ec 3101 microeconomic analysis ii€¦ · week 1course overview; intertemporal choice, ch.10 week...

EC 3101Microeconomic

Analysis II

Instructor: Indranil ChakrabortySng Tuan Hwee

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My contact information• WEBSITE: http://profile.nus.edu.sg/fass/ecsci/

• EMAIL: [email protected]

• PHONE: 6516 3729

• OFFICE: AS2 05‐23

• OFFICE HRS: Tuesday 3pm – 5pm or by appointment

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Note: Week 3 lecture will be held on Week 2 Thursday (August 21, 6-8pm in LT11)

Textbook

Intermediate Microeconomics –A Modern Approach

(8th edition)

by Hal Varian

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Syllabus (subject to change)Week 1 Course Overview; Intertemporal Choice, Ch.10Week 2 Uncertainty, Ch. 12Week 3 Exchange, Ch.31 Week 4 Monopoly, Ch.24Week 5 Monopoly, Ch.24; Oligopoly, Ch.27Week 6 Oligopoly, Ch.27

– Recess Week –Week 7 MidtermWeek 8 Game Theory, Ch.28Week 9 Game Applications, Ch. 29Week 10 Game Applications, Ch. 29Week 11 Externalities, Ch. 34; Public Goods, Ch. 36Week 12 Asymmetric Information, Ch. 37Week 13 Review; AOB

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Assessment

• Homework, 10%

• Participation, 10%

• Midterm Exam, 40%

• Final Exam, 40%

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Homework

• Two individual problem sets

• To be posted on IVLE one week before due date (W?, W? )

• Please submit in hardcopy to tutor’s mailbox

• 20% of total possible points will be deducted each day for late submission

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Participation

• Practice Problems from week ? onwards

• To be discussed in tutorial the following week

• You will present solutions during tutorial

• Everyone needs to present at least once

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Some Ground Rules

• Attendance to be taken in tutorials (Faculty policy)

• No texting or other cellphone use during class

• Academic dishonesty is unacceptable

• Consult syllabus posted on IVLE for all other details for EC3101

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INTERTEMPORAL CHOICE

Week 1(Chapter 10, except 10.4,

10.10, 10.11)

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Chinese Idiom: Three at dawn, Four at dusk

• A Songman raised monkeys.

• He wanted to reduce the monkeys’ ration.

• He suggested giving them 3 bananas in the morning and 4 in the evening. They protested angrily.

• "How about 4 in the morning and 3 in the evening?"

• The monkeys were satisfied. 10

Intertemporal Choice

• Are the monkeys irrational?

• Is one banana in morning equivalent to one in the evening?

• Is a dollar today the same as a dollar tomorrow?

• Should I take a loan from a bank purchase an apartment and rent it out?

• Should I pay off my credit card debt today or not?

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Present and Future Values

• Begin with some simple financial arithmetic.

• Take just two periods; 1 and 2.

• Let r denote the interest rate per period.

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Future Value

• E.g., if r = 0.1 then $100 saved in period 1 becomes $110 in period 2.

• The value next period of $1 saved now is the future valueof that dollar.

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Future Value

• Given an interest rate r, the future value one period from now of $1 is

FV = 1 + r

• Given an interest rate r, the future value one period from now of $m is

FV = m(1 + r)

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Present Value• Q: How much money would have to be saved now to obtain $1 in the next period?

• A: $k saved now becomes $k(1+r) in the next period, Set k(1+r) = 1So k = 1/(1+r)

• k = 1/(1+r) is the present‐value of $1 obtained in the next period.

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Present Value• The present value of $1 available in the next period is

PV = 1/(1 + r)

• And the present value of $m available in the next period is

PV = m/(1 + r)

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Higher r leads to lower PV

• E.g., if r = 0.1 then the most you should pay now for $1 available next period is

• And if r = 0.2 then the most you should pay now for $1 available next period is

PV 11 0 1

$0 91

PV 11 0 2

$0 83

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The Intertemporal Choice Problem

• Suppose there are 2 time periods: 1 and 2

• Let m1 and m2 be incomes (in $) received in periods 1 and 2.

• Let c1 and c2 be consumptions (in physical units) in periods 1 and 2.

• Let p1 and p2 be the prices of consumption (in $ per unit) in periods 1 and 2.

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The Intertemporal Choice Problem• The intertemporal choice problem: Given incomes m1 and m2, and given consumption prices p1 and p2, what is the most preferred intertemporal consumption bundle (c1, c2)?

• For an answer we need to know:– intertemporal budget constraint– intertemporal consumption preferences

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The Intertemporal Budget Constraint

• To start, let us ignore price effects by supposing that

p1 = p2 = $1 (per unit)

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• Suppose that the consumer chooses not to save or to borrow.

• Q: What will be consumed in period 1?• A: c1 = m1.• Q: What will be consumed in period 2?• A: c2 = m2.

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c1

c2So (c1, c2) = (m1, m2) is theconsumption bundle if theconsumer chooses neither to save nor to borrow.

m2

m100

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• Now suppose that the consumer spends nothing on consumption in period 1; So, c1 = 0 and s1 = m1.

• The interest rate is r.

• What will c2 be?

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• Period 2 income is m2.

• Savings plus interest from period 1 sum to (1 + r )m1.

• So total income available in period 2 is m2 + (1 + r )m1.

• So period 2 consumption expenditure isc2 = m2 + (1 + r )m1.

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c1

c2

m2

m100

the future‐value of the incomeendowment

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m2 (1 r)m1


c1

c2

m2

m100

(c1, c2) = (0, m2 + (1 + r )m1) is the consumption bundle when all period 1 income is saved.

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m2 (1 r)m1


• Now suppose that the consumer spends everything possible on consumption in period 1, so c2 = 0.

• What is the most that the consumer can borrow in period 1 against her period 2 income of $m2?

• Let b1 denote the amount borrowed in period 1.

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• Only $m2 will be available in period 2 to pay back $b1 borrowed in period 1.

• So b1(1 + r ) = m2.

• That is, b1 = m2 / (1 + r ).

• So the largest possible period 1 consumption level is

c1 m1 m2

1 r28

BI is the present value of M2


c1

c2

m2

m100

m2 (1 r)m1

m1 m2

1 r

the present‐value ofthe income endowment

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• More generally, suppose that c1 units are consumed in period 1. This costs $c1 and leaves m1‐ c1 saved. Period 2 consumption will then be

• Rearranging gives us,

c2 m2 (1 r)(m1 c1)

c2 (1 r)c1 m2 (1 r)m1.

slope intercept

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m2

m100

m2

(1 r)m1

m1m2

1 r

slope = ‐(1+r)

c2 (1 r)c1 m2 (1 r)m1

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c1

c2


(1 r)c1 c2 (1 r)m1 m2is the “future‐valued” form of the budget constraint since all terms are in period 2 values. This is equivalent to

c1 c2

1 r m1

m21 r

which is the “present‐valued” form of the constraint since all terms are in period 1 values.

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• Now let’s add prices p1 and p2 for consumption in periods 1 and 2.

• How does this affect the budget constraint?

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• Given her endowment (m1,m2) and prices p1, p2 what intertemporal consumption bundle (c1*,c2*) will be chosen by the consumer?

• Maximum possible expenditure in period 2 is

• So, maximum possible consumption in period 2 is

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m2 (1 r)m1

c2 m2 (1 r)m1

p2


• Similarly, maximum possible expenditure in period 1 is

• So, maximum possible consumption in period 1 is

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m1 m2

1 r

c1 m1

m21 r

p1


• Finally, if c1 units are consumed in period 1 then the consumer spends p1c1 in period 1, leaving m1 ‐ p1c1saved for period 1. Available income in period 2 will then be

so

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m2 (1 r)(m1 p1c1)

p2c2 m2 (1 r)(m1 p1c1)

PZCZ is total amt avail 4 spending in Period 2.


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p2c2 m2 (1 r)(m1 p1c1)Rearranging,

(1 r)p1c1 p2c2 (1 r)m1 m2

This is the “future‐valued” form of the budget constraint since all terms are expressed in period 2 values.

Equivalent to it is the “present‐valued” form:

p1c1 p2

1 rc2 m1

m21 r


c1

c2

m2/p2

m1/p100

m1 m2 / (1 r)p1

(1 r)m1 m2p2

Slope = (1 r) p1p2

(1 r)p1c1 p2c2 (1 r)m1 m2

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Price Inflation

• Define the inflation rate by π where

• For example,π = 0.2 means 20% inflationπ = 1.0 means 100% inflation

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p1(1 ) p2

Price Inflation

• We lose nothing by setting p1 = 1 so that p2 = 1+ π.

• Then we can rewrite the budget constraint

as

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p1c1 p2

1 rc2 m1

m21 r

c1 11 r

c2 m1 m2

1 r

Price Inflation

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c1 11 r

c2 m1 m2

1 rrearranges to

c2 1 r1

c1 1 r1

m21 r

m1

so the slope of the intertemporal budget constraint is

1 r1

Price Inflation

• When there was no price inflation (p1=p2=1) the slope of the budget constraint was ‐(1+r).

• Now, with price inflation, the slope of the budget constraint is ‐(1+r)/(1+ ). This can be written as

(rho) is known as the real interest rate.

(1 ) 1 r1

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Real Interest Rate

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(1 ) 1 r1

gives

r 1

• For low inflation rates ( 0), r ‐ .

• For higher inflation rates this approximation becomes poor.

Real Interest Rate

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r 0.30 0.30 0.30 0.30 0.30

0.0 0.05 0.10 0.20 1.00

r - 0.30 0.25 0.20 0.10 -0.70

r 1

0.30 0.24 0.18 0.08 -0.35

Comparative Statics

• The slope of the budget constraint is

• The constraint becomes flatter if the interest rate r falls or the inflation rate rises (both decrease the real rate of interest).

(1 ) 1 r1

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Comparative Statics

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c1

c2

m2/p2

m1/p100

(1 ) 1 r1

slope =

The consumer saves.

Comparative Statics

c1

c2

m2/p2

m1/p100

The consumer saves. Anincrease in the inflation rate or

a decrease in the interest rate “flattens” thebudget constraint.

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(1 ) 1 r1

slope =

Comparative Statics

c1

c2

m2/p2

m1/p100

If the consumer saves thenwelfare is reduced by a lower

interest rate or a higher inflation rate.

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(1 ) 1 r1

slope =

Comparative Statics

c1

c2

m2/p2

m1/p100

The consumer borrows.

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(1 ) 1 r1

slope =

Comparative Statics

c1

c2

m2/p2

m1/p100

The consumer borrows. A fall in the interest rate or a rise in the

inflation rate “flattens” the budget constraint.

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(1 ) 1 r1

slope =

Comparative Statics

c1

c2

m2/p2

m1/p100

If the consumer borrows thenwelfare is increased by a lower

interest rate or a higher inflation rate.

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(1 ) 1 r1

slope =

Valuing Securities• A financial security is a financial instrument that promises to deliver an income stream.

• E.g.; a security that pays$m1 at the end of year 1,$m2 at the end of year 2, $m3 at the end of year 3.

• What is the most that you should pay to buy this security?

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Valuing Securities

• The PV of $m1 paid 1 year from now is m1/ (1+r)

• The PV of $m2 paid 2 years from now is m2/ (1+r)2

• The PV of $m3 paid 3 years from now is m3/ (1+r)3

• The PV of the security is therefore

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PV m1

1 r

m2(1 r)2

m3

(1 r)3

PV of Y1 payout + PV of Y2 payout + PV of Y3 payout.

Valuing Bonds

• A bond is a special type of security that pays a fixed amount $x for T‐1 years (T: no. of years to maturity) and then pays its face value $F upon maturity.

• What is the most that should now be paid for such a bond?

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Valuing Bonds

PV x1 r

x(1 r)2

x(1 r)T1

F(1 r)T

End of Year 1 2 3 … T‐1 T

Income Paid $x $x $x $x $x $F

Present Value x/(1+r) x/(1+r)

2 x/(1+r)3 … x/(1+r)T‐1 F/(1+r)T

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Valuing Bonds

• Suppose you win a lottery.

• The prize is $1,000,000 but it is paid over 10 years in equal installments of $100,000 each.

• What is the prize actually worth?

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PV $100, 0001 0 1

$100, 000(1 0 1)2

$100, 000(1 0 1)10

$614, 457

Valuing Consols

• A consol is a bond which never terminates, paying $x per period forever.

• What is a consol’s present‐value?

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Valuing Consols

EndofYear 1 2 3 … t …

IncomePaid $x $x $x $x $x $x

PV

… …

PV x1 r

x(1 r)2

x(1 r)t

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Valuing Consols

PV x1 r

x(1 r)2

x(1 r)3

11 r

x x1 r

x(1 r)2

11 r

x PV

Solving for PV gives PV xr

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Valuing Consols

E.g. if r = 0.1 now and forever then the most that should be paid now for a console that provides $1000 per year is

PV xr $1000

0 1 $10,000

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ec 3101 microeconomic analysis ii€¦ · week 1course overview; intertemporal choice, ch.10 week...

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