Exam 1-Results

• Average total score: 26.8 (74%)– Average score Part A: 4.7 (58%)– Average score Part B: 9.1 (76%)– Average score Part C: 13 (81%)

• Answer key will be posted today and we’ll go over the test in Discussion on Friday

Exam score(max =

8+12+16= 36)

Exam %(max 100)

# of students % of students

≥ 31 ≥ 87 3 10

28-30 77 - 86 10 34

24-27 67 - 76 12 41

≤ 23 ≤ 66 4 14

Lecture 11: Introduction to the Theory of the Firm

Production in the short run

Theory of the firm (1)

• Firm=producer=supplier=seller• How do firms decide how and how much to

produce in order to maximize profit?• Firm’s decision has two components: – Production—how to combine inputs to produce

outputs?– Cost – how do costs vary with output?

Theory of the firm (2)

• The firm’s decision will depend on: – Time frame: short-run versus long-run– Market structure: • Perfect competition • Imperfect competition • Monopoly

Parallels with consumer theoryConsumer Producer

Bundle of goods Input mix

Utility function Production function

Marginal utility Marginal product

Indifference curve Isoquant

MRS MRTS

Production Process or Function: The relationship that describes how inputs are combined to produce outputs

Prices and money do not appear here. Production is a

physical process

Categories of inputs or factors of production

• Labor– Workers– Management/entreprenuership

• Capital– Physical capital - machinery, equipment, buildings• Land is sometimes a separate input category, especially

for agriculture

– Materials - Inputs like energy, chemicals, plastic, and other materials

Categories of outputs or products

• Goods– Pizzas, cars, buildings, clothes, computers,

paintings• Services– Pizza delivery, medical exams, cleaning service,

income tax preparation, rock concert• Both goods and services are outputs of

production processes

In Class Assignment 1

• Name 3 inputs, at least 1 labor and 1 capital, required to produce a:– McDonald’s Happy Meal – Bicycle – Divorce decree– Vikings game – University of Minnesota graduate – BBQ in your back yard

In Class Assignment 1 – some examples of inputs

• Name 3 inputs, at least 1 labor and at least 1 capital, required to produce a:– McDonalds Happy Meal (ingredients, equipment,

workers, building)– Bicycle (parts, workers, equipment, building)– Divorce (lawyers, judge, office supplies, buildings)– Vikings game (players, stadium, referees)– University of Minnesota graduate (buildings,

teachers, students)– BBQ in your back yard (backyard, food, grill)

In Class Assignment Follow Up

• Which inputs would you need more of to go from producing 1 to producing 10 units?

• McDonalds Happy Meal -- ingredients, equipment, workers (per hour), building

• bicycle -- parts, workers, equipment, building• Divorce (lawyers, judge, office supplies, buildings)• Vikings game –players, stadium, referees (if on

different days)• University of Minnesota graduate (buildings,

teachers, students)• BBQ in your back yard (backyard, food, grill)

Inputs that might change if production goes from 1 to 10 units

• Q = f (K, L) where Q is output; K is capital and L is labor

Production function

Q

L

K

Q1

Q2

Production surface = amount of Q produced with different combinations of K and L

Common functional forms for production functions

• Cobb Douglas : Q = K‐ 0.7L0.5

• Quadratic : Q= 10L– L2+6K–0.3K2

Example: Cobb Douglas

• Q = K0.7L0.5

– If K=10 and L=20, Q=10.7x 20.5= 22.4

L

K 5 10 15 20 25

5 6.9 9.8 11.9 22.0 15.4

10 11.2 15.8 19.4 22.4 25.1

15 14.9 21.1 25.8 29.8 33.3

20 18.2 25.7 31.5 36.4 40.7

25 22.4 30.1 36.9 42.6 47.6

Example: Cobb Douglas

• Q = K0.7L0.5

• When both inputs increase…

L

K 5 10 15 20 25

5 6.9 9.8 11.9 22.0 15.4

10 11.2 15.8 19.4 22.4 25.1

15 14.9 21.1 25.8 29.8 33.3

20 18.2 25.7 31.5 36.4 40.7

25 22.4 30.1 36.9 42.6 47.6

Example: Cobb Douglas

• Q = K0.7L0.5

• When only one input increases…

L

K 5 10 15 20 25

5 6.9 9.8 11.9 22.0 15.4

10 11.2 15.8 19.4 22.4 25.1

15 14.9 21.1 25.8 29.8 33.3

20 18.2 25.7 31.5 36.4 40.7

25 22.4 30.1 36.9 42.6 47.6

15.8 -11.2 =4.6

25.1-22.4 =2.7

• Law of diminishing returns: if other inputs are fixed, the increase in output from an increase in the variable input must eventually decline.

Law of diminishing returns• Q = K0.7L0.5

Change in Q when L goes from

K 5 to 10 10 to 15 15 to 20 20 to 25

5 2.9 2.2 1.8 1.610 4.6 3.6 3.0 2.715 6.2 4.7 4.0 3.520 7.5 5.8 4.9 4.325 7.7 6.8 5.7 5.0

Example: Quadratic• Q= 10L– L2+6K–0.3K2

L

K 3 6 9 12

3 36.3 39.3 24.3 -8.7

6 46.2 49.2 34.2 1.2

9 50.7 53.7 38.7 5.7

12 49.8 52.8 37.8 4.8

Example: Quadratic• Q= 10L– L2+6K–0.3K2

L

K 3 6 9 12

3 36.3 39.3 24.3 -8.7

6 46.2 49.2 34.2 1.2

9 50.7 53.7 38.7 5.7

12 49.8 52.8 37.8 4.8

Example: Quadratic• Q= 10L– L2+6K–0.3K2

L

K 3 6 9 12

3 36.3 39.3 24.3 -8.7

6 46.2 49.2 34.2 1.2

9 50.7 53.7 38.7 5.7

12 49.8 52.8 37.8 4.8

Question: Why might total output decline when more inputs are added?

Typical production function with one input

Production technology• “Production technology” describes the

maximum quantity of output a firm can produce from a given quantities of inputs.

Production function with 1 input

Production technology

• Example: There are two restaurants selling identical sandwiches and pizzas. Firm 1 uses a conventional oven while firm 2 uses a “improved” oven. Their production functions are: – Firm 1: Q1 = 50K.5L.5

– Firm 2: Q2=100K.5L.5 – For the same K and L, Firm 2 will produce more Q

Technical change

• Technical change: an advance in technology that allows more output to be produced with the same level of inputs. Examples: – Ovens that cook faster – Higher-yielding seed varieties – Faster, smaller computers

The Effect of Technological Progress in Food Production

(Q= food production, L = labor)

Production in the short and long run

• Refers to the time required to change inputs, holding technology constant– Not the same as technical change

• Long run: the shortest period of time required to alter the amounts of all inputs used in a production process– Defined by the input that takes longest to change

• Short run: the longest period of time during which at least one of the inputs used in a production process cannot be varied• If the long run is 5 years, the short run is less than 5

years

Fixed and variable inputs

• Variable input: an input that can be varied in the short run

• Fixed input: an input that cannot vary in the short run

• Short and long run, and fixed and variable inputs vary for different products and producers

Short and Long Run Production with 2 inputs

Short run < # of units (hours, days,

weeks, years)

Long run > # of units

(hours, days, weeks, years)

Input 1 Variable Variable

Input 2 Fixed Variable

In Class assignment 2: Fill in the following table for: 1) McDonald’s Happy Meal and a University of Minnesota

graduate

Short run < # of units (hours, days,

weeks, years)

Long run > # of units

(hours, days, weeks, years)

Input 1 Variable Variable

Input 2 Fixed Variable

In Class Answer1) McDonald’s Happy Meal

Short run < 1 year (hours,

days, weeks, years)

Long run > 1 year

(hours, days, weeks, years)

Ingredients (lbs/day) or workers (per hour) Variable Variable

Restaurant Fixed Variable

Fill in the following table for: University of Minnesota graduate

Short run < 2 years (hours,

days, weeks, years)

Long run > 2 years

(hours, days, weeks, years)

Teachers (per semester) Variable Variable

Classrooms Fixed Variable

Short-run (SR) production

• Production with at least one fixed input• Q= f(K , L) where Q is total output, K is the fixed input, and L is

variable input• In SR, firm decides how much L to use given K. • Two key measures that firms can use to make decisions about

how much L to use are:

– Average product of labor: output per unit of labor• APL = Q/L

– Marginal product of labor: the additional output produced from one addition unit of labor• MPL = ∂Q/∂L

Example-calculating AP and MP at a point

• From previous example of Q = K0.7L0.5

– If K =10 and L=20, Q=10.7x 20.5= 22.4

• What are APL and MPL at that point?

• APL = Q/L– Plug in values of K and L to get 22.4/20 = 1.12

• MPL= ∂Q/∂L = .5K.7L -.5 – Plug in values for K and L: (.5)(10.7 )(20-.5 )= (.5)(5)(.22)

= .55

• Q = K0.7L0.5

– If K =10 and L=20, Q=10.7x 20.5= 22.4

• What are APL and MPL at that point?

• APL = Q/L= 22.4/20 = 1.12

• MPL= ∂Q/∂L = .5K.7L -.5 = (.5)(5)(.22) = .56

If L increases, will the APL go up or down?

It will go down because if each additional unit is contributing less than the average (.56 < 1.12) , the average has to go down

Example- Calculating AP and MP in short run when K is fixed

• Q = K0.7L0.5

• If K is fixed at 10 and L is variable, what are APL and MPL?– APL = Q/L= (10.7L .5)/L = 5L.5/L

– MPL= ∂Q/∂L = .5K.7L -.5 = (.5)(5) L -.5 = 2.5L -.5

If L increases, will the APL go up or down?

It depends…

In class # 3 – Graph Q on one graph and MPL and APL on another, on the hand outL (person

hours) Q (meals) MP L AP L

0 0

1 2 6 2.00

2 14 12 7.00

3 28 14 9.33

4 43 15 10.75

5 59 16 11.80

6 72 13 12.00

7 80 8 11.43

8 80 0 10.00

9 72 -8 8.00

Relationship between MP and AP curves

• When the marginal product curve lies above the average product curve, the average product curve must be rising

• When the marginal product curve lies below the average product curve, the average product curve must be falling.

• The two curves intersect at the maximum value of the average product curve.

Application of average v marginal: How should the police department allocate

officers to maximize arrests per hour? Number

of police

West Philadelphia(Arrests per hour)

City Center(Arrests per hour)

TP AP MP TP AP MP

0 0 0 0 0

100 40 40 40 45 45 45

200 80 40 40 80 40 35

300 120 40 40 105 35 25

400 160 40 40 120 30 15

500 200 40 40 125 25 5

They should send 400 to West Philadelphia and 100 to City Center. Total arrests: 160+45+205Number

of police

West Philadelphia(Arrests per hour)

City Center(Arrests per hour)

TP AP MP TP AP MP

0 0 0 0 0

100 40 40 40 45 45 45

200 80 40 40 80 40 35

300 120 40 40 105 35 25

400 160 40 40 120 30 15

500 200 40 40 125 25 5