Theory of Producer 08-10-2011 With Answer

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Theory of Producer1. Total Product Curve

2. Deriving Isoquant curves from 3Ddiagram

3. Producer Choice in Long Run



Case Study• Prior to the early 1990s, the Walt Disney

Company dominated the market for

animated films. Disney’s films were

produced using hundreds of animators

drawing most of the film by hand. Each film

may contain as many as 170,000 individual

drawings.

• In 1994, The Lion King was produced at cost

$50 million only but earned more than $1

billion in profit. Then Disney and other film

makers produced more animated film and

the demand for animators and the salaries

for them increase sharply.



• In 1996, Pixar Animation released Toy

Story, which is the first animated film

that using computer to produce. Withmore development in the computer

software, the cost of producing

animated film decreases a lot and more

films like Toy Story 2 and The Incredible

were produced by computer instead of

animator.

What is reason changing the trend

of animated movies?



1. Total Product Curve

•

The production function can be expressed byQ = A*F(L,K)

• The maximum amount of output that can be

produced with K units of capital and L units of labor.



K L ΔL Q APL = Q/L APK = Q/K MPL = dQ/dL

(Fixed Input) (Variable

Input)

(Change in

Labor)

(Output or

Total product)

Average

Product per L

Average

Productper K

Marginal

Product per L

2 0 0

2 1 1 76 76 38 76

2 2 1 248 124 124 172

2 3 1 492 164 246 244

2 4 1 784 196 392 292

2 5 1 1100 220 550 316

2 6 1 1416 236 708 316

2 7 1 1708 244 854 292

2 8 1 1952 244 976 244

2 9 1 2124 236 1062 1722 10 1 2200 220 1100 76

2 11 1 2156 196 1078 -44



• If we hold A and K constant, the total product curve

of Labor is:

L

TPL

Increasing

Marginal

Returns Diminishing

Marginal

Returns



Marginal Product Curve

• Marginal Product on an Input: change in total

output by adding one more unit of input – Marginal Product of Labor: MPL = dQ/dL

• Measures the output produced by one additional worker.

• Slope of the short-run production function (with respect to

labor). – Marginal Product of Capital: MPK = dQ/dK

• Measures the output produced by one additional capital.

• When capital is allowed to vary in the short run, MPK is the

slope of the production function (with respect to capital).



Increasing

Marginal

Returns

Increasing

Marginal

Returns

Diminishing

Marginal

Returns

Diminishing

Marginal

Returns

Law of diminishing marginal product – when more and more variable inputs

are added into production in short run, the marginal product will rise at first

but will eventually fall.



Average Product (AP) Curves• Average Product of an Input: measure of output

produced per unit of input. – Average Product of Labor: APL = Q/L.

• On average, how many outputs can be produced by onelabor

–

Average Product of Capital: APK = Q/K.• On average, how many outputs can be produced by one

capital



APL = 150/3=167

167

Turning pt of APL

Turning pt of APL



Q

L

Q=F(K,L)

Increasing

Marginal

Returns

Diminishing

Marginal

Returns

Negative

Marginal

Returns

MP

AP

Increasing, Diminishing and

Negative Marginal Returns

When AP is rising, MP mustbe greater than AP. When

AP is decreasing, MP must

be smaller than AP. Why?



2. Deriving Isoquant curves from 3D diagram

• According to our production function, we can derive the TP

curve for L and K:

TPL

L

TPK

K

K = 1

K = 2

K = 3

L =1

L = 2

L = 3



The 3D production diagram

XY

U = f(X,Y)

01

2

3

1

2

3

Isoquant curves shows any

combination of L and K that yields

the same level of output.



Q 1

Q 2

Q 3

K

L

Increasing

Output

• Marginal Rate of Technical Substitution

(MRTS) – Slope of Isoquant curves• The rate at which two inputs are

substituted while maintaining the same

output level.

L

KL

K

MPdK

MRTSdL MP

• In general English, it means, how many K

can be saved from hiring one more unit of

L.

The Isoquant curves



Isocost Curves

• The combinations of inputs

that produce a given level of output at the same cost:

wL + rK = C

• Rearranging,

K= (1/r)C - (w/r)L

• For given input prices, isocosts

farther from the origin are

associated with higher costs.

K

LC1

C 1/r

C 1/w C

0

C 0/w

C 0/r

New Isocost Line

associated with higher costs (C 0 < C 1 ).

• The slope of Isocost is the

relative price of L, w/r.

• In general English, it means, inthe market, if you hire one more

unit of Labor, how many K it

costs



• Changes in input prices change the slope of

the isocost line.

L

KNew Isocost Line for

a decrease in the

wage (price of labor:

w 0 > w 1 ).

C /w 0 C /w 1

C /r



Q

L

K

Producer

equilibriumC/r

C/w

Cost Minimization• Producer equilibrium

represents a point that thetotal cost of production is

minimized given that our

output is produced at a target

level.

L1

K1• When the amount of K saved

from increasing 1 unit of L is

equal to the cost (in terms of K)

in hiring 1 unit of L, it reaches

producer equilibrium.



Q

L

K

C/r

C/w

Cost Minimization

Cost is not minimized at

this point

By this cost level, we

cannot produce outputlevel Q.



Cost Minimization• When MRTS = Relative price of labor, cost is

minimized given output at a specified level.

L

KL

K

MP w MRTS

MP r

• You can also say, when the amount of capital

saved is equal to the price of labor (in terms of

capital) in the market, cost is minimized.



Exercise

• Draw an isoquant-isocost line graph to illustrate

the following situation: Johnson can rentphotocopy machines for $200 per day and hire

workers for $100 per day. Currently, she is using

5 machines and 10 workers to produce 20,000copies per day and has total costs of $2000.

Johnson’s marginal rate of technical substitution

(MRTS) = -1. Explain why this means that she isnot minimizing costs and what she could do to

minimize costs.



Price Increase for On-campus Catering Outlets

Dear students and colleagues,

We are writing to give you advance notice that menu prices at the on-campus catering outlets will be increased from 20 July 2011. The

affected outlets include Student Canteen, City Chinese Restaurant

(8/F), City Top (9/F), Garden Cafe and Coffee Cart.

The University approved the request from the on-campus caterers to

raise menu prices after carefully consideration of the following factors:

• Continue rising food costs;

• Appreciation of Renminbi; and

• Rising labor and other operating costs.

Use Isoquant-Isocost analysis, illustrate the effect of rising labor cost

on the input combination of student canteen.



Exercise1. You are an efficiency expert hired by a manufacturing firm that

uses K and L as inputs. The firm produces and sells a givenoutput. If w = $40, r = $100, MPL = 4, and MPK = 40 the firm:a. Is cost minimizingb. Should use less L and more K to cost minimizec. Should use more K and less L to cost minimized. Is profit maximizing but not cost minimizing.

2. Which of the following conditions is true when a producerminimizes the cost of producing a given level of output?a. The MRTS is equal to the ratio of input pricesb. The marginal product per dollar spent on all inputs are equalc. The marginal products of all inputs are equald. The MRTS is equal to the ratio of input prices and the

marginal product per dollar spent on all inputs is equal3. Isoquants are normally drawn with a convex shape because:

a. Inputs are perfectly substitutableb. Inputs are perfectly complementaryc. Inputs are not perfectly substitutable

d. Inputs are not perfectly complementary



Exercise4. Given the linear production function Q = 10K + 5L, if

Q = 10,000 and K = 500, how much labor is utilized?

a. 600 unitsb. 800 unitsc. 500 unitsd. 1000 units

5. Which of the following sets of economic data isminimizing the cost of producing a given level of output?

a. MPL = 20, MPK = 40, w = $16, r = $32 b. MPL = 20, MPK = 40, w = $32, r = $16c. MPL = 40, MPK = 20, w = $16, r = $32d. MPL = 40, MPK = 40, w = $16, r = $32

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Theory of Producer 08-10-2011 With Answer