel Institute of Technology

University of Haifa – The Graduate School

Tevet 5777 Haifa January 2007

Approved By ________________________________ Date ____________ Supervisor

Approved By ________________________________ Date ____________ Dean Of Graduate School Technion

Approved By ________________________________ Date ____________

Dean Of Graduate School University Of Haifa

Approved By ________________________________ Date ____________

Chairman Of M.A / Doctorate Committee Department Of Economics

The Research Theses Were Carried Out

Within The Framework

Of The Joint Program In Economics

Of The Technion – Israel Institute Of Technology

And The University Of Haifa

Under The Supervision of

Professor Dan Peled

Table Of Contents

Chapter 1: Introduction ............................................................................................ 1

1.1 Goals and purposes of the work.......................................................................... 1

1.2 Venture capital ................................................................................................... 2

1.2.1 VC in financing R&D...................................................................................... 2

1.2.2 Organizational aspects of VC activity .............................................................. 4

1.3 Informational asymmetry in the VC market ........................................................ 6

1.4 Description of the work ...................................................................................... 8

1.5 Results of the work........................................................................................... 10

Chapter 2. A Model with Endogenous Investments ................................................ 14

2.1 The Market Environment.................................................................................. 14

2.2 Benchmark case: Equilibrium with single project type...................................... 15

2.3. Equilibrium with heterogeneous projects ......................................................... 17

2.3.1 Full information case ..................................................................................... 17

2.3.2 Asymmetric information case ........................................................................ 17

2.3.3 Uniqueness and existence conditions of the separating equilibrium................ 20

2.4. Results of the Chapter...................................................................................... 21

Chapter 3: Entrepreneurial Effort ........................................................................... 22

3.1. Modelling entrepreneurial effort ...................................................................... 22

3.2. Equilibrium contracting with homogenous projects ......................................... 24

3.2.1. Observable effort .......................................................................................... 24

3.2.2 Unobservable effort ....................................................................................... 25

3.3 Two types of project ......................................................................................... 28

3.3.1 Observable type............................................................................................. 29

3.3.2 Unobservable type and effort ......................................................................... 31

3.4 Numerical example........................................................................................... 33

3.4.1. Equilibrium contracts in case of observable type and effort........................... 33

3.4.2. ZPIC contract set .......................................................................................... 34

3.4.3 Equilibrium contracts in case of observable type........................................... 34

3.4.4 Equilibrium contracts in case of unobservable types ..................................... 36

3.5 Results of the Chapter ...................................................................................... 38

Table Of Contents (Continued)

Chapter 4: Venture Capital Effort........................................................................... 39

4.1. Modeling the impact of VC effort.................................................................... 39

4.2 Single Project Type .......................................................................................... 40

4.2.1. Observable VC effort.................................................................................... 40

4.2.2. Unobservable VC effort................................................................................ 42

4.3 Two types of project ......................................................................................... 43

4.3.1. Observable VC effort.................................................................................... 43

4.3.2. Unobservable VC effort................................................................................ 46

4.4 Numerical example........................................................................................... 49

4.5 Results of the Chapter ...................................................................................... 56

Conclusions............................................................................................................ 57

Bibliography .......................................................................................................... 58

List of Tables

Table 3.1 Functions used in the model……………………………………………….. 23

Table 3.2 Functions used in the numerical example…………………………………. 33

Table 3.3 Calculated equilibrium values for full information case…………………... 34

Table 3.4 Calculated equilibrium values for observable type case…………………... 36

Table 3.5 Utilities from the contracts C and D……………………………………….. 37

Table 3.6 Utilities from the contracts F and D……………………………………….. 37

Table 3.7 Equilibrium contracts for the unobservable type case……………………... 38

Table 3.8 Equilibrium contracts for all cases…………………..…………………….. 38

Table 4.1 Functions and parameters used in the numerical example………………… 49

Table 4.2 Calculated equilibrium contracts…………………………………………... 50

List of Figures

Figure 2.1: Single Type Equilibrium………………………………………………………. 16

Figure 2.2: The non-existence of pooling equilibrium…………………………………….. 18

Figure 2.3: Separating Equilibrium………………………………………………………… 19

Figure 3.1: The contracting process with unobservable effort……………………………... 27

Figure 3.2: The separating equilibrium with observable type and effort…………………... 29

Figure 3.3: The separating equilibrium with observable type and unobservable effort…… 30

Figure 3.4: ZPIC lines for G and B………………………………………………………… 34

Figure 3.5: Utility value as function of CH and CL along ZPIC lines for G and B………… 35

Figure 3.6: Utility value along the ZPIC line………………………………………………. 35

Figure 3.7: The finding of contract set that satisfies ASC constraints……………………... 36

Figure 4.1: Calculated values for three cases………………………………………………. 51

Figure 4.2. Case 2: Choosing effort level………………………………………………...... 51

Figure 4.3. Case 2: Possible G payoff sets (CHG , CLG) for different VC effort levels…….. 52

Figure 4.4. Case 3: Choosing effort level.…………………………………………………. 53

Figure 4.5. Case 3: Possible G payoff sets (CHG , CLG) for different VC effort levels…….. 54

List of Symbols and Abbreviations

GDP - Gross Domestic Product

ICT - information and communications technology

OECD - Organisation for Economic Co-Operation and Development

R&D - research and development

R-S - the model of Rothschild and Stiglitz (1979)

ASC - adverse selection constraint

B - low quality project

CH - payoff to entrepreneur in case of high outcome of the project

CL - payoff to entrepreneur in case of low outcome of the project

C - payoff to entrepreneur in case of unobservable effort

d(e) - effort cost function of venture capitalist

E - entrepreneur

e - effort level exerted by entrepreneur

e* - equilibrium effort level in case of observable effort

e - equilibrium effort level in case of unobservable effort

e0 - minimal effort level

e1 - maximal possible effort level

G - high quality project

h(e) - disutility of entrepreneur from effort

I* - entrepreneur's choice of investment size

I0 - initial endowment

I - fixed level of investment

K - set of alternative contracts

MHC - moral hazard constraint

List of Symbols and Abbreviations (Continued)

N - venture capitalist’s profits in case of observable effort

N - venture capitalist’s profits in case of unobservable effort

p - probability of project’s high outcome

p(e) - probability function of the project’s high outcome

q - proportion of high quality projects in the market

RH - high outcome of the project

RL - low outcome of the project

s - state of nature, },{ LHs ∈

U(⋅) - utility function of the entrepreneur

VC - venture capitalist

VE - expected utility of entrepreneur

W - venture capitalist’s profits if he does not fund any risky project

w - part of calculated expected venture capitalist’s profits over W

Y - venture capitalist’s expected net profits

Y-line - venture capitalist’s zero expected profits line

Z(I,R) - outcome function

Z~ - project gross profit

ZPIC - zero profit incentive compatible contracts set ψ - equilibrium contract set

∆ - proportion of w that keeps the incentive compatibility constraint

Financing Risky R&D Projects under Asymmetric Information

Noppe Lev

Abstract

We develop a model of competitive venture capital market for R&D projects financing

and analyze the conflicts of interest and contracting process in the presence of informational

asymmetry. We consider the effects of different types of informational asymmetries on

equilibrium in these markets. The informational asymmetries can be single and two-sided, and

can include the project’s innate quality, as well as the effort exerted by the inventor and

venture capitalist. Assuming away monitoring of inventors during the R&D process, we study

the equilibrium screening and funding of projects when the only instruments available are ex-

ante self-selection by inventors among funding contracts, which specify investment levels in

the project and ex-post distribution of project’s random returns between the inventor and the

financier. We find that investment levels can be optimal even when the project types are

unobservable to the venture capitalist. The informational asymmetry about both the quality of

project and entrepreneur actions reduces the utility of entrepreneurs with better projects but

increases their efforts and consequently the chances of project success. The informational

asymmetry about venture capitalist’s actions leads to the further decrease of entrepreneurial

utility and to an equilibrium level of effort by the venture capitalist which is lower than the

level that both parties prefer.

אינפורמציה לא סימטרית תחתפ "מימון פרויקטי מו

מחקר על חיבור

התואר לקבלת הדרישות של חלקי מילוי לשם

בכלכלה למדעים מגיסטר

לישראל טכנולוגי מכון - הטכניון לסנט הוגש

2007 ינואר חיפה ז"תשס טבת

אינפורמציה לא סימטרית תחתפ"מימון פרויקטי מו

מחקר על חיבור

התואר לקבלת הדרישות של חלקי מילוי לשם

בכלכלה למדעים מגיסטר

לב נופה

לישראל טכנולוגי מכון - הטכניון לסנט הוגש

2007ינואר חיפה ז"תשס תבט

נעשה בהנחיית המחקר

פרופסור דן פלד

המשותפת לכלכלה במסגרת התוכנית

הבטכניון ובאוניברסיטת חיפ

:וכן הענייניםת

1.................................................................................................................מבוא. 1פרק

1.......................................................................................................מטרות העבודה 1.1

2...............................................................................................................הון סיכון 1.2

2................................................................................פ"מימון פרויקטי מולהון סיכון 1.2.1

4.........................................................היבטים ארגוניים של פעילות של קרנות הון סיכון 1.2.2

6...............................................................................ןבשוק הון סיכואסימטריות המידע 1.3

8.........................................................................................................תיאור המחקר 1.4

10.......................................................................................................תוצאות המקר 1.5

41..................................................................................ת אנדוגניות השקעועםמודל . 2פרק

41........................................................................................................סביבת השוק 2.1

15........................................................................פרויקטיםאחד של שווי משקל עם סוג 2.2

17...........................................................................שווי משקל עם פרויקטים הטרוגניים 2.3

71.........................................................................................................מלא עמיד 2.3.1

71.................................................................................................סימטרי-י מידע א 2.3.2

20...................................................................מיוחדות ותנאי קיום :שווי משקל מפריד 2.3.3

21.......................................................................................................תוצאות הפרק 2.4

22......................................................................................................מאמצי היזם. 3פרק

22......................................................................................מאמצי היזםעם מודלבניית 3.1

24.................................................................... שיווי משקל עם פרויקטים הומוגנייםיחוז 3.2

24...........................................................................................ה של היזם נצפץמאמ 3.2.1

25.......................................................................................ה של היזם לא נצפץמאמ 3.2.2

28.................................................................................................ים פרויקטסוגיי נש 3.3

29..............................................................יםפרויקטידועה של ה שווי משקל עם איכות 3.3.1

31....................................................................ידועיםלא היזםץומאמהפרויקט איכות 3.3.2

33......................................................................................................ה מספריתדוגמ 3.4

33...............................................יםנצפהיזם ץ סוג הפרויקט ומאמכאשרחוזי שווי משקל 3.4.1

ZPIC.........................................................................................34 קבוצת החוזים 3.4.2

34................................................................ידועפרויקט ה סוג כאשרחוזי שווי המשקל 3.4.3

36...........................................................לא ידוע סוג הפרויקט כאשרחוזי שווי המשקל 3.4.4

38.......................................................................................................תוצאות הפרק 3.5

)המשך (תוכן העניינים

39................................................................................................. המשקיעמאמצי. 4פרק

39..................................................................מאמצי המשקיעשל ההשפעעם בניית מודל 4.1

40...............................................................................................חדאסוג פרויקטים מ 4.2

40......................................................................................משקיעה של הנצפ ץמאמ 4.2.1

42..................................................................................המשקיעה של לא נצפ ץמאמ 4.2.2

43.................................................................................................טיםשני סוגי פרויק 4.3

43......................................................................................המשקיעשל הנצפ ץמאמ 4.3.1

46..................................................................................המשקיעשל הלא נצפ ץמאמ 4.3.2

49..................................................................................................... דוגמה מספרית 4.4

56.......................................................................................................תוצאות הפרק 4.5

57............................................................................................................סיכום ומסקנות

58............................................................................................................רשימת מקורות

רשימת טבלאות

23 ................................................................................הפונקציות המשמשות במודל 3.1טבלת

33 .................................................................המספרית בדוגמה המשמשות הפונקציות 3.2 טבלת

34 ....................................................................עם מידע מלא משקל שוויחוזי מימון ב 3.3 טבלת

36 ..........................................................ידועה הפרויקט איכות כאשר משקל שווי חוזי 3.4 טבלת

D........................................................................................ 37-ו C מחוזים תועלות 3.5 טבלת

D........................................................................................ 37-ו F מחוזים תועלות 3.6 טבלת

38 .................................. יםפרויקטהאיכויות לא ידועות של של במקרה משקל שווי חוזי 3.7 בלתט

38 .............................................................................טבלה מסכמת: משקל שווי חוזי 3.8 טבלת

49 .................................. זה למודלהמספרית בדוגמה המשמשים והפרמטרים הפונקציות 4.1 טבלת

50 .................................................................................................משקל שווי חוזי 4.2 טבלת

ציוריםרשימת

16 .............................................................................. ים זהיםפרויקט עם משקל שווי 2.1 ציור

18 .......... ..........................................................................מאחד משקל שווי קיום-אי 2.2 ציור

19 ...............................................................................................שווי משקל מפריד 2.3ציור

27 ..............................................................נצפים לא מאמצים של במקרה חוזהכריתת 3.1 ציור

29 ....................................ידועים היזםומאמצי ת הפרויקטוכאשר איכ מפריד משקל שווי 3.2 ציור

30 ............................ה נצפ לאהיזם ץומאמידוע כאשר איכות הפרויקט מפריד משקל שווי 3.3 ציור

B .............................................................. 34-ו G הפרויקטלסוגי ZPIC קבוצות קווי 3.4 ציור

B ................. 35- וG לסוגי פרויקט ZPICבקבוצות CL-ו CH של קציהכפונהיזמים תועלת 3.5 ציור

B ................................................. 35- וG לסוגי פרויקט ZPICבקבוצות היזמים תועלת 3.6 ציור

36 .................................... אילוץ בחירה שליליתהמקיימים מגבלת החוזים תוקבוצ מציאת 3.7 ציור

51 ......................................................................... המקרים שלושהל תוצאות החישוב 4.1 ציור

51 ................................................................................ המאמץ רמת בחירת: 2 מקרה 4.2 ציור

52 ......................... שונים למאמצים (CHG , CLG) האפשריים התשלומים צירופי: 2 מקרה 4.3 ציור

53 ............................................................................... ץהמאמ רמת בחירת: 3 מקרה 4.4 ציור

54 .........................שונים למאמצים (CHG , CLG) ייםהאפשר התשלומים צירופי: 3 מקרה 4.5 ציור

אינפורמציה לא סימטריתתחתפ "מוי מימון פרויקט

לב נופה: שם המחבר

תקציר

אינטרסיםהניגוד פ ובוחנים את "חים מודל של שוק הון סיכון תחרותי למימון פרויקטי מותאנחנו מנ

יכולה להיות אסימטריות המידע . מסוגים שוניםעות המידסימטרי- בתנאי אי החוזה חתימתותהליך

פרטי על איכות מידע לידי ביטוי במצבים שבהם לאחד או לשני הצדדים יש הבאו ,תצדדי- דו וא - חד

. לצד אחרות ידוען אשר אינ הננקטות על ידוהפרויקט או על פעולות

מימון של פרויקטים האלה שונה . קרנות הון סיכון מתמחות בשלבים מוקדמים של מימון הפרויקטים

לגבי תוצאות הפרויקט וקשיי התחלית ודאות - משמעותי מסוגים אחרים של פעילויות המימון עקב אי

גם לאחר מעשה קשה להפריד בין ההשפעה על , יתר על כן. הערכת הפוטנציאל המסחרי שלו

של היזם ושל הלצפיי ושל המאמצים הבלתי ניתנים, תוצאות הפרוייקט של איכותו המקורית מחד

המקשה על ההתקשרות סימטריות - איגורמים אלה יוצרים. המממן המסייע במהלך הפרוייקט מאידך

. החוזית בין הצדדים

בעיות האלה ולהתחרות המהן התכונות המיוחדות של קרנות הון סיכון שמאפשרות להן להתגבר על

מחקרים אמפיריים בתחום זה ? פ"ו במימון פרויקטי מבהצלחה עם ארגונים פיננסיים אחרים

: במידעסימטריות - אילפתרון בעיות הנובעות מדרכים הבאות של קרנות הון סיכון החים על ומדו

ניטור בשלבי המימון והשתתפות בניהול ,סינון לפני מימון, החוזהמיוחד של כתיבת תהליך

ן להתגבר על סוגים שונים יכולת של קרנות הון סיכואת ההעבודה שלנו מיועדת לבדוק . הפרויקט

. מימוןהשל בעיות המידע בשלבים המוקדמים של

לא סימטרי בין אנחנו מנתחים מודל שוק תחרותי של קרנות הון סיכון עם מידעזו בעבודה

או מניטורתוך התעלמות , יםהחוזומאפייני אנחנו בוחנים סינון מוקדם של פרויקטים . הצדדים

לנו מאפשרזה דבר . ם המשך מימון הפרויקט תלוי בתוצאות ביניים בהפרויקט בשלביםהמימון

תיואיכופרויקטים בעלי בין היזם למשקיע כמכשיר להבחנה בין ניםסיכוהחלוקת את להדגיש

למידע הפרטי של בנוסף כלומר ,צדדית- ת דווטריסימ- בעבודה זאת אנחנו מתייחסים לאי. שונות

מאמצים האת גם אנחנו בוחנים שהוא משקיע בהצלחתווהמאמצים , איכות הפרויקט על יזם ה

.נצפים של קרנות הון סיכוןהבלתי

חוסר מידע מלא : בספרות על קרנות הון סיכוןטופלה עד כה גישה זאת מעלה בעיה מעניינת שלא

רוב החוקרים . הפרויקט להצלחת וחשיבותה)קרנות הון סיכון(הגורם המממן של על מידת המאמץ

שקעתה בפרויקט גורמת לה השכן עצם מידע מצד קרן הון הסיכון בסימטריות - ן אימניחים שאי

אבל קיימת אפשרות שקרן הון סיכון עלולה לפעול באופן לא יעיל . להצלחתוה כמיטב יכולתותעשל

העובדה . בהינתן שאר פעולותיהפיננסייםו ניהוליים משאביםמגבלות על שונות כגוןעקב נסיבות

. הןפרטי שלה להצלחת הפרויקט נותנת חשיבות רבה למידע קריטי של קרנות הון סיכון ןדופקישת

נצפות של הבלתי פעילויות הציפיות היזם לגבי ששווי המשקל רגיש גם לתוצאות העבודה מראות

את קרן הון סיכון מעונינת לספק מאמצים נוספים ולשפר בו אנחנו מתארים מצב . סיכוןהקרן הון

כי ציפיות היזם לגבי הכוונות שלה לא אך נמנעת מכך בשווי משקל, ת הפרויקטסיכויי הצלח

. בפעולה כזותומכות

בעלי מתחרות על פרויקטים ) VC ( קרנות הון הסיכוןבושוק ב שווי המשקלאנו מנתחים את

(I) חייב בהשקעות,על מנת להתבצע ,כל פרויקט. (E) היזמים שהומצאו על ידי ותהשונת יואיכו

כאשר , הצלחה וכשלון: משתי התוצאותתאחבאופן אקראי מפיק פרויקטכל ). e (אמציםומ

ובמאמצים שהיזם , בסוג הפרויקט, ההוניתהשקעההיקף הביכולה להיות תלויה התפלגות התוצאות

שונים ה) bad (Bאו ) G )good: פרויקט יכול להיות אחד משני סוגים. והקרן מקדישים לפרוייקט

מטפל הוא אדיש לסיכון וVCכל . במאמצים של שני הצדדיםגם תלויה הלחה בהסתברות ההצ

,כלומר. לעיסוק בהון סיכוןכניסה ויציאהגבלות מ ואין, כמות גדולה של יזמים בשוק התחרותיב

,החוזהלפי . )הוא לא ייכנס לשוקשווה לרווחים שלו אם (Wסף שווה לרווח VCרווח של כל ה

VCהיכולים להיות תלויים בתוצאות פרויקט ומשלם ליזם תשלומים מקבל את כל תוצאות ה

אשר ד יחייש לו פרויקט , שונא סיכוןל נחשבכל יזם . החוזהחתימתהוגדרו במועד כפי ש, הפרויקט

הוא מוכר את כל . אחד בלבדVC עם חתום חוזהוהוא יכול ל, דרושה השקעה הונית להפעלתו

החוזה הוא ההסכם בין הצדדים על .הפרויקטהצלחת תוצאות הפרויקט תמורת התשלום התלוי ב

סכום ההשקעות וכמות , מתוצאות הפרויקטתכלומר התשלומים בכל אח, תנאים הניתנים לבדיקהה

.) לבדיקהתבתנאי שהינה ניתנ(המאמצים של כל צד

המפריד משקל השיווי ):1976(סטיגליץ - במודל אנחנו משתמשים בניסוח שווי משקל של רוטשילד

,Wרווח סף מיםמפיק רווחים לא פחות *K- כל חוזה ב) 1 :כך ש *K קבוצת חוזי השקעותואה

*Kמחוץ לקבוצהלא קיים חוזה ) 2; חופשי בין החוזים בקבוצהבאופן יזמים יכולים לבחור הכש

שני קיימים רק מודל זה ב . למשקיעW- מפיק יותר תועלת ליזם כלשהו ומפיק רווח לא פחות מה

שיווי משקל בשווי משקל משותף כל היזמים מקבלים חוזה אחיד וב. אפשרייםשקלסוגי שווי מ

. חוזים שוניםב בוחריםמפריד יזמים שונים

השפעת מידע לא ספרות על הסקירת , הפרק הראשון של העבודה מוקדש לתיאור שוקי הון סיכון

אנחנו בוחנים את בפרק השני . ותיאור כללי של המודל ותוצאות המחקרפ "סימטרי במימון מו

בסוג הפרויקט ובהיקף אלא רק הפרויקט לא תלויה במאמצי הצדדים בו הצלחתהמודל הבסיסי

הפרויקט לא כאשר איכותאנחנו בוחנים את יכולת השוק להשיג שווי משקל . ההונית בוההשקעה

תייבעבמצב זה קיימת . והיזמים יכולים לבחור באופן חופשי את סכום ההשקעותVC- לידועה

לגבי איכות הפרויקט פוגע ביזמים בעלי עת המידוסימטרי- המצב כשקיום אי (בחירה שלילית

אך היכולת לשנות , בלבדאנחנו מראים שבשוק זה קיים שווי משקל מפריד). הפרויקטים הטובים

. את גודל ההשקעה בפרויקט איננה מסייעת בהפרדה בין היזמים בעלי פרויקטים באיכויות שונות

ההשקעות שממקסמת את עודף רווחי סכום ים בוחרמיםיזה כל :ה העיקרית של מודל זההמסקנ

.Gכצפוי בעיית בחירה שלילית מורידה את התועלת של היזמים מסוג . הפרויקט

מאמצי היזם משפיעים על הסתברות הצלחת שווי המשקל כאשרבפרק השלישי אנחנו בוחנים את

ע בעיות המידותבשוק קיימ, כלומר. VC- לידועים לא , הפרויקטבנוסף לאיכות, והםהפרויקט

אשר המצב כ (סיכון מוסריו ,)י איכויות שונותלבין פרויקטים בע( בחירה שלילית: משני הסוגים

סוגים : הןמסקנות הפרק העיקריות). י המשקיע"ע ותלא נצפלאחר חתימת החוזה לות היזם ופע

בעיית : ה שונוחי היזמים והצלחת הפרויקטים באופןמשפיעים על רו עסימטריות המיד- שונים של אי

שלילית הבחירה הבעיית . גי היזמיםוכמות המאמצים של כל סומוסרי מורידה את התועלת הסיכון ה

. ומעלה את רמת המאמצים שלהםGיזמים מסוג פוגעת בתועלת של ה

בחירה : צדדים משני העסימטריות המיד- אישווי המשקל תחת את בפרק הרביעי אנחנו בוחנים

הפרויקט לא איכותאנחנו מניחים כי . ת בו זמני,VC- שלילית מצד היזמים וסיכון מוסרי מצד ה

. י היזמים"ענצפים שאינם VC והסתברות הצלחת הפרויקט תלויה במאמצים של VC- לידועה

להשקיע מאמצים מעל לרמה VC- בחירה שלילית גורמת ל :אנחנו מגיעים למסקנות הבאות

זה מעלה את ההסתברות הצלחת הפרויקט אך גם את ההוצאות . ת את עודף רווחי הפרויקטשממקסמ

(G) משקיע בפרויקט הטובהואנצפים אינם VCשל מאמצים הר שא כ.נוספיםה מאמציםה עקב

בין למרות התחרות סףה מעל לרווח עולים ורווחיו) B (פחות מאמצים מאשר בפרויקט הרע

בים א להשתמש בכל המשVC- מונעת מ VC מצד עסימטריות המיד- שאי אומר הז. בשוקהמשקיעים

.כדי לנצח בתחרותשלרשותו

:המסקנות העיקריות של העבודה

לא מידע יכול להתקיים חרף קשיים הנובעים מ בשוק הון סיכון תחרותישווי משקל .1

.סימטרי

פרויקטים בעלי הכנסות של יזמים בהקטנת ה יאהסימטרי לא ההשפעה העיקרית של מידע .2

.פרויקטים הלא איכותייםקיומם של בגלל ,טובים

.הצדדיםשני ת המאמצים של ורמעל צורות הפוכות במשפיעות עבעיות המיד .3

הסתברות הצלחת הפרויקט ולכן את VC לא סימטרי מעלה את רמת המאמצים של מידע .4

.מקרה של מידע מלאב המעל לרמ

שתמש בכל המשאבים לצורך התחרות ולכן להVC- צדדי לא מאפשר ל- לא סימטרי דומידע .5

.סף מפיק רווחים מעל לרווח הוא

על שוקי הון סיכון דורשעעל סמך תוצאות העבודה אפשר לטעון שנושא השפעת אסימטריות המיד

לא תחרותיים ם בשווקיעלבחון השפעת בעיות המיד) 1: זהמחקר כ הכיוונים האפשריים ל.ףמחקר נוס

כדאיות להסיק לגבי יהיה מכך אפשר . פ"קטי מויבהקצאת הון לפרו שונים שווקים היעילות של על

.גדול של סוגי הפרויקטיםמספר את המודל עם להרחיב ) 2 . בשוקי הון סיכוןהממשלהתערבות ה

רשימת סמלים וקיצורים

GDP - תוצר לאומי גולמי

ICT - טכנולוגיות המידע והתקשורת

OECD - ח כלכליהארגון לשיתוף פעולה ופיתו

R&D - מחקר ופיתוח

R-S - )1979(סטיגליץ -המודל של רוטשילד

ASC - אילוץ בחירה שלילית

B - פרויקט בעל איכות נמוכה

CH - תשלום ליזם במקרה של הצלחת הפרויקט

CL - תשלום ליזם במקרה של כשלון הפרויקט

C - תשלום ליזם במקרה של מאמצים לא נצפים

d(e) - פונקציות ההוצאות על מאמצים של קרן הון סיכון

E - היזם

e - מאמצי היזם

*e - רמת שווי משקל של מאמצים במקרה של מאמצים נצפים

e - רמת שווי משקל של מאמצים במקרה של מאמצים לא נצפים

e0 - ת של מאמצים ירמה מינימאל

e1 - ת של מאמציםיה מקסימאלרמ

G - פרויקט בעל איכות גבוהה

h(e) - סבל מאמץ של היזם

*I - בחירת היזם של רמת ההשקעות בפרויקט

I0 - ת שברשות היזםיהשקעה הראשונ

I - רמת ההשקעות הקבועה K - קבוצת החוזים

MHC - אילוץ סיכון מוסרי

)המשך (ים וקיצוריםרשימת סמל

N - במקרה של מאמצים נצפיםרווחי קרן הון סיכון

N - במקרה של מאמצים לא נצפיםרווחי קרן הון סיכון

p - הסתברות הצלחת הפרויקט

p(e) - פונקצית הסתברות הצלחת הפרויקט

q - בשוקהאיכותייםפרופורציה של הפרויקטים

RH - לחת הפרויקטהצמקרה

RL - כשלון הפרויקטמקרה

},{מצב הטבע LHs ∈ - s

(⋅)U - פונקצית התועלת של היזם

VC - קרן הון סיכון

VE - תוחלת התועלת של היזם

W - קרן הון סיכוןרווח סף של

w - מעבר לרווח סףקרן הון סיכוןחלק של רווחי

Y - הון סיכוןקרן תועלת הרווחים של

Y-line - קרן הון סיכוןקו רווחי סף של

Z(I,R) - פונקצית תוצאות הפרויקט

~Z - רווחים גולמיים של הפרויקט ZPIC - תמריציםהקבוצת החוזים עם רווח סף והתאמת

ψ - קבוצת חוזי שווי משקל

∆ - תמריציםהמקיימת אילוץ התאמת ש wפרופורציה של

Chapter 1: Introduction

1.1 Goals and purposes of the work

The role of venture capital in innovation process financing has been examined

extensively by researchers in economics and finance. Venture capital firms (VC) specialize in

the early stage financing of entrepreneurial projects. The financing process of such projects

differs significantly from other kinds of investment activity because of the high uncertainty

about the results of research process and the inherent difficulties in evaluating the progress of

the project and its commercial success. These features lead to high level of informational

asymmetry concerning the project quality and exerted efforts.

What are the particular features of venture capital contracts that can overcome these

problems to compete successfully with other financial structures? The empirical studies in this

field report the following ways used by venture capital firms to circumvent the informational

asymmetry: special structured contracting, pre-investment screening, post-investment

monitoring and participation in project management (Kaplan and Stromberg, 2001). Our work

is dedicated to analysis of venture capitalist’s responses to various kinds of informational

problems in the early stages of the investing process.

We propose a model of competitive venture capital market with informational

imperfections. We consider initial project screening and contracting, abstracting from

monitoring or staging of capital infusion, which are sometimes used in actual VC contracts.

This allows us to emphasize the trade-off between risk allocation and project quality in the

investment contract. In this work we address the venture market reaction to the different

forms of informational asymmetry including single and double-sided informational

asymmetry. We consider not only entrepreneurial hidden information, such as project quality

or entrepreneurial effort, but also unobservable actions by the venture capitalist.

Our approach underscores the interesting problem that was not developed in the venture

capital literature – the observability of venture capitalist actions and its importance for the

project success. Most of the authors assumed that there is no informational asymmetry from

venture capitalist’s side because he is an organizer and is interested to do his best to promote

the project. But this point of view does not take into consideration that venture capitalist could

act inefficiently because of lack of resources, management problems, improper use of

investments or other circumstances. The fact that venture capitalist actions play crucial role

2

for project success makes the hidden information concerning his actions very important. Our

results reveal the importance of entrepreneur’s belief about the real actions of venture

capitalist. In particular, we show a situation where in equilibrium the venture capitalist avoids

providing additional efforts that improve the project success chances because such action is

not supported by entrepreneur’s beliefs about these unobservable actions.

The results that we got by means of this model let us conclude that the influence of

informational imperfections on the different parameters of competitive venture capital market

can be ambivalent. The analysis shows the particular market inefficiencies concerning this

influence. To evaluate this we consider several key parameters of the market: efforts by

participants, their final wealth, investment size and probability of the project success. The

results may help answering the question of how the presence of VC market affects the

entrepreneurs’ incentives to innovate, thus clarifying some of the economic growth effects of

venture capital.

In the following sections of this chapter we give a brief overview of the venture capital

market and its role in financing of the innovation process. After that we turn to the general

concepts of the informational theory that we will use in the work. In the end of the chapter we

characterize the model framework and list the main results of this work.

1.2 Venture capital

Venture capital organizations raise money from individuals and institutions for

investment in early stage businesses that offer high potential but high risk. Venture capital is

provided by specialized financial firms acting as intermediaries between primary sources of

finance (such as pension funds or banks) and entrepreneurs. In this section we briefly consider

what are the venture capital firms and their role in financing of R&D.

1.2.1 VC in financing R&D

The distinctive feature of the venture capital is financing high-risk, high-return projects

which have small probability of success but when are successful, bring extremely high

returns. Sahlman (1990) notes the significant disparities in the venture projects’ outcomes.

From the group of 383 companies (13 venture capital partnerships) about one third of the

projects ended up with partial or total loss, 30% showed profits from 0 up to 200%, 19.8% -

3

up to 500%, 8.9% - up to 1000% and 6.8% resulted in payoffs greater than ten times cost and

yielded 49.4% of the ending value of the aggregate portfolio.

The compensation for such risks is the impressive profits from the successful projects that

could cover the losses from the large number of faults. Sahlman (1990) wrote that the total

market value of the 579 venture capital backed companies, which went public during the 11

years ending in 1988, exceeded 30% of the total market value of all comparable companies

that went public during the same period. The list of such companies includes Apple

Computer, Microsoft, Intel, Sun Microsystems and many other names that are now associated

with worldwide success.

Venture capital investment is quite small and varies from about 1% of GDP in Israel to

0.01% in Japan. Nevertheless, it is a major source of funding for new technology-based firms

that attracted 60% of OECD venture capital investments. It plays a crucial role in promoting

the radical innovations often developed by such firms. VC investments in high-technology

sectors vary from 93% in Ireland to only a quarter or less in Portugal. In Israel, ICT sector

share of VC investments increased from 50% in 1990s to 70% in 2005.

Another aspect of venture capital investment is the specialization on the early stages of

firms’ life-time. Over 2000-2003 early-stage investments on average were about half the size

of investments in expanding firms (SourceOECD).

Israel had a higher level of venture capital as a share of GDP in the period 1998-2001

than any OECD country. Growing rapidly in the 1990s, venture capital investments (domestic

and international) reached over 1% of GDP in 2000, but then declined with the downturn in

technology markets. Most Israeli venture capital is channelled to early stage companies,

particularly start-ups in sectors based on ICT technology and biotechnology (Baygan 2003).

For the mentioned sectors venture capital has an advantage over other financial sources.

A number of studies have identified reluctance by banks and other large financial institutions

to finance high-technology start-ups. For example Moore (1994) finds that a sample of 89

high-tech companies raised only 7% of the start-up finance from banks, compared with a

figure close to 40% for small and medium-sized enterprises generally. What is special about

venture capital that distinguishes it from other financing structures? We will review this in the

following subsection.

4

1.2.2 Organizational aspects of VC activity

VCs are the financial intermediaries that act as agents for investors in entrepreneurial

projects. Their relationships can be divided into two groups: agent relationships with investors

and principal towards entrepreneurs. The first group is defined by the legal form of venture

capital firm that typically is a limited partnership between two types of partners: Limited

Partners that are several investors and General Partner – VC manager (Sahlman 1990, Kandel

2004). Limited Partners do not participate in the active management and their liabilities are

limited to the amount of their commitment. The General Partner makes the investment

decisions. The VC partnership has a limited life span - usually 5-10 years, during which the

withdrawal of partners is prohibited. After the date of termination all projects must be closed

and the partnership is dissolved. This limited life span allows Limited Partners to control the

General Partner’s management results, limits the risk and prevents the retaining of profits

within the fund by infinitely postponing the project maturity (Kandel 2004).

The second type of relationships involves the contracts between the VC fund itself and

the entrepreneurs. Venture capitalist manages the processes of selecting potentially successful

projects, contracting, financing and monitoring. He takes on all the relationships with the

entrepreneurs and can even participate in the entrepreneurial management by entering his

representatives in the Board of Directors.

The development of a venture-backed company has three basic financing stages:

• Seed capital is provided to research, assess and develop an initial

concept.

• Start-up financing is provided for product development and initial

marketing. Companies may be being set up or may have been in

business for a short time, but have not yet sold their product

commercially.

• Expansion financing is provided for the growth and expansion of a

company that is breaking even or trading profitably. Capital may be

used to finance increased production capacity, market or product

development and/or to provide additional working capital.

Venture capitalist’s participation in the project can begin in every stage and ends by

selling or closing in accordance with participation plan or in case of predefined dissolution.

5

What sets VC financing apart from other types of financing is the potential ability of VC

to increase the likelihood of successful project outcome by active involvement in project

organizing and promoting. Casamatta (2002) emphasizes that VCs provides value-added

support activities. According to the empirical study of Kaplan and Stromberg (2002) in more

than one third of the investments, the VC expects to provide value-added services such as

strategic advice or customer introductions. Casamatta's results confirm the conclusion that

VCs assist founders in running and professionalizing the business.

The success of the project depends on both the efforts put forth by the entrepreneur as

well as by the VC. However, neither effort by both parties can be fully observed by the other,

though the relationships between venture capitalist and entrepreneur are characterized by

considerable degree of informational asymmetry about the success prospects of the project.

The informational problems from entrepreneurial side were recognized by most of the studies.

For example, Brierly (2001) emphasized that at the time of consideration of an investment,

the venture capitalist is faced with a potential adverse selection problem because of the

difficulty of assessing the entrepreneur’s performance. In the same time there was not much

researchers’ attention towards VC’s private information.

Most researchers, (for overview see Lumma 2001), note the following common practices

for solving the informational problems concerning projects quality and entrepreneurial team

skills and effort:

1. Staging the infusion of capital

2. Monitoring of project execution and involving in project management

3. Compensation schemes that provide entrepreneurs with appropriate

incentives

The first two ways amount to reducing of the contract uncertainty by dividing the

investment risks by using the option to exit. These methods can be applied only to the part of

informational asymmetry that is actually available for costly revelation. But venture projects

usually contain part of uncertainty that cannot be resolved even by costly monitoring. At the

same time also the staging of financing is not a panacea from financial losses because even a

good project start does not guarantee the success in the long run when the stakes are higher

(Sahlman 1990). Then we cannot describe the relations between VC and entrepreneur only by

referring to first two methods and ignoring the incentive mechanisms of risky project

contracting.

6

In this work we focus exclusively on the incentive effects of funding contracts under

asymmetric information. The reason why we do so is that this process emphasizes the very

nature of the investor-entrepreneur relations. The analysis of the incentive schemes provides

us with a measure of the parties’ ability to reach the agreement as well a measure of its costs.

This view does not contradict the importance of costly monitoring because the inefficiencies

caused by risk allocation based contract can be also presented as alternative costs for costly

monitoring constructions.

An example of using of the incentive schemes in the venture project financing can be the

wide use of convertible preferred stock as financing instrument. Kaplan and Stromberg (2000)

provide evidence which shows that convertible preferred stock is by far the most commonly

used financing instrument, appearing in 189 out of the total of 200 financing rounds. Such

instruments generally ensure that the cash flow rights, voting rights and control rights of the

venture capitalists and entrepreneurs are contingent on observable measures of financial and

non-financial performance. State-contingent provisions not only motivate entrepreneurs to

provide effort, but also discourage entrepreneurs with poor projects from accepting the

contract (Prendergast 1999).

1.3 Informational asymmetry in the VC market

The venture capitalist – entrepreneur contracting attracted significant attention both in

theoretical and empirical literature. In the wild range of aspects analysed in these works the

most developed subjects are:

1. The optimal debt/equity financing of venture projects (Tresler 1998, Admati and

Pfleiderer 1994)

2. The conflicts of interests between venture capitalists and entrepreneur as a

principal-agent relations (Guesnerie et al 1989)

3. The role of venture capital in innovation process (Kortum and Lerner 2000)

4. Organizational structure of venture financing (Teece 1996)

5. The impact of government subsidies on the venture capital market (Ber 2002)

All these studies emphasize the role of informational asymmetry in this market as one of

the main determinants of the equilibrium. The theoretical basis of these applications to

financial contracting under informational problems is the series of works built for various

7

markets including insurance markets, labour markets, banking and even lawyer services. In

our work we use the appropriate constructions from the relevant literature.

Next we bring a brief review of the works that provide the theoretical foundation of

models of financing activity under asymmetric information.

The concept of asymmetric information was first introduced in the paper of Akerlof

(1970). Akerlof argues that the information asymmetry about the good’s quality leads to

adverse selection that is the process of the worse individuals starting to dominate the market.

Stiglitz (1975) explores whether this informational disadvantage can be rectified by the

seller (employer) by screening the applicants (potential employees) into categories that

reflect their productivity or some other capability.

Rothschild and Stiglitz (1976) study the effects of imperfect information using insurance

market as an example. They define a competitive equilibrium in the insurance market of their

model as a set of contracts chosen by the customers to maximize their expected utility such

that: (i) no contract in the set makes negative expected profits to insurance companies, (ii)

there is no contract outside the equilibrium set that would make a nonnegative profit if

offered. They found that under asymmetric information no pooling equilibrium is possible and

if equilibrium is found it is always a separating equilibrium. In the equilibrium the high-risk

individuals cause a negative externality by their being on the market so that the low-risk

individuals cannot get their preferred insurance policy, which they would get in a symmetric

information market.

The disputable feature of R-S equilibrium concept is the situation when there is no

equilibrium in case of existence of profitable pooling contract, which “skims” only low-risk

individuals. Alternative variation of the screening equilibrium that proposes a way to avoid

this non-existence was developed in the works of Wilson (1977) and Miyasaki (1977). They

weakened the Nash equilibrium concept by requiring that any new offer remains profitable

after the withdrawal of loss-making offers. Riley (1979) introduces the “reactive equilibrium”

where firms anticipate further entries when they consider offering deviating contracts. It

results in the original R-S equilibrium pair being sustained even when the R-S equilibrium

does not exist. Further development of this branch of theory was made by the works of

Dasgupta and Maskin (1986), Dubey and Geanakoplos (2002), Ania, Troger and Wambach

(2002) and others. The other developments of the theory are the dynamic models of the

screening equilibrium and multi-entrepreneurial models.

8

The moral hazard concept was first introduced by Bengt Holmstrom (1979). The

problem arises when actions of the agent are not observable or not verifiable for the principal.

The solution to this problem is the optimal incentive scheme that forces the agent to perform

in appropriate manner. This approach is very popular for the various financial contracting

models because it gives an instrument to describe the relationships about agent’s

unobservable actions. Later, there were series of works that analysed models with

simultaneous adverse selection and moral hazard.

Much less researched direction of the information theory is the bi-directional information

asymmetry models that assume the existence of the private information for both contracting

parties. Rubinfeld and Scotchmer (1993) present such approach as an extension of the model

of the market for attorney services. In this work there was considered the case of moral hazard

from the attorney side versus unknown type of client. The model based on the concept of M-

reactive equilibrium (Judd 1984) that allowed authors to describe the equilibrium with cross

subsidization of contracts. Emmons (2004) expands the approach of Rubinfeld and

Scotchmer. He also pointed out the direct analogy between his model of attorney services

market and models of the financial markets with incomplete information.

Our work deals with a combination of different informational problems and accordingly

we rely on many of the reviewed concepts for building the model. In the next part we describe

briefly the model framework.

1.4 Description of the work

In our work we analyze the model of the market with large number of venture capital

firms that are competing in the market for financing risky projects. We examine the

contracting equilibria between venture capital firms and entrepreneurs that arise under

different types of informational asymmetry due to:

• unobservable quality of projects

• unobservable actions of entrepreneurs

• unobservable actions of the venture capitalist

The informational asymmetry in the market can be also double-sided when both parties of

the contract have private information on some relevant aspect of their relationship.

9

Within this environment we examine the existence of equilibrium contracts and its

properties, hoping that the analysis sheds some light on the interplay between conflicting

incentives involved in venture capital financing. What kinds of equilibria can be reached in

such markets under different informational complications? How efficient is the competitive

venture capital financing process?

The model we use for our analysis is based on the insurance market model of Rothschild-

Stiglitz (1979), modified to suit markets for financing risky projects. This basic model has

many useful features and is suitable for the modelling competitive market with informational

asymmetries. Like every other model it has shortcomings that will be discussed later.

Here we discuss the general description of the market environment: Assume a market of

venture capital where capitalists (VC) are competing for entrepreneurial projects. The projects

need the investment for execution and also can potentially benefit from the efforts of the

entrepreneur and the venture capitalist. The project yields only two types of outcomes with

different probabilities given by a probability function that includes effort as input. The project

(and accordingly the entrepreneur) can be of two types: “good” and “bad” (G and B) with

different success (or high outcome) probability functions.

Assume also that each entrepreneur is a risk-averse utility maximizer, has only one project

and can deal with one investor only. He agrees to exchange his property rights on the project

with an investment by the VC and a lump sum payoff that can be contingent on the project

outcome. A risk neutral venture capitalist deals with a large number of entrepreneurs in a

competitive market with free entry and exit, so his expected profits should be at least as large

as some alternative profit rate available elsewhere for his funds. Through funding the project

he becomes the owner of project results and pays to the entrepreneur the agreed upon payment

in the contract.

Consequently, the venture contract between the parties is the agreement about payoffs in

every state of nature and other observable conditions, such as investment size or verifiable

effort. Contracts can be pooling (i.e. same contract for all types of entrepreneurs) or

separating (different contracts are offered for self-selection by each type). VC has only one

way to influence on the entrepreneurial actions: He can vary the riskiness of the

entrepreneurial contract conditions by using the contingency of the payoff.

Our analysis is organized as follows: In Chapter 2 we present the basic environment that

serves as a foundation for our analysis. In this environment all projects have the same possible

10

outcomes support, and differ only the probability distribution of these outcomes. Project

types, in the sense of this probability distribution over outcomes, can be observable or can be

private information of the entrepreneur who owns the project. We focus on examining the

ability of the market to keep Rothschild-Stiglitz-like contracting equilibria when the level of

investment is endogenous, that is the entrepreneurs can freely choose the funding level in the

contract.

After proving that endogenizing the funding level does not influence the resulting

equilibrium, we turn in subsequent chapters to other complications and forms of asymmetric

information and examine how they affect the ensuing equilibrium. In Chapter 3 we study the

contracting process when entrepreneurial actions can affect the probability of project

outcomes and these actions as well as project types are unobservable. This generates adverse

selection and moral hazard problems and obviously affects the equilibrium shape of contracts.

Finally, in Chapter 4 we study an environment with bi-directional informational

asymmetry with both adverse selection problem from the entrepreneurial side and moral

hazard from the side of venture capitalist, simultaneously. Numerical examples in Chapters 3

and 4 will help us to concretize the model results and to see their magnitudes for some

plausible parameter set.

1.5 Results of the work

1. Equilibrium

We show that only separating equilibrium can exist. That is, entrepreneurs of different

types choose different contracts, characterized by different payoff sets. We then show that the

separating equilibrium can be reached under different combinations of adverse selection and

moral hazard problems.

VC applies the separation policy that makes entrepreneurs of different types choose

particular contracts and exert unobservable effort in accordance with VC’s expectations. The

separating equilibrium is reached by applying two types of incentive compatibility

constraints. The first type makes every contract preferable only for particular entrepreneur’s

type that solves adverse selection problem. The second type of constraints ensures that

particular effort level will be chosen by contractor that solves an appropriate moral hazard

problem.

11

2. Investment level

We found that in the competitive environment equilibrium investment level maximizes

project surplus for both project types. Initially we expected deviation from optimality, but the

analysis shows that both parties are interested in optimal funding levels. The reason for this is

that in the competitive market the entrepreneur gets the entire project surplus, and deviations

from optimal investment level will only lower this payoff. Therefore entrepreneurs are

interested in project efficiency and choose optimal investment level.

Nevertheless for non-competitive environment we can predict non-optimality of

investment demanded by entrepreneurs.

3. Entrepreneurial effort

In the full information environment the entrepreneurial choice of effort maximizes

project surplus because the VC gives the entrepreneur a full range of possible effort levels to

choose from. In the market where both project types and effort levels exerted by

entrepreneurs are private information, the VC is forced to offer entrepreneurs more restrictive

contract conditions to ensure both self-selection of types and resource compatible payments.

This circumstance, in turn, makes entrepreneurs exert effort in accordance with proposed

payoffs allocation. This choice can be non-optimal, but it is the only feasible form of

contracting that lead to equilibrium. In the numerical example the "bad" entrepreneur's effort

is optimal but the "good" one is forced to exert more effort than he would have chosen for his

expected payoff.

4. Venture capitalist’s effort

In the full information environment contractors are interested to exert effort that

maximizes project surplus for both types. When the project type is unobservable the “good”

entrepreneur gets risky contract and is interested in the additional efforts form VC’s side.

Therefore in this case VC can exert more efforts than in the full information case.

When VC’s effort level is unobservable he cannot ensure the entrepreneur that he will

exert the proposed effort. Therefore he offers in the contract only the effort level that would

maximize his profits given the contract payoffs allocation. So VC’s effort level will be lower

in this environment even if both contractors would prefer higher effort.

12

5. Payoff allocation and entrepreneurial wealth

As we have already mentioned, the competition between VCs increases entrepreneurial

expected profit share to 100% of project surplus net of investment. In our model VC

distributes all the profits from the project to the entrepreneur, he also can make payoff

contingent on the project outcome, that’s to pay entrepreneur more in case of high project

outcome and less for low one.

The separating equilibrium which can be reached allows “good” entrepreneur to obtain

significantly higher expected profits than “bad” one. But the presence of adverse selection can

sufficiently reduce profits of “good”. In addition, the existence of entrepreneurial moral

hazard hurts the wealth of both entrepreneur types. The reason for this is the project risks are

loaded on the entrepreneurs in equilibrium and this lowers their utility.

Due to entrepreneurs' risk aversion, the best payoff allocation is a non-contingent one.

For the full information environment this is the equilibrium allocation. But in presence of

asymmetric information problems the results of the model show that under incentive

compatibility constraints the allocation of payoffs must be dependent on the project outcome.

Particularly, adverse selection problems make the equilibrium payments to “good”

entrepreneur risky, while entrepreneurial moral hazard problem implies that payments to both

types are risky. This lowers entrepreneurial expected utility.

The second factor that can reduce entrepreneurial utility in the presence of informational

asymmetry is the influence over entrepreneur's effort levels. In order to reach a separating

equilibrium, VC offers restrictive contract conditions that can cause entrepreneur effort level

to be different from the one they would have chosen given their payoffs. This in turn lowers

the project overall profits and accordingly the final wealth of entrepreneur.

In case of VC’s moral hazard, effort level is lowered that fact also influences negatively

on the entrepreneurial wealth.

6. VC’s wealth

In the competitive market the expected profits of VC are reduced to his reservation

level. The model shows that in the case of VC’s moral hazard this result can be violated. The

reason for this fact is VC's inability to commit to a particular effort level. Therefore, VC

proposes to entrepreneur the effort level that would maximize profits for himself given

contract payoff scheme. The combination of type separating contracts and effort levels chosen

13

without pre-commitment device creates the possibility that VC’s expected profits will exceed

his reservation level.

It is important to note that these profits are characteristic of all competitive VC markets

and cannot be transferred to entrepreneurs through contract payoffs to gain advantages over

competing VCs. An attempt to exploit this higher than minimally acceptable profits will

change the ex-post effort choice of VC, and will result in lower expected utility to

entrepreneurs. Hence, this VC advantage is not wiped off by the competition among VCs.

14

Chapter 2: A Model with Endogenous Investments

2.1 The Market Environment

The first model we consider is the market of capital to be invested in risky projects,

where investors compete for risky R&D projects. We want to check the optimality of projects

funding in different informational environment.

We assume that all projects in the market have the same outcome function. The outcome

of any project can be either favorable or not. High outcome is indexed by RH and occurs with

probability p. Low outcome, RL occurs with probability (1-p). The resulting project results

with outcome R, implemented with capital level I, is given by Z(I,R). The outcome function

Z(·,·) has the usual properties: increasing in I and R, differentiable and concave in investment:

0,0,0 2

2

<∂∂

>∂∂

>∂∂

IZ

RZ

IZ .

Entrepreneurs (E-s), which are the initial owners of the inventions and the executors of

the project, have some initial endowment I0 that is not enough to execute the project. They are

forming the projects, defining the investment needed and searching for the investors to give

up all property rights to the project in exchange of the lump sum payoff. Each E has one

project and can deal with one investor only. All E-s are risk averse with utility function

denoted by U(⋅), U’>0, U’’<0.

Venture capitalist (VC) is the risk neutral investor. The market for venture capital is

competitive, with free entry and exit, so in equilibrium VC’s expected profits are equal to

some reservation value that, as we assume, here is equal to zero. VC offers to E-s an

investment contract or a set of contracts that consist of the sum to be invested in the project

and the division of project profits. Investment sum is declared by E. VC controls all the

project profits and transfers to E his share. We define the contract as following:

An investment contract for an R&D project is defined as {I*, CH*, CL*}, which specify:

1. Payoff to E in each state of nature {CH*, CL*}, with the residual output of the project

going to VC in each state of nature

2. The E’s choice of investment size {I*}

15

The sequencing of events of contracting is as follows:

Let Y be the VC’s expected net profits from investing I in a project under a contract that

pays off CS to E in state },{ LHs ∈ . In a competitive equilibrium VC’s expected profits are:

0))1((),()1(),( 00 =−−+−+−++= ICppCRIIZpRIIpZY LHLH (2.1)

so that the entrepreneur's expected compensation is:

IRIIZpRIIpZCppC LHLH −+−++=−+ ),()1(),()1( 00 (2.2)

All E-s are risk averse with utility function denoted by U(⋅), U’>0, U’’<0. Given a set K

of alternative contracts, say, },,{ ** KkCCI Lk

Hkk ∈ , E chooses the contract from that set

which maximizes his expected utility:

)()1()( LHE CUpCpUV −+= (2.3)

A competitive equilibrium in funding R&D projects is a set of contracts that maximize

E’s expected utility subject to yielding non-negative expected profits to the VC. Accordingly

VC’s problem is:

)()1()(max,

LHE

CCCUpCpUV

LH−+= (2.4)

s.t. IRIIZpRIIpZCppC LHLH −+−++=−+ ),()1(),()1( 00

2.2 Benchmark case: Equilibrium with single project type

We first consider the case when in the market there is only one type of projects. VC’s

equilibrium contract offer maximizes E’s expected utility and just break even. On the Figure

2.1 this is the tangency point A of E’s indifference curve (defined by (2.3)) and the VC’s zero

expected profits line (Y-line, defined by (2.2)). This contract satisfies the two conditions of

equilibrium – its breaks even and no better contract will bring VC non-negative expected

profits.

VC designs a menu of contracts

E-s choose contracts from

the menu

The realization of the state of

nature

Outcome and

payoffs

E-s form the projects and define the

investment needed

16

Figure 2.1: Single Type Equilibrium

Since E-s are risk averse, the equilibrium contract brings to E the equal payoff in both

states (CH=CL). The contract point is located at the intersection of the Y-line and the 45°-line

(representing the equal payoff to E for both outcomes of the project). To see this note that the

marginal rate of substitution for E is equal to the slope of the Y-line only when CH = CL and

accordingly )()( LH CUCU ′=′ :

pp

CUpCpUCC

CC

L

HLH

VH

L

−=

−=

∂∂

1)(')1()('),(

(2.5)

Hence, E will choose )()()( * ICICIC LH == , such that:

IRIIZpRIIpZIC LH −+−++= ),()1(),()( 00* (2.6)

In the equilibrium E will choose the investment level I*, that yields him the highest

expected utility (highest right-hand side of (2.2)) and satisfies:

01)*,()1()*,( 00 =−+∂∂

−++∂∂ LH RII

IZpRII

IZp

(2.7)

As we see the equilibrium contract for single project type {I*, C*} consists of the fixed

payoff and the investment level that provides maximal project productivity. The explanation

for this is that E gets all the profits in the competition and is interested to maximize them.

A

p/(1-p) CH

CL

CH=CL

VE

Y*

17

2.3. Equilibrium with heterogeneous projects

Assume now that there are two types of projects in the market: G, “good probability

project” (with probability of getting RH is pG) and “bad” project (B) with pB<pG.

Entrepreneurs are marked in accordance with their project types: G and B.

2.3.1 Full information case

Here we assume that the type of E is fully observable by VC. Because of the full

information assumption VC can recognize the type of E and knows his probability of getting

“high” outcome. Therefore VC can offer to each E a contract that maximizes that type’s

expected payoffs. For each E, the equilibrium contract is in the tangency point of the

indifference curve and the corresponding Y-line for that type. This condition for entrepreneur

of type i is formulated as:

},{,1)(')1(

)('),( BGip

pCUp

CUpCCCC

i

i

iLi

iHiiLiH

VH

L

i

∈−

=−

=∂∂

(2.8)

Therefore the equilibrium set of contracts is { }),,(),,,( BBLBHGGLGH ICCICC where:

),(],)~,([)( 0~* BGiIRIIZEICCC i

ii

RiiiLiH

i∈−+=== (2.9)

),(,1))~,((: 0* BGiRIIZ

IEI i

ii ∈=+∂∂

(2.10)

Clearly IG*>IB*, that leads to CG*>CB*. Consequently, B prefers the allocation {CG*} to

the allocation {CB*}, but he can not improve his position because his real type is observable

for VC.

2.3.2 Asymmetric information case

Consider the case when participants of the market have different information about the

subject of contracting. Assume that all the parameters of the project are public information

except the type of the particular E’s project. Venture capitalist cannot verify it at the time of

contracting. The proportions of the G and B project types are also unobservable. In this

environment the market is subject to adverse selection problem that makes the full

information equilibrium unreachable, since both entrepreneurs would choose the contract

{CG*}, that implies negative VC profits for B projects.

18

This market can have only two kinds of equilibrium:

• Pooling equilibrium – different E-s select the same contract and getting the same

investment from VCs;

• Separating equilibrium – different E-s select different contracts with different

investment levels and repayment schedules.

Proposition 2.1: The equilibrium in this market cannot be pooling equilibrium.

Proof: Suppose that there is a pooling equilibrium in some point A. Consider the average

probability of getting high outcome in the market: LH pqqpp )1( −+= , where q is the

proportion of G projects in the market. Assume VC offers to both types the pooling contract.

His profits from the pooling contract must be zero otherwise it contradicts the definition of

equilibrium; hence the point A must lie on some YM-line with the slope p . In this point the

slopes of G and B indifference curves are differ by: )1()1(

HH

LL

pppp

−

− . The curves intersect at A,

therefore there exists some contract D that will be preferable only for G (it lies below B

indifference curve and above G indifference curve). VC that will offer this contract will earn

strictly positive profits. The existence of contract D contradicts to the definition of

equilibrium. Q.E.D.

Figure 2.2: The non-existence of pooling equilibrium

We have shown that if the equilibrium exists in the market it must be separating. Now

consider the contracting process. In the Figure 2.3 is shown the separating equilibrium in the

D

A

p/(1-p) CH

CL

CH=CL VB

YM VG

19

market with adverse selection. At the first step each E chooses the investment level that

maximizes her utility level by (2.10). The curve ZGZB is the upper border of all possible

project output combination with different probabilities of high outcome. Points ZG and ZB are

maximum project profit points for each project type. These are the tangency points of project

profitability upper border and Y-lines with according slopes (defined by the probability for

each type).

Because of risk aversion of both entrepreneurs, the maximum utility contract for every

E’s type is in the intersection of according Y-line and “certainty line”. The equilibrium

contract for B (point B) indeed is situated in the intersection of YB line with “certainty line”

where Y-line is tangent to the indifference curve. But if the equilibrium contract for G, {IG,

CGH, CGL}, would be in the point C, it would be both preferable and reachable for both types

and therefore cannot be offered. The payoff allocations must keep the incentive compatibility

constraint (every entrepreneur must prefer the contract of his type). We will use the non-

strict form of this constraint by allowing that B will be at least indifferent between the two

contracts and assume that in this case he will stay with his type’s contract.

To maximize the utility for each type VC will offer to B the full insured contract (point

B) and to G the best contract that can be offered without attracting B type. This occurs at the

intersection of VB indifference curve and YG zero expected profit line (point A). G therefore

will get allocation with high investment level but risky enough to be non-preferable for B.

Figure 2.3: Separating Equilibrium

CL

CH=CL VB

YG

YB B A

ZB

ZG

C

VG

CH

20

Proposition 2.2: The separating equilibrium in the asymmetric information case provides full

risk protection to B and loads some of the risks on G. The separating equilibrium is the set

{ }),,(),,,( BBLBHGGLGH ICCICC such that:

**0

*0

** ),()1(),()( BLBBHBBBBLBH IRIIZpRIIZpICCC −+−++=== (2.11)

)()()1()( *BBLGBBGHBB CUCUpCUp =−+ (2.12)

**0

*0 ),()1(),()1( GLGGHGGGLGGHG IRIIZpRIIZpCpCp −+−++=−+ (2.13)

The investment levels are defined by:

1))~,((: 0* =+

∂∂

GGG RIIZ

IEI ; 1))~,((: 0

* =+∂∂

BBB RIIZ

IEI

(2.14)

In the equilibrium B gets the same non contingent payoffs allocation as in the full

information case and G gets risky allocation that causes a decline in his expected profit

because of his risk-averse utility. In the equilibrium the investment levels, demanded by both

types of E, maximize total project surplus.

2.3.3 Uniqueness and existence conditions of the separating equilibrium

1. Uniqueness. First, B gets optimal allocation on the Y-line. All allocations above or

below Y-line will provide non-zero expected profits to VC. Reducing B utility along

the Y-line will also hurt the allocation for G because of incentive compatibility

constraint. The allocation for G also can not be changed because it is constrained by

both YG-line and incentive compatibility constraint.

2. Existence conditions. If the proportion of “good” projects (q) is large enough, then

the market can have no equilibrium. The reason is that when q is large the incentive to

attract all the agents increases despite the risk of attracting “bad” projects. Hence the

pooling contract can offer greater utility for both type of E-s then the separating one,

but, as it was shown in Proposition 2.1, there is no pooling equilibrium in the market,

so equilibrium in the market does not exist. Another possible reason for non-existence

of equilibrium is the small difference in probabilities of high outcome for different

project types. The result in this case is just the same.

21

2.4. Results of the Chapter

1. Only separating equilibrium exists in the market.

2. In the full information environment every project type gets the contract with non-

contingent payoffs and investment level, which are different for different project

types.

3. In the adverse selection environment G gets contingent payoff allocation and his

expected profits are lower than in the full information case.

4. Every entrepreneur’s type chooses investment level that maximizes project’s

expected surplus.

22

Chapter 3: Entrepreneurial Effort

3.1. Modelling entrepreneurial effort

In the Chapter 2 we introduced the model of venture capital with adverse selection

problem concerning unobservable quality of the project. Here we consider more complicated

problem: an entrepreneur with the project of unobservable quality must accomplish the

research works or the developing of the final product and his diligence of work is also

unobservable by the VC. Possible disincentives for the agent in exerting optimal effort, when

his conduct cannot be observed directly or inferred from the outcome, fall under the class of

Moral Hazard problems (Holmstrom 1967). Introducing this problem here increases the

asymmetry of information between parties and can have adverse effect on the equilibrium

allocation of profits. In this section we consider the contracting environment with both

Adverse Selection and Moral Hazard stemming from the entrepreneurial side.1

Entrepreneurial effort can affect the profitability of the project in various ways. If that

effort can be observed directly or can be inferred from the outcome, entrepreneurial effort can

be rewarded in a manner that depends on the effort exerted, thus providing incentives that will

induce the entrepreneur to behave in accord with the VC’s interests. However, if this inference

or direct observation is not available, the equilibrium contracts must confront this

complication. This complication can occur when the project outcome is determined by both

the entrepreneurial effort and some exogenous event, and these cannot be untangled.

We consider here a version of this problem, where the effort of the entrepreneur has a

positive effect on the probability of the project’s good outcome. If the effort exerted is

unobservable by the VC, he can not control it by final project outcome because this is just one

realization of the probabilistic distribution and can not be traced to the effort exerted. At the

same time effort is costly to entrepreneur that makes him reluctant to make effort without

being compensated for it.

1 In Chapter 4 we consider a variant of the environment where the venture capitalist can affect the outcome with his effort, which cannot be observed by the entrepreneur.

23

The time-schedule of the project is:

Probability is presented now as continuous monotonic differentiable function,

]1,0[],[: 10 →eep , where e is the effort level exerted by E, and )(ep is the probability of the

project’s good outcome. The entrepreneur’s utility is a special case of Bernoulli utility

function which has been often used in the literature: )()(),( ehCUeCV −= , where U(C) is the

utility from the project’s payoffs, and h(e) is a disutility from effort. We summarize our

assumptions about the function properties in the following assumption:

Assumption 3.1: We assume that the functions used are of the following properties:

Table 3.1 Functions used in the model

Function name )(xf ′ )(xf ′′ )( 0xf ′ )( maxxf ′

Utility, U(C) 0)( >′ CU 0)( <′′ CU 1)0( =′U

Probability, p(e) 0)( >′ ep 0)( <′′ ep 1)( 0 =′ ep 1)( 1 ≤′ ep

Effort cost, h(e) 0)( >′ eh 0)( >′′ eh 0)( 0 =′ eh ∞ →′→ 1)( eeeh

In this Chapter we will talk about cases of observable and unobservable effort level. For

this purpose we introduce the contract definition in the following way:

1. The contract for observable effort case is ),,( eCC LH , that specify payoffs for

possible project outcomes and the effort level to be exerted by E.

2. The contract for unobservable effort case is ),( LH CC , that specify payoffs for

possible project outcomes only because the effort level cannot be included in the

contract.

In the previous Chapter we established that the entrepreneur is interested in the

investment level which maximizes the expected outcome of the project, regardless of payoffs

allocation. Thus we can relax the assumption about variable investment level and simplify the

VC designs a menu of contracts

E chooses a contract from

the menu

E chooses and supplies particular

level of effort

The realization of the state of nature

Outcome and

payoffs

24

analysis by assuming that a fixed level of investment I is required for any project.

Consequently the project gross profit Z~ is a random variable defined as:

ZH with probability p(e)

ZL with probability (1-p(e)), ZL <ZH

3.2. Equilibrium contracting with homogenous projects

Starting from the single project type case we put off the adverse selection problem

focusing only on the moral hazard of entrepreneur. Assume that E can choose every level of

effort from the interval ],[ 10 eee∈ such that: 1)()(0 10 <<< epep . Because E’s effort choice

may be different for the non-contingent and risky payoff allocations, we define *e as the

equilibrium effort level in case of fully insured allocation, and e as equilibrium effort level

for all other allocations.

3.2.1. Observable effort

First we consider the equilibrium when there is no informational asymmetry in the

market. VC observes the effort level made by E and uses it as contract condition. Here we

keep our assumption that the reservation value of the profits in the competitive market still

zero. For each effort level ],[ 10 eee∈ VC’s problem is to maximize E’s utility subject to no

expected loss:

)}()())(1()()({max,

ehCUepCUepV LHE

CC LH−−+= (3.1)

s.t. IZepZepCepCep LHLH −−+≤−+ ))(1()())(1()( (3.2)

In the competitive environment all payoff allocations that will bring positive profits to VC

are non-optimal because in this case he can provide to E better allocation. Hence equilibrium

solutions will always satisfy inequality constraint (3.2) as equality:

IZepZepCepCep LHLH −−+=−+ ))(1()())(1()( (3.3)

The solution for this problem is the payoff schedule: )}(),({ ** eCeC LH for each level of effort.

As we have shown in Subchapter 2.2, relying on E’s risk aversion, the best solution for

this problem provides equal payoff to E under both outcomes of the project:

25

IZepZepeCeC LHLH −−+== ))(1()()()( ** (3.4)

Given this set of available contracts E’s choice of effort level will be:

)}()))(1()(({maxarg)}())(({maxarg ** ehIZepZepUeheCUe LH

ee−−−+=−= (3.5)

Proposition 3.1: In case of single entrepreneur and observable effort, the optimal

equilibrium contract is )}(),(,{ ***** eCeCe LH such that:

1. IZepZepeCeC LHLH −−+== ))(1()()()( **

2. )}()))(1()((max{arg* ehIZepZepUe LH

e−−−+=

When in the market there is a single project type and the effort level is observable, in the

equilibrium E gets fixed payment and exerts effort level that maximizes project’s profits. This

state we will name the benchmark first-best allocation.

3.2.2 Unobservable effort

Now we assume that VC cannot observe the effort chosen by the entrepreneur.

Accordingly, it is impossible to include the effort in the contract directly. However, VC must

offer a compensation schedule (CH,CL) that will not result in expected losses given that the

effort is eventually set by the entrepreneur. We will use the term “project budget” proposed

by VC to name the right side of (3.3) that can be also defined as the project expected net

profits. If the entrepreneur exerts lower effort than was assumed in (3.3), VC will suffer

expected loss, while expected profits will occur if actual effort exceeds the level assumed in

(3.3). An equilibrium contract induces the entrepreneur to exert the effort level

anticipated VC.

If 0* ee = then the best compensation schedule that VC can offer the entrepreneur without

sustaining expected losses is the “full insurance” allocation associated with the lowest

possible effort, as in (3.4). For any 0* ee > , when effort is unobservable, VC cannot offer the

non-contingent contract defined in (3.4) because given that contract the entrepreneur will

always prefer to exert the lowest possible effort, thus producing negative profits to VC:

0*0* )())(()())(( eeeheCUeheCU >∀−>− (3.6)

26

Having non-contingent payoff, E is reluctant to exert any effort but e0. This moral hazard

problem can be solved by offering risky contract that makes E’s payoff contingent on results

of his effort.

The VC’s problem is to offer the payoff scheme that:

• maximizes the expected profits of E given zero expected profits for VC for every

possible effort level

• makes incentives for E to exert exactly the effort level that is proposed by the

project budget (3.3)

To obtain the second property consider the E’s choice of the effort level. Given a payoff

set ),( LH CC E solves the problem:

)}()())(1()()({max],[ 10

ehCUepCUepV LHE

eee−−+=

∈ (3.7)

First order condition is:

0)()()()()(=

∂∂

−∂

∂−

∂∂

=∂∂

eehCU

eepCU

eep

eV LH

that can be transformed to:

eepeehCUCU LH

∂∂∂∂

=−)()()()(

(3.8)

We have got the rule that defines E’s reaction to every possible payoffs combination. The

difference in utilities from payoffs must be equal to the ratio of marginal cost and marginal

probability. VC uses this rule to define how risky must be the payment scheme to make E

exert particular effort level, therefore we define this condition as incentive compatibility

constraint for moral hazard problem (MHC).

Lemma 3.1: Zero profit incentive compatible contracts set (ZPIC) is the set of contracts that

satisfy (3.3) and (3.8). In this set every contract corresponds solely to particular zero

expected profit line. For every zero expected profit line there is at most one such contract.

ZPIC line is depicted in the Figure 3.1 where for the particular Y-line there is only one

contract D that satisfies constraints (3.8) and (3.3).

Proof: First note that the right part of (3.8): )()( epeh ′′ is monotonically increasing in e from

zero at e0 to infinity when approaching to e1, given our assumption about the shape of these

27

functions (Assumption 3.1). Therefore there is unique correspondence between the effort level

and the riskiness of the payoff allocation.

Consider the effort level that will be exerted by E along a zero expected profit line

(defined by (3.3.) with some presumed particular effort level that is the slope of Y-line). He

chooses effort level by (3.8). When moving along zero expected profit line, from point where LH CC = up to the project profits point A ( },{ LLHH ZCZC == ), CH is increasing and CL is

decreasing monotonically. Hence )()( LH CUCU − is increasing monotonically from zero to

some positive value. Accordingly the right part of equality (3.8) also must increase

monotonically that is happen when e increases. Therefore the effort to be exerted increases

monotonically along zero expected profit line and there is at most one point where effort level

that satisfies (3.3) also satisfies (3.8). For less risky allocations E exerts less effort than

assumed by (3.3) and for more risky allocations E exerts greater effort than in (3.3) Q.E.D.

Figure 3.1: The contracting process with unobservable effort

Lemma 3.2: Within ZPIC contract group for every payoff set there is only one effort level

being corresponded. All the contracts from this group can be uniquely indexed by the effort

level.

Proof: As we have showed in the Lemma 3.1 for every VC zero expected profit line there is at

most one contract that holds (3.8). Every VC zero expected profits line has the unique slope

defined by particular effort level. Hence ZPIC contract set consists of contracts with different

effort levels. When ordering ZPIC contract set by the increasing slope of VC zero expected

profit lines (and accordingly increasing effort level) we get the contract set where every pair

A CH

CL

CH=CL

Y

D ZPIC

28

of payoffs is indexed by definite effort level. As we see in the Figure 3.1, effort level is

increasing along the ZPIC line because the slope of corresponding Y-lines increases Q.E.D.

This Lemma will be very useful for considering the numerical example below.

Now we reformulate the VC problem for the case of unobservable effort level:

)}()())(1()()({max,

ehCUepCUepV LHE

CC LH−−+= (3.9)

s.t. IZepZepCepCep LHLH −−+=−+ ))(1()())(1()(

),( LH CCee = , is implicitly defined by the entrepreneur’s

F.O.C. of (3.7): eepeehCUCU LH

∂∂∂∂

=−)()()()(

The solution for this problem is the equilibrium contract }ˆ,ˆ{ LH CC within ZPIC

contract set, with corresponding effort level )ˆ,ˆ(ˆˆ LH CCee = .

Is the effort level different in the unobservable case? First we note that the effort level

in both cases is the maximization of the same utility function. But the pairs of payments

},{ LH CC in these functions are different. Therefore the equilibrium choice of effort level

also must be different: LH CCee ˆˆˆ * ≠⇔≠ .

3.3 Two types of project

Now we are prepared to analyze the complex case with adverse selection and moral

hazard problems. Consider the market with two types of projects: BGi ,= . The type is

characterized by the probability function: 00)()(1 eeepep BG >∀>>> . Also we assume for

simplicity that: )()( 00 epep BG = . Every E holds only one project and must exert some effort

],[ 10 eee ∈ to execute it. We will name as G the entrepreneur that holds the project of type G

and as B the one holds type B project.

We assume away the cases when the model parameters are such that for both types the

profitability of the project is so poor that both types in the equilibrium will exert minimal

effort level e0.

29

3.3.1 Observable type

Here we will see how the moral hazard problem affects the equilibrium allocation. For

this purpose we will assume the observability of the project type for VC and will compare the

equilibrium in observable and unobservable effort cases. First we consider the separating

equilibrium in the market with no informational asymmetry. As it was shown in the

Subsection 3.2.1 the first best case with observable effort allows for full insurance contract

(CH=CL) that is optimal because of E’s risk aversion. Therefore each E chooses effort by

maximizing his utility within the set of non-contingent contracts. Inasmuch different

probability functions imply different project budgets so the optimal payoff allocations for G

and B will be also different.

Proposition 3.2: In case of heterogeneous projects, observable effort level and project type,

the equilibrium set of contracts is )]}(),(,[)];(),(,{[ ********** GGLGGHGBLBBHBB eCeCeeCeCe

such that:

1. BGiIZepZepeCeCeC LiiHiiiLiiHiii ,,))(1()()()()( *** =−−+=== (3.10)

2. BGieheCUe iii

eee

i ,)],())(([max *

],[

*10

=−=∈

(3.11)

In the Figure 3.2 is depicted the separating equilibrium for this environment. Points D

and F are the full insurance equilibrium contract points for B and G accordingly. These points

are located in the intersection of the certainty line and corresponding Y-lines.

Figure 3.2: The separating equilibrium with observable type and effort

D

A CH

CL

CH=CL

YB

F

YG

30

Now let’s see what will happen when the effort is unobservable. Non-verifiable effort

implies that having non-contingent contract each E is reluctant to exert any effort except e0

(by (3.6)). As long as type is observable, VC can solve each type’s problem separately. Hence

VC’s problem now is just the combination of the two problems we discussed in the

Subsection 3.2.2. For each type he solves the problem defined in (3.9). The separating

equilibrium consists of the contracts for each project type.

Proposition 3.3: In the case of two observable project types and unobservable effort the

equilibrium set of contracts is: ]}ˆ,ˆ[];ˆ,ˆ{[ LGHGLBHB CCCC within corresponding ZPIC contract

sets that are defined by:

1. BGiIZepZepCepCep LiHiiLiiiHiii i

,,,))(1()())(1()( =−−+=−+ (3.12)

2. BGieepeehCUCU iii

iiLiHi ,,,

)()()()( =

∂∂∂∂

=− (3.13)

The separating equilibrium is depicted in the Figure 3.3 where point A is the contract

profits allocation, YG and YB are VC’s zero expected profit lines for entrepreneurs G and B,

ZPICG and ZPICB are according ZPIC contract sets, points D and F are the equilibrium

contracts for types B and G accordingly.

Figure 3.3: The separating equilibrium with observable type and unobservable effort

Note that ZPICG line is situated above ZPICB line. To explain this, consider the following

lemma:

A CH

CL

CH=CL

YB

D

F ZPICG

YG

ZPICB

31

Lemma 3.3: For every given effort level MHC constraint (3.13) provides more risky

allocation for the project with worse probability function.

Proof: G has better probability function and for every effort level the slope of pG(e) will be

greater than the slope of pB(e).Consequently, the denominator of the indicated division in the

right part of (3.13) is greater for G hence the difference in the payoffs is smaller. This means

that for every given effort level this constraint implies more risky payment allocation for B

than for G. The explanation of this fact is obvious: better probability function gives G better

incentives to apply additional effort that ease moral hazard problem. Q.E.D.

Now we can define the influence of the moral hazard problem on the equilibrium in the

market when the project type is observable for VC. In the equilibrium both entrepreneur types

are getting risky payoff allocations that fact definitely decreases the utility of both.

Accordingly they exert less effort than in the observable effort case (because contingency

hurts the utility level). Therefore moral hazard lowers wealth and effort level of all

entrepreneurs.

3.3.2 Unobservable type and effort

Consider now the equilibrium in the market with the complex informational problem,

when VC does not observe both project type and effort level. To keep non-negative profits for

every contract VC must be sure that:

1) The project is of the particular type (has particular probability function)

2) E exerts particular effort that along with the project type defines the probability of

getting high outcome.

The first problem is the adverse selection problem. The similar problem we have

considered in the Chapter 2. There we have showed that this problem can be solved by

implying incentive compatibility constraint, changes the payoff allocation in such way that

makes every contract non-preferable for entrepreneurs of the other type. This constraint type

we will name as adverse selection constraint (ASC).

The second problem is the entrepreneurial moral hazard problem we have discussed in the

subchapters 3.2.2 and 3.3.1. It can be solved by implying incentive compatibility constraint

(MHC) that forces E to choose particular effort level.

32

Now, when both problems arise simultaneously, the equilibrium contracts must satisfy

the constraints of both types. The contract creates the incentives for E to reveal real project

type and to choose particular effort level.

We already have showed that VC offers contracts for each type only within the

corresponding ZPIC set, that is the contracts that satisfy MHC and zero expected profit

condition. The separating equilibrium exists if every ZPIC set contains a contract that will be

at least equally preferable for this type E to any contract in other type’s ZPIC set.

E will deviate to the contract of the other type if he will get greater expected utility, also

he will exert the effort level that will maximize his utility. To sum it up we will formulate the

ASC condition as following:

BGjijieCCVeCCV iLjHjiiLiHii ,,,),~,,(),,( =≠≥ (3.14)

where: BGjiehCUepCUepe iLjiiHjii

e

ii

,,)},()())(1()()({max~ =−−+= (3.15)

This enables us to formulate VC’s problem for the case of the complex informational

problem:

BGiehCUepCUepV iLiiHiiEi

CC LiHi,)},ˆ()())ˆ(1()()ˆ({max

,=−−+= (3.16)

s.t. a) BGiIZepZepCepCep LiHiLiiHii ,,))(1()())(1()( =−−+=−+

b) BGiCCee LiHiii ,),ˆ,ˆ(ˆˆ == with F.O.C.: iii

iiLiHi

eepeehCUCU

∂∂∂∂

=−)()()()(

c) BGjijiCCVCCV LjHjiLiHii ,,;),,(),( =≠≥

Constraints (a) and (b) form ZPICi sets. Constraint (c) is the ASC constraint that prevents

deviations to the other type contract. The solution for this problem is the contract set

]}ˆ,ˆ[];ˆ,ˆ{[ LGHGLBHB CCCC , such that:

• Payoff set creates incentives for E-s to exert effort in accordance with the level

proposed by (3.13).

• Each contract at most non-preferable for the other type E-s.

Surely, the simultaneous influence of both types of informational problem makes stronger

distortion in the payoff allocations than in the case of single asymmetric information problem.

Particularly, on the market there are two contracts with contingent payoff allocations that are

33

preferable for one E’s type only. The wealth of each E as well as his effort level decreased

comparatively to the previous case as the consequence of additional constraint. The particular

allocation of payoffs and effort level depends on the parameters of the model.

To show the contracting process afoot and to be insured about attainability of the problem

solution in the next section we consider the numerical example.

3.4 Numerical example

We have evaluated the VC’s problems defined in Proposition 3.3.1 and 3.3.2 for the

values: ZH=1, ZL=0.1 and the following functions set:

Table 3.2 Functions used in the numerical example

Function name f(x) f’(x)

Utility, U(C) 5.0C 5.021

C

Probability of G, pG(e) 22 ee − )1(2 e−

Probability of B, pB(e) 2

2ee − e−1

Effort cost, h(e) 2e e2

Utility function is the simple CRRA function. Functions PG(e), PB(e) and h(e) were

chosen to satisfy: ∞→∂∂∂∂

→∂∂∂∂

→→ 10 ;0 eiei ePeh

ePeh .

Accordingly: e

eeP

ehG −

=∂∂

∂∂1

and e

eeP

ehB −

⋅=∂∂

∂∂1

2

Given these functions the right part of F.O.C. for E’s problem (3.8) increases on [0,1]

from zero to infinity.

3.4.1. Equilibrium contracts in case of observable type and effort

We start with the benchmark case of full information. The contracts presented in the

following table are the equilibrium allocations for G and B when VC observes both project

types and effort levels of entrepreneurs:

34

Table 3.3 Calculated equilibrium values for full information case

Contract for G type Contract for B type

Utility 0.664985 0.484415

Effort level 0.361295 0.284651

Probability 0.592056 0.244138

CH 0.632851 0.319724

CL 0.632851 0.319724

The utilities are reaching their maximal values. Later on we will see how they will be

decreased by implying incentive compatible constraints. The effort level as we will see later

can be even increased for G but it will cost the further decreasing in G’s utility.

3.4.2. ZPIC contract set

In the Figure 3.4 we can see two calculated lines of ZPIC contract sets defined by (3.12)

and (3.13). The form of these lines we have predicted in subsection 3.2.2.

Figure 3.4: ZPIC lines for G and B

These lines are formed by the pairs of payoffs corresponding to the range of effort levels,

from the point on “certainty line” to the contract outcomes (point A). We can see that ZPICG

line is situated above the ZPICB line that corresponds to Lemma 3.3.

3.4.3 Equilibrium contracts in case of observable type

In the Figure 3.5 is shown the dependence between E’s utility and payoffs set within the

according axes:

CH

CL

CH=CL

ZPICG

ZPICB

A

35

Figure 3.5: Utility value as function of CH and CL along ZPIC lines for G and B

This form of representing the relationships of the model is not very useful. For exploring

the contracting mechanisms we will use the Lemma 3.2 to make the solution way simpler.

Lemma 3.2 enables us to rank the contracts in ZPIC set by effort level. This way we switch to

2D space and can easily compare the utilities from different contracts. In the Figure 3.6 there

are two utility lines representing how the utilities change along the ZPIC contract sets,

indexed by ei.

Figure 3.6: Utility value along the ZPIC line: (I) VG utility along ZPICG line; (II) VB utility

along ZPICB line.

We see that the utilities for G and B reach their maximum in the points C and D

accordingly. In the following table there are equilibrium values. We note the decrease in

utility levels of both E’s as well as in effort level and probability.

VG VB

CH CH

CL CL

VG VB

eG eB

{I} {II} C

D

36

Table 3.4 Calculated equilibrium values for observable type case

Contract C (for G type) Contract D (for B type)

Utility 0.626354 0.437983

Effort level 0.295987 0.172517

Probability 0.504366 0.157636

CH 0.850714 0.670737

CL 0.251916 0.161617

3.4.4 Equilibrium contracts in case of unobservable types

In the unobservable type environment the previous equilibrium contracts must be checked

for consistency with the ASC constraint (3.16.c). Therefore we must evaluate for each E type

the utility from deviation to the other’s type contract. In the Figure 3.7 the graphs (I) and (IV)

shows E’s utilities along the corresponding ZPIC lines. Points C and D are the equilibrium

contracts for observable types case. The graphs (II) and (III) show the utilities in case of

deviation – along other type’s ZPIC lines.

The deviation utilities were defined by (3.14) and (3.15). For instance, with every

contract from ZPICB set rated by eB effort, G applies eG effort level defined in (3.15).

Figure 3.7: The finding of contract set that satisfies ASC constraints:

(I) VG utility along ZPICG line; (II) VG utility from deviation along ZPICB line; (III) VB utility

from deviation along ZPICG line; (IV) VB utility along ZPICB line.

VG VG

dev

VBdev

VB

eG

eG

eB

eB

{I}

{III}

{II}

{IV}

C

C

D

D F

F

M

M

N

37

In the graphs (I) and (II) we see that the utility of G from G-contract tops the utility from

any B’s contract. Hence he has no incentives to deviate from his type’s contract to any

contract within ZPICB and the constraint (3.16.c) is satisfied. Oppositely, B’s utility in case of

his deviation to the contract of G, exceeds the utility from his type’s contract (graphs (III) and

(IV)), therefore in case of unobservable type he will deviate to G’s contract. The market faces

adverse selection problem because all E-s will choose G-type contract.

Table 3.5 Utilities from the contracts C and D

Entrepreneur Utility from contract C Utility from contract D

G 0.626354 0.524717

B 0.437983 0.538427

To satisfy ASC constraint, G-type contract must be at most equally preferred for B as B-

type contract. On the Figure 3.6(III) such contracts (points F and M) are corresponded

horizontally to the contract D in (IV). It is obviously from ZPICG line (I) that the contract F

brings much more utility to G than the contract M. Consider the utilities for the new pair of

contracts:

Table 3.6 Utilities from the contracts F and D

Entrepreneur Utility from contract C Utility from contract D

G 0.604852 0.524717

B 0.437983 0.437983

We see that for the new contract set each E is reluctant to deviate from his type’s

contract. To check if there is no better contract pair, consider the Figure 3.6. B has the

contract that maximizes his utility within ZPICB contract set. G has the contract F that is

better than any other contracts within ZPICG set except the segment:[N,F). But all the

contracts from this segment will be preferred for B than his contract D. Therefore contract F is

the best possible contract for G.

38

Table 3.7 Equilibrium contracts for the unobservable type case

Contract F (for G type) Contract D (for B type)

Utility 0.604852 0.437983

Effort level 0.385432 0.172517

Probability 0.622306 0.157636

CH 0.980663 0.670737

CL 0.13186 0.161617

Finally we consider the summary table of payoff and effort allocations for the three cases

we have considered:

Table 3.8 Equilibrium contracts for all cases

Type G project:

full information benchmark

Type B project:

full information benchmark

Type G project:

observable type,

unobservable effort

Type B project:

observable type,

unobservable effort

Type G project:

unobservable type and

effort

Type B project:

unobservable type and

effort

Utility 0.664985 0.484415 0.626354 0.437983 0.604852 0.437983

Effort level 0.361295 0.284651 0.295987 0.172517 0.385432 0.172517

Probability 0.592056 0.244138 0.504366 0.157636 0.622306 0.157636

CH 0.632851 0.319724 0.850714 0.670737 0.980663 0.670737

CL 0.632851 0.319724 0.251916 0.161617 0.13186 0.161617

3.5 Results of the Chapter

1. The separating equilibrium in the market with the complex informational problem can

be reached.

2. The moral hazard problem causes the contingency of contractual payoff for both types

that decrease the equilibrium effort levels.

3. The adverse selection problem can cause further decreasing of G’s utility but

increasing of his effort level.

39

Chapter 4: Venture Capital Effort

4.1. Modelling the impact of VC effort

In this Chapter we consider the role of information concerning the actions of VC. Earlier

we have discussed the informational problems that arise when some unobservable actions by

the entrepreneur (E) affect the project outcome, in addition to his privately known type. But

what will happen if VC has something to hide? We already have mentioned in the introduction

that the role of VC in the project can be considered not only as a finance mediator but also as

the agent, taking on some important management functions. VC’s actions as well as his

applying of accumulated organizational, informational and skilled labor resources can play

crucial role in the project success. These resources, of course, have their costs, so VC must

decide how much to invest in the project. Naturally, the contractor - E has limited ability to

control or even observe the hardworking of VC that can lead to the project fault. Here we refer

to VC’s non-financial input into the project as “VC efforts”. This enables us to describe these

relationships as the familiar moral hazard problem, where VC plays the agent role and E

becomes principal.

Our new setting here will include the competitive market of projects with two E’s project

types and VC’s effort as private information. As in the Chapter 3 we assume that effort level

influences on the probability of high project outcome. That probability is a continuous

monotone differentiable function, ]1,0[],[: 10 →eep , where e is the effort level exerted by VC,

and )(ep is the probability of the project’s high outcome. The expected project net surplus,

therefore, is IedZepZep LH −−−+ )())(1()( , where )(ed is VC’s effort cost function. The

expected utility function of E is:

)())(1()()(),,( LHLHE CUepCUepCCeV −+= (4.1)

For the following analysis we also need to define the utility function of VC. While still

assumed to be risk neutral, his utility now includes the disutility from effort

IedCZepCZepeCCN LLHHLH −−−−+−= )()))((1())((),,( (4.2)

We also assume that W is the VC’s utility if he does not fund any risky project. To ensure

that the market for risky projects operates we assume that the project is sufficiently productive

relative to W. That is, for all effort levels the expected project net surplus is at least W:

40

],[,)())(1()( 10 eeeWIedZepZep LH ∈∀≥−−−+ (4.3)

The time-schedule of the project is:

The questions we want to address in this chapter are: Is there equilibrium with two-sided

informational problems? What is the influence of this problem on efficiency and on the

welfare of both parties? Can VC use the private information to improve his gain or to offset

the informational asymmetry?

4.2 Single Project Type

4.2.1. Observable VC effort

Here we present the first best case of full information. Both the project type and the effort

exerted by VC are observable by all. Hence VC effort must be included in the contract, to be

denoted by: ),,( eCC LH . The inclusion of VC effort in the contract makes sense because the

project outcome, and consequently E’s utility, are dependent on the probability of getting the

high outcome, and thus depend on VC effort.

Definition 4.1: Equilibrium with observable VC effort is a set of contracts },,{ eCC LH=ψ

such that:

1. For all contracts in the equilibrium set, VC’s expected profits are at least

W: WeCCN LH ≥),,( ;

2. There is no contract outside the equilibrium set that, if offered, will attract some

entrepreneurs and still make profit greater than or equal to W.

Competition with other venture capitalists will force each VC to offer E the best possible

contract that maximize E’s utility. This results in the following Lemma:

VC designs a menu of contracts

E chooses a contract from

the menu

VC chooses and supplies particular

level of effort

The realization of the state of

nature

Outcome and

payoffs

41

Lemma 4.1 In equilibrium with observable VC effort VC's utility is just W: WeCCN LH =),,(

Proof: Suppose that in equilibrium WeCCN LH >),,( so VC can offer E more utility and still

maintain the profit not less than W. This violates Condition 2 in Definition 4.1 and therefore

this contract cannot be equilibrium. Q.E.D.

As we show later, the low reward to VC – equal to his reservation utility - can be avoided

under competition among VCs when the VC effort is unobservable.

Corollary: In equilibrium with observable VC effort, E's equilibrium expected utility is:

WedIZepZepCepCep LHLH −−−−+=−+ )())(1()())(1()( (4.4)

According to this corollary all surplus from the project, after compensating the VC for his

investment and disutility from effort, goes to E.

Lemma 4.2 In equilibrium with observable VC effort, the contract with non-contingent

payment C* maximizes E’s utility when:

WedIZepZepCCC LHLH −−−−+=== )())(1()( ****** (4.5)

Equilibrium VC effort maximizes the project expected net surplus:

})())(1()({maxarg* IedZepZepe LH

e−−−+= (4.6)

Proof: For every given VC effort, VC’s problem is to maximize E’s utility given (4.4):

In the Chapter 2 we have shown that the solution for this problem is non-contingent

payoff (2.6). In the present case it takes the form of (4.5).

To choose equilibrium effort level that maximizes E’s utility from non-contingent payoff

VC solves:

{ })())(1()()(),,(max ***

,

LHLHE

CCCUepCUepeCCV

LH−+= (4.7)

s.t. WedIZepZepCepCep LHLH −−−−+=−+ )())(1()())(1()( *****

{ }])())(1()([),,(max ** WedIZepZepUeCCV LHEe

−−−−+= (4.8)

42

Because the utility is monotonic and W is constant, the solving of (4.8) is equivalent to:

That is the maximization of the project net surplus (4.6). Q.E.D.

The conclusion of Lemmas 4.1and 4.2 is the following Proposition:

Proposition 4.1 In the market with single project type and observable effort the equilibrium

includes the single equilibrium contract },,{ *** eCC LH such that:

WedIZepZepCCC LHLH −−−−+=== )())(1()( ******

})())(1()({maxarg* IedZepZepe LH

e−−−+=

In the first-best full-information case the payoff is non-contingent and VC’s effort

maximizes project surplus.

4.2.2. Unobservable VC effort

Assume now that E cannot verify the effort level that will be exerted by VC after the

contract is approved by E. To express the sequence of events in this case we define the

expected utility of VC in the following way:

})()))((1())(({max),(ˆ IedCZepCZepCCN LLHH

e

LH −−−−+−= (4.10)

At the time of contracting the parties can only define the payoff scheme because the

contract cannot include non-verifiable effort. So the equilibrium in this market takes the

following form:

Definition 4.2 An equilibrium with unobservable VC effort is the set of contracts

},{ LH CC=ψ such that:

1. VC’s expected profits in all equilibrium contracts are at least as large as W:

WCCN LH ≥),(

2. There is no contract outside the equilibrium set that, if offered, will attract some

entrepreneurs and still make profit not less than W.

In the next Proposition we characterize the equilibrium in the market with single project

type and unobservable VC effort:

{ })())(1()(max edIZepZep LH

e−−−+ (4.9)

43

Proposition 4.2 The equilibrium with unobservable effort consists of a single contract }{ *C ,

where *C is the payoff in the observable effort case (4.5). VC exerts the same effort *e as in

the observable case (4.6) and gets minimal utility level W.

Proof: Under competition, VC offers to E the maximum utility contract. By Lemma 4.2 in the

observable effort case the contract with non-contingent payment *C maximizes E’s utility. In

the unobservable effort case this contract also feasible, therefore it will be offered by VC. But,

by Lemma 4.2, VC can provide this payment only by exerting *e effort. Then in the

unobservable effort case VC will exert *e effort and offer contract }{ *C . Q.E.D.

Our first result in this case deserves some explanations: with a single project type, (i.e. no

adverse selection problem among entrepreneurs) VC’s moral hazard dilemma does not

influence the equilibrium effort level nor the reward of either party. The reason for this is that

E is indifferent to the effort level exerted by the VC through his full-insurance compensation,

so that whether VC’s effort is observable or not makes no difference. This insight suggests

that things may work out differently with adverse-selection problem among entrepreneurs of

different types, where full-insurance contracts may not be the equilibrium. We study this case

below.

4.3 Two types of project

Assume for now that in the market there are two project types: G and B. The difference

between types is in the probability function: 00)()(1 eeepep BG >∀>>> . If the type is

observable, the equilibrium is obviously the combination of contracts BGiC i ,},{ * ∈ , each of

them is defined as in the Subsection 4.2.2 for the corresponding probability functions. Thus

we can turn directly to the case where project types are unobservable by VC at the contracting

time. We will consider separately the cases of observable and unobservable VC effort.

4.3.1. Observable VC effort

In this Subsection we deal with the adverse selection problem because of unobservable

project type, but the effort exerted by VC is observable. We modify the equilibrium definition

(4.1) for multiple project types:

44

Definition 4.3 A separating equilibrium for two project types with observable VC effort is a

set of contracts ψ containing a contract for each entrepreneurial type,

)},,(),,,{( BLBHBGLGHG eCCeCC=ψ , such that:

1. No contract in ψ earns expected profits less than W: },{,),,( BGiWeCCN iLiHi ∈≥

2. There is no contract outside ψ such that if offered will attract some entrepreneurs and

still make profit not less than W.

First we must note again that a pooling equilibrium in this market does not exist because

in this case VC profits on B type projects is less than W which contradicts the definition of

equilibrium. This is why we named it as separating.

The next basis point is that the separating equilibrium in the market with adverse

selection requires incentive compatibility condition to be applied. This follows from the first

part of the Definition 4.3: if it is profitable for one E’s type to take the contract of the other

type it will cause the pooling of entrepreneurs that, as we noted above, will bring the non-

existence of equilibrium in the market. We conclude it in the following Lemma:

Lemma 4.3 In the separating equilibrium the incentive compatibility condition must be

satisfied:

BGjijieCCVeCCV jLjHjiiLiHii ,,;),,,(),,( ****** ∈≠≥ (4.11)

Finally, we rule out the possibility that the equilibrium set of contracts consists only of

the contracts with non-contingent payoffs, as in the single project type. Because of the

adverse selection problem the full-insurance contracts of the kind BGieCC iii ,},,,{ *** ∈

(where *iC and *ie for each type are defined in Proposition 4.1) cannot be an equilibrium. If

such contracts are offered and if iBiG CC > , then both types will choose the contract for G,

(the effort level is defined in Proposition 4.1). But as we already have noted, there is no

pooling equilibrium in the market. Hence there cannot exist a separating equilibrium with

full-insurance payments to both types. Contracts must be risky enough not to attract

entrepreneurs of other type.

These three points enable us to characterize equilibrium with observable VC effort and

multiple unobservable project types:

45

Proposition 4.3 In the equilibrium VC offers to B the maximal non-contingent payoff contract

},{ ** BB eC and exerts the effort level which maximizes the expected net surplus from type-B

projects:

The type-G contract is },,{ *** GLGHG eCC where:

{ })())(1()()(maxarg},,{

* LGGGHGGG

CCe

G CUepCUepeHLHGG

−+= (4.14)

s.t. )()())(1()()( *BLGGBHGGB CUCUepCUep =−+ (4.15)

( ) ( ) WedICZepCZep GLGLGGHGHGG =−−−−+− )())(1()( (4.16)

Proof: Because the effort level is observable we can apply Lemma 4.1 to this case, so VC’s

equilibrium expected profit from each contract is W: },{,),,( BGiWeCCN iLiHi ∈= .

Consequently, the equilibrium expected payoff to each type of entrepreneur is:

In equilibrium VC can offer B his maximum utility contract, },,{ *** BBB eCC , as defined

in the Proposition 4.1 for B’s appropriate probability of high project outcome. The effort level

eB*, defined by Lemma 4.2, maximizes the project expected net surplus for B type project

(4.13).

The G-type contracting is based on a different principle. Because of adverse selection

problem the equilibrium contract for G must satisfy (4.11) (by Lemma 4.3). This means that

G-type contract must be risky enough not to be preferable to B but still preferable for G. The

incentive compatibility condition allows for maximum utility for G when it binds (when the

utility of B from contract for G will be exactly )( *BCU ). This guarantees that this contract is

maximum profitable for G but still non-preferable for B (4.15).

The effort level for G is chosen to maximize the expected utility of G (4.14), and not the

project net surplus as in (4.13). The reason for this is the contingent nature of the contract

making Lemma 4.2 not applicable here. Accordingly the effort to be exerted for G-type

project in this case will be different from that exerted for a B-type project, or the effort that

would have been exerted in equilibrium where only G-type projects were present. We will

demonstrate these differences in the numerical example at the end of this Chapter.

WedIZepZepCCC BLBBHBBBLBHB −−−−+=== )())(1()( ****** (4.12)

})())(1()({maxarg* IedZepZepe LBHB

e

B −−−+= (4.13)

},{,)())(1()())(1()( BGiWedIZepZepCepCep iLiiHiiLiiiHiii ∈−−−−+=−+ (4.17)

46

So we have characterized the equilibrium set of contracts which satisfies the definition of

the equilibrium. No other contract set brings at least W and attracts some entrepreneurs if this

contract set is offered. Q.E.D.

The equilibrium defined in Proposition 4.3 has the following properties:

1. The B-type contract is just the same as it is in the single type case (for

corresponding probability function).

2. G’s utility is lower than in the single entrepreneurial type case, (which is the first-

best), due to incentive compatibility constraints that must be imposed on the

contracts in the presence of adverse selection problems.

3. The effort level for G-type entrepreneur maximizes his expected utility and not

the project net surplus as in the single type case.

4.3.2. Unobservable effort

The final and most interesting case that we are considering is when E cannot observe the

effort level exerted by VC and VC cannot observe the type of E’s project. This causes the

adverse selection problem from the side of E and moral hazard problem from VC’s side.

In the competitive market VC exerts effort after the contract is accepted by E, so he will

choose the effort level that maximizes his own utility. We therefore present the utility

function of VC from a contract promising a payment ),( LH CC to a type i project as follows:

},{},)()))((1())(({max),(ˆ BGiIedCZepCZepiCCN LLiHHi

e

LHi ∈−−−−+−= (4.18)

The effort level is not observable and therefore non-contractible. Accordingly, the

definition of the equilibrium in this case takes the following form:

Definition 4.4 A separating equilibrium for two types with unobservable VC effort is a set

of contracts ψ containing a contract for each entrepreneurial type,

)},(),,{( LBHBLGHG CCCC=ψ , such that:

1. In every equilibrium contract VC earns expected profits of at least W:

( ) ψ∈∈≥ LiHiLiHi CCBGiWiCCN ,},,{,)|,( ,

2. There is no contract outside ψ that if offered will attract some entrepreneurs and still

make expected profit not less than W.

47

Notice that in contrast to Definition 4.2, here equilibrium contract do not specify the VC’s

effort. We now examine what is the equilibrium impact of the inability to contract on the VC’s

effort.

Despite the fact that effort level is unobservable it still influences E’s expected utility. E

assumes that the effort level will be chosen by VC according to (4.18), despite the competition

among VCs (under which they have incentives to promise ex-ante higher effort levels but

have no way to commit to such promises), and may have ex-post incentives to renege on

them. Moreover, the existence of the adverse selection problem in the market imposes

compatibility constraints (defined by the Lemma 4.3) on equilibrium contracts. Taking all this

into consideration, the equilibrium in characterized by the following Proposition:

Proposition 4.4 In the market with unobservable project types and unobservable VC’s effort

the equilibrium is characterized as follows:

1. VC offers to B the maximal non-contingent payoff contract }{ *BC and exerts *Be

effort just as in the observable VC effort case:

WedIZepZepCCC BLBBHBBBLBHB −−−−+=== )())(1()( ****** (4.19)

})())(1()({maxarg* IedZepZepe BLBBHBB

e

B

B−−−+= (4.20)

2. VC exerts effort level Ge for contract G according to the schedule 12:ˆ ℜ→ℜe defined by:

{ }IedCZepCZepCCe GLGHGGHGHGG

e

LGHGG

G−−−−+−= )()))((1())((maxarg),(ˆ (4.21)

and offers the risky compensations }ˆ,ˆ{ LGHG CC to G that solves:

{ })()),(ˆ(1()()),(ˆ(max,

LGLGHGGGHGLGHGGG

CCCUCCepCUCCep

LGHG−+ (4.22)

s.t. )()())),(ˆ(1()()),(ˆ( *BLGLGHGGBHGLGHGGB CUCUCCepCUCCep =−+ (4.23)

Proof: By Proposition 4.3 the non-contingent payoff *BC (4.12) is the best contract terms for

B type, VC effort level in this case actually does not matter for him because his utility then is

independent of project outcome. Note also, that this payoff can be provided by VC only with *Be exerted. The contract }{ *BC is feasible also in the unobservable effort case and therefore

will be provided by VC, which must exert *Be effort for this purpose.

48

In contrast, non-contingent payoff allocation for G is not feasible here because of adverse

selection problem. Hence VC offers to G the contract that satisfies the incentive compatibility

condition (4.11), captured here by the constraint (4.23) on B’s expected utility. Incentive

compatibility in the opposite direction is ensured by the fact that if G will take B contract then

he will get exactly the same expected utility as B, because in the non-contingent contract his

utility does not depend on the effort level. Thus, because B’s utility is always lower than G’s,

the latter will never deviate to take B’s contract.

Note that because the effort level is unobservable, VC will exert effort level that

maximizes his own expected profits according to (4.21). In this case, this is the reason for

VC’s profits to be higher than W. VC would like to forego some of these “excess profits” and

attract additional G-type entrepreneurs from competing VCs, (which would drive his total

profits up). But he has no commitment power to credibly convince entrepreneurs that once he

gets their business his exerted efforts will indeed be higher than those suggested by (4.23).

Because this result is very important and very subtle, let us try and explain it in another

way. Suppose that VC that already have calculated his expected profits from a G-type project,

say (W+w), and considers increasing expected payments to G by w to win his project from the

competition. But G that now faces in the market two contracts for his type: }ˆ,ˆ{ LGHG CC and

}ˆ,ˆ{ wCwC LLGHHG ∆+∆+ (where wH∆ and wH∆ are chosen to keep incentive compatibility

constraint), but believes that the second contract’s payoffs will lead to the different choice of

e, defined by (4.21). Because HGC and LGC maximize the utility of G given (4.21) the second

contract type will not be chosen by any G-type entrepreneur. Therefore in the equilibrium VC

can get profits more than W. Q.E.D.

Proposition 4.4 characterizes the equilibrium for the unobservable project types and VC

effort, if it exists. In particular, if the VC’s expected profits from the type G contract in (4.21)

falls short of W, (VC’s reservation profits), then there is no equilibrium for this case. Or

maybe, in this case, there is just one contract offered in equilibrium by VC, the intended for

type B. Entrepreneurs of both types will take this contract, since it is the only one offered in

equilibrium. On type B projects VC makes profits W but on type G, which takes the same

contract, he makes more than W.

49

4.4 Numerical example

Here we will consider the simple numerical example of the market with VC’s effort to

check if this construction leads to equilibrium and to evaluate numerically the results of this

chapter. Another purpose of this section is to clarify the particular features of the equilibrium,

formulated in the Subsection 4.3.2.

For the numerical example we chose the following functions and parameter set:

Table 4.1 Functions and parameters used in the numerical example

Function set: Parameter set:

21

)( CCU = 2)( eed =

2)( meneepG −=

)(*)( epkep GB =

e∈[0,1]

ZH=1

ZL=0.1

n=1

m=0.5

k=2

I=0

W=0

The criterion for choosing these parameters was to show a simple and illustrative

example of the model.

We will compare the following cases for two project types:

1. Observable project type and VC’s effort (the first best case).

This case of two project types is nevertheless is based on the Subsection 4.2.1

because of full information environment. The payoffs and effort level for each type

are defined by the Proposition 4.1 for the corresponding probability functions

2. Unobservable project type and observable VC’s effort

The case is based on the subsection 4.3.1. Contract for B is just the same as in the

previous case (that fact is explained in the subsection 4.3.1). The contract for G is

defined by the Proposition 4.3.

3. Unobservable project type and VC’s effort

The case of the subsection 4.3.2. Contract for B is still the same. The contract for

G is defined by the Proposition 4.4. For the calculation purposes we interpret it as

50

follows: VC always exerts effort level Ge for contract G that maximizes his

reservation utility WN ≥ (4.21) thus presents an effort level as a function of payoff

set: ),(ˆ LGHGG CCe . Assuming the convexity of the function N (that is maximized in

(4.21)) we will use the F.O.C.:

0)(=

∂∂

eeN (4.24)

To attract entrepreneurs VC offers payoff set that maximizes E’s utility given

effort choosing rule (4.24).

The following table includes the calculation results for all three cases:

Table 4.2 Calculated equilibrium contracts

Type B project:

cases (1)-(3) above

Type G project: case (1)

Type G project: case (2)

Type G project: case (3)

Utility, Vi 0.489546 0.725476 0.689308 0.592191

Effort, ei 0.310345 0.473684 0.536769 0.286187

Probability, pi(ei) 0.262188 0.722992 0.785417 0.490471

CHi 0.239655 0.526316 0.63754 0.648765

CLi 0.239655 0.526316 0.0839748 0.149692

VC’s excess profit above W, (Ni)

0 0 0 0.0650483

In the next Figure we show these values in form of diagram. We see here:

• E’s expected utility for G and B project types (V)

• the effort level to be exerted by VC in the equilibrium (e)

• the probability of the project good outcome (p(e))

• the riskiness of the entrepreneur equilibrium compensation, captured by the ratio

of his payoffs, (low/high or CL/CH)

• VC’s net profits (N)

51

0

0,2

0,4

0,6

0,8

1

V e p(e) Cl/Ch N

Type G project: case 1 Type G project: case 2Type G project: case 3 Type B project, all three cases

Figure 4.1: Calculated values for three cases.

The following Figure displays the calculated graphical solution of the VC problem for G

type from Case 2 (Proposition 4.3: (4.14)-(4.16)). In the Figure are depicted the values of G’s

expected utility (VG) and VC profits (N) for the range of effort levels:

00.10.20.30.40.50.60.70.8

0.09

0.15

0.21

0.27

0.33

0.39

0.45

0.51

0.57

0.63

0.69

0.75

0.81

VC effort

Exp

ecte

d ut

ility

VN

Figure 4.2. Case 2: Choosing effort level. V: The expected utility of

G; N: the expected utility of VC

V=0.689308

52

The graph of E’s utility has its maximum in e = 0.536769, while VC’s profits are equal to

zero for all effort levels.

The following Figure will help us to describe the choice of payoff set for G in the Case 2.

In the Figure 4.3 there are payoff sets (CHG, CLG) for different effort levels that can be offered

to G by VC, in other words satisfy (4.15) and (4.16). In this Figure all the payoff allocations

form the line that along with the increasing of VC effort makes a clockwise loop. In other

words, along with increase in provided effort level the contingency of payoff is first

increasing and then decreasing up to the effort level of e=0.86 when CH=CL. Obviously, this

is exactly the point CH=CL=CB*=0.239655, the non-contingent payoff allocation of B type,

that is consistent with (4.15).

The equilibrium allocation is correspond to the point where e=0.536769. Note also that

for instance the point e=0.16 provides E with more payoff in both outcomes than the

equilibrium point e=0.536769, but brings less utility because of low effort level associated

with it and therefore cannot be an equilibrium point.

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9Ch

Cl

e=0.536769

e=0,86

e=0,16

Ch=Cl

Figure 4.3. Case 2: Possible G payoff sets (CHG , CLG) for different VC effort levels

53

On the next Figure there is calculation based graphical solution of the VC problem for G

type from Case 3 (Proposition 4.4). In the Figure there are depicted the values of G’s expected

utility (VG) and VC profits (N) for the range of effort levels. We see that unlike the observable

effort case VC’s profit is not constantly zero but increases monotonically. The fact that VC

has non-zero profit is explained in the Proposition 4.4, here we see that in the equilibrium

point, when the expected utility of G is maximized, he has strictly positive profit.

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

00.0

40.0

80.1

20.1

6 0.2 0.24

0.28

0.32

0.36 0.4 0.4

40.4

80.5

20.5

6 0.6

VC effort

Expe

cted

util

ity VN

Figure 4.4. Case 3: Choosing effort level. V: The expected utility of G; N: the expected

utility of VC

V=0.592191

N=0.0650483

54

In the last Figure there is the line of the payoff sets that VC can offer to E in the Case 3.

The form of the line is much simpler than the one from the Case 2. We see here that along

with the increasing of the effort level to be exerted by VC the contingency of the payoff set to

E is decreasing all the time up to the point where e=0.47 and CH=CL=CB*= 0.239655, that is

the payoff set for type B project.

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1Ch

Cl

e=0.286187

e=0,47

Ch=Cl

Figure 4.5. Case 3: Possible G payoff sets (CHG , CLG) for different VC effort levels

Finally we will emphasize the following results of the numerical example:

1. There is a small decrease in the expected utility of G in the case of observable VC

effort comparatively to the first best case. In case of non-observable effort the

decrease is more considerable but in all cases G’s expected utility is better than the

expected utility of B, which is equal in all cases). This is what we expected: the

existence of informational asymmetry hurts the wealth of better entrepreneurs.

2. We have got the interesting results that VC effort level for G in the case of observable

VC effort is better than in the first best case and in the non-observable effort case VC

effort is even less than the effort for B project! These results seem discouraging but

can be explained easily.

First, in the first best case G gets full insurance contract and doesn’t care about effort

level to be applied, so VC chooses the effort level that maximizes total project profits.

But when in the observable effort case G has the payoffs contingent on the project

55

outcome he is highly interested in the high probability of good outcome and therefore

expects from VC to exert additional effort level. In this case VC maximizes not the

project profits but G’s expected utility function.

Second, when the effort level is unobservable VC maximizes his own utility function

and therefore the chosen effort level can be even lower than the effort level for B

contract.

3. The highest probability of good outcome is reached in the observable effort case that

is caused by high effort exerted. In the unobservable effort case the high outcome

probability of G contract is sufficiently higher than of B contract despite the lower

effort level exerted (because of better probability function).

4. The payoff allocation sets are highly contingent for G in both observable and

unobservable effort cases. In the Figures 4.3 and 4.5 we see that the deriving of

contingency level of the payoff allocations for G is non linear because this is defined

by complex process.

5. The results of the numerical example support the argument of the Proposition 4.4

about the positive VC’s profits in case of unobservable effort case despite a

competitive environment (Figure 4.4).

56

4.5 Results of the Chapter

In this Chapter we have considered the model of the competitive investment market with

bi-directional informational asymmetry. As we expected the adverse selection problem can

adversely affect the good entrepreneurs, an outcome of the negative externality created by the

lower quality projects in the population.

The more interesting result is the situation when VC has positive profit in the case of

unobservable effort despite the competition in the market. But it is important to understand

that this situation is the symptom of inefficiency of the market. VC just cannot use this surplus

in the competition against other VCs because of informational limitation.

Another point to notice is the increase in VC’s effort with unobservable project types and

observable effort in comparison to the known project type (first-best) case. The reason for this

is that full-insurance contracts cannot be offered to G-type projects due to adverse selection

(or incentive compatibility) constraints, and consequently these entrepreneurs are affected by

the probability of high outcome determined by the VC’s effort.

The next non-typical result is the possibility of the situation when VC exerts more efforts

on the bad projects than on the good ones (in case of unobservable VC effort). The reason is in

the contract limitations for good projects that hinder VC exert more effort.

We now can answer to the question if VC can use his private information to improve the

situation in the market? No he cannot, on the contrary it hinders him to use fully his recourses

for the competition purposes.

The general result of the Chapter can be formulated as follows: The equilibrium in the

competitive market of investment can be reached even in presence of the bi-directional

informational problem. The main effect of the informational problems is the reduction in the

welfare of good entrepreneurs. It may have ambiguous effect on other performance measures

of the projects, such as the effort exerted by VC and the chances of the project to succeed. The

interesting consequence of the informational limitations is the situation of inability of VC to

exert additional effort in the project even in the situation when both parties are interested in

this.

57

Conclusions

We develop a model of competitive venture capital financing market to examine the

influence of different informational problems on the equilibrium allocations and on the

efficiency of the market. First, we analyzed the informational problems concerning the

entrepreneurial actions and project quality. We found that investments can be allocated

efficiently even if VC cannot observe the quality of the project. Also we show that

informational problems expectedly hurt entrepreneurs with better projects, but can stimulate

their efforts and therefore the chances of the project to succeed.

Second, we introduce the problem of informational imperfections from venture

capitalist’s side. We show that this information can influence the equilibrium recourses

allocation. Particularly, we show the situation when the venture capitalist cannot increase his

efforts because of entrepreneurs’ belief about his way of acting, even if both parties are

interested in additional efforts.

Our findings indicate further theoretical developments of the approach in the following

directions. First, the model is based on the assumption of competitive market. The question

arising is what would be the influence of asymmetric information if we assume that the

market of venture capital is not competitive or even monopolistic? This would raise the issue

of the need for government regulations of these markets.

Finally, because of the model restrictions, we cannot enlarge the number of different

project types to analyze whether the results hold for more complex environments. Introducing

a large number of projects would let us understand better the mechanisms of decision making

in this markets. Third, we can add an additional player – the initial investor. This would let us

analyze the ambivalent role of venture capitalist as agent in relations with investor and

principal towards entrepreneur.

58

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61

Chapter 1: Introduction .......................................................................................................... 1

1.1 Goals and purposes of the work.................................................................................... 1 1.2 Venture capital............................................................................................................. 2

1.2.1 VC in financing R&D................................................................................... 2 1.2.2 Organizational aspects of VC activity........................................................... 4

1.3 Informational asymmetry in the VC market.................................................................. 6 1.4 Description of the work................................................................................................ 8 1.5 Results of the work .................................................................................................... 10

Chapter 2. A Model with Endogenous Investments .............................................................. 14 2.1 The Market Environment ........................................................................................... 14 2.2 Benchmark case: Equilibrium with single project type ............................................... 15 2.3. Equilibrium with heterogeneous projects................................................................... 17

2.3.1 Full information case.................................................................................. 17 2.3.2 Asymmetric information case ..................................................................... 17 2.3.3 Uniqueness and existence conditions of the separating equilibrium............. 20

2.4. Results of the Chapter ............................................................................................... 21 Chapter 3: Entrepreneurial Effort ......................................................................................... 22

3.1. Modelling entrepreneurial effort................................................................................ 22 3.2. Equilibrium contracting with homogenous projects ................................................... 24

3.2.1. Observable effort....................................................................................... 24 3.2.2 Unobservable effort .................................................................................... 25

3.3 Two types of project................................................................................................... 28 3.3.1 Observable type.......................................................................................... 29 3.3.2 Unobservable type and effort...................................................................... 31

3.4 Numerical example .................................................................................................... 33 3.4.1. Equilibrium contracts in case of observable type and effort ....................... 33 3.4.2. ZPIC contract set....................................................................................... 34 3.4.3 Equilibrium contracts in case of observable type ....................................... 34 3.4.4 Equilibrium contracts in case of unobservable types .................................. 36

3.5 Results of the Chapter ................................................................................................ 38 Chapter 4: Venture Capital Effort ........................................................................................ 39

4.1. Modeling the impact of VC effort ............................................................................. 39 4.2 Single Project Type .................................................................................................... 40

4.2.1. Observable VC effort ................................................................................ 40 4.2.2. Unobservable VC effort............................................................................. 42

4.3 Two types of project................................................................................................... 43 4.3.1. Observable VC effort ................................................................................ 43 4.3.2. Unobservable effort ................................................................................... 46

4.4 Numerical example .................................................................................................... 49 4.5 Results of the Chapter ................................................................................................ 56

Conclusions ......................................................................................................................... 57 Bibliography........................................................................................................................ 58