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Theory of FirmProduction

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Chapter 6 Slide 2

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Slide 3

Lecture Plan, theory of firm

1.Production function

2.

3.Cost of production

4.

5.Revenue and Profit

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The Technology of Production

n Production Function:l Indicates the highest output that a firm

can produce for every specifiedcombination of inputs given the stateof technology.

l Shows what is technically feasible when

the firm operates efficiently .

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The Technology of Production

n The Production Processl Combining inputs or factors of

production to achieve an output or desired level

n Categories of Inputs (factors of production)

l Labor l Materials/rawl Capital

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Firm’s Costs and Production Decision

n A firm chooses:l What quantity of the good to produce,l The price of the good (sometimes...).

n Firm’s decision depends on:l Costs of production.l

The degree of competition in the market(if there are more sellers, morecompetitive).

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Role of a Firm

n The firm is an economic institution thattransforms factors of production intoconsumer goods – it:

l Organizes factors of production.l Produces goods and services.l Sells produced goods and services.

l Objective is to Maximize profit

ProfitProfit = Total= Total RR evenue - Totalevenue - Total CC ostost

l

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The Production Process

A firm chooses from all

possible productiontechniquesAll inputs are variable

The production process can be divided into the long runand the short run, depends on availability of inputs.

The terms long run and short run do not necessarily refer tospecific periods of time, but to the flexibility the firm has inchanging the level of output

Short run Long runA firm is constrained in regard

to what productiondecisions it can makeSome inputs are fixed

1

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nRailways – short run –’easy’ to increaselabour, long lead timesfor new rolling stock – 5 years?

n Supermarkets – short run – can buy new

shelving, hire staff, etc but opening of newstores takes several yearsn Local Builder – short run buys new tools,

hires assistant; long run – purchasing a new

van – a coupleof months?

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The Technology of Production

n The production function for one input:Q = F(L)| all other inputs are fixed

nThe production function for two inputs:

Q = F(K,L)

Q = Output , K = Capital, L = Labor

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Slide 11

Production function with one input

Q = F(L)| all other inputs are fixedProduction depends upon labor only.

It’s a Short Run Process

Subject to Law of diminishing MarginalProduct:

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Law of Diminishing Marginalproductivity

Number of workers Total output Marginalproduct Averageproduct

Increasing marginalreturns

Diminishingmarginal returns

Diminishingabsolute returns

4

6765310

25

1234

5

67

89

10

045

5.75.85.6

5.24.6

4.03.32.5

—4

10

172328

3132

323025

0

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Outp ut

Diminishi ng marginal

returns

Diminishi ng absolute

returns 32 30 28 26 24

22 20 18 16 14 12 10 8

6 4 2

01 2 3 4 5 6 7 8 9 10

Increasi ng marginal

returns

Number of workers

TP

Outp ut

p er

worker

1 2 3 4 5 6 7 8 9 10 Number of workers

7

6

5

4

3

2

1

0

MP

Diminishi ng marginal

returns

Diminishi ng absolute

returns

( )a Total product ( )b Marginal and average product

AP

The Law of Diminishing Marginal Productivity

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Graphing a ProductionFunction

Q

Increasingmarginal

productivity

Diminishingmarginal

productivity

DiminishingAbsolute

productivity

Number of

workers

TPA production function is the relationship between

32

26

20

14

821 2 3 4 5 6 7 8

9 10

12-14

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Graphing Marginal andAverage Productivity

Increasingmarginal

productivity

Diminishingmarginal

productivity

DiminishingAbsolute

productivity

Number of workers

AP

MP

QMarginal productivity first increThen m arginal productivity declEventually marginal productivity is

8

6

4

2

0

-2

-4-6

1 2 3 4 5 6 7 89 10

12-15

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Law of Diminishing Marginal Productivity # of workers

TotalOutput

MarginalProduct

AverageProduct0 0 4

6765

310-2-5

---1 4 42 10 53 17 5.74 23 5.8

5 28 5.66 31 5.27 32 4.68 32 4.0

9 30 3.310 25 2.5

Law of diminishingmarginal productivity

states as more of avariable input is added to

an existing fixed input,after some point the

additional output from theadditional input will fall

Increasingmarginal

productivity

Diminishingmarginal

productivity

DiminishingAbsolute

productivity 12-16

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Slide 17

n When the labor input is small, MP increases dueto specialization.

n When the labor input is large, MP decreases dueto inefficiencies.

n Can be used for long-run decisions to evaluatethe trade-offs of different plant configurations

n Assumes the quality of the variable input isconstant

n

The Law of Diminishing Marginal ReturnsThe Law of Diminishing Marginal Returns

Production withOne Variable Input (Labor)

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Slide 19

Role of Engineers !!!!!

How could we enhance the productionand profit if we have one input factor?

h ff f

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Slide 20

The Effect of Technological Improvement

Labor per time period

Outputper time

period

50

100

0 2 3 4 5 6 7 8 9 101

A

O 1

C

O 3

O 2

B

Labor productivitycan increase if thereare improvements in

technology, even thoughany given production

process exhibitsdiminishing returns to

labor.

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Slide 21

Production with two variables

Examples:l Cobb-Douglas Production Functionl Linear Production Function

l Leontief production functionl The Constant Elasticity of Substitution

(CES) Production Function

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Slide 22

Production Function: for Food ( Q=F(l,K)

1 20 40 55 65 75

2 40 60 75 85 90

3 55 75 90 100 105

4 65 85 100 110 1155 75 90 105 115 120

Capital Input 1 2 3 4 5Labor Input

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Slide 23

Isoquants

n Isoquantsl In Latin, "iso" means equal and "quant"

refers to quantity. This translates to"equal quantity". The isoquant curvehelps firms to adjust their inputs tomaximize output and profits.

l Curves showing all possible combinationsof inputs that yield the same output

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Slide 24

Production with Two Variable Inputs ( L,K )

Labor per year

1

2

3

4

1 2 3 4 5

5

Q 1 = 55

The isoquants are derivedfrom the production

function for output of of 55, 75, and 90.A

D

B

Q 2 = 75Q 3 = 90

C

E Capitalper year The Isoquant MapThe Isoquant Map

P d i i h

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Slide 25

Production withTwo Variable Inputs

n Long-run production K& L are variable.

n Isoquants analyze and compare thedifferent combinations of K & L andoutput

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Slide 26

The Shape of Isoquants

Labor per year

1

2

3

4

1 2 3 4 5

5

In the long run bothlabor and capital are

variable and bothexperience diminishing

returns.

Q 1 = 55

Q 2 = 75Q 3 = 90

Capitalper year

A

D

B C

E

P d ti ith

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Slide 27

n Substituting Among Inputsl The slope of each isoquant gives the

trade-off between two inputs whilekeeping output constant.

Production withTwo Variable Inputs

P d ti ith

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Slide 28

n Substituting Among Inputsl The marginal rate of technical substitution

equals:

inputlabor inangecapital/ChinChange - MRTS =

LK MRTS ∆∆−=

Production withTwo Variable Inputs

M i l R f

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Slide 29

Marginal Rate of Technical Substitution

Labor per month

1

2

3

4

1 2 3 4 5

5Capitalper year

Isoquants are downwardsloping and convex

like indifferencecurves.

1

1

1

1

2

1

2/31/3

Q 1 =55

Q 2 =75

Q 3

=90

P d ti ith

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Slide 30

u If output is constant and labor isincreased, then:

0 K))( (MP L))( (MP K L =∆+∆MRTS L)K/ ( - ))/(MP (MP K L =∆∆=

Production withTwo Variable Inputs

I t Wh I t

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Slide 31

Isoquants When Inputs arePerfectly Substitutable

Labor per month

Capitalper

month

Q 1 Q 2 Q 3

A

B

C

Fi d P i

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Slide 32

Fixed-ProportionsProduction Function

Labor per month

Capitalper

month

L1

K 1 Q 1

Q 2

Q 3

A

B

C

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Slide 33

A Production Function for Wheat

n Farmers must choose between a capitalintensive or labor intensive techniqueof production.

I t D ibi th

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Slide 34

Isoquant Describing theProduction of Wheat

Labor (hours per year)

Capital(machinehour per

year)

250 500 760 1000

40

80

120

10090

Output = 13,800 bushelsper year

AB

10- K =∆

260 L =∆

Point A is morecapital-intensive, and

B is more labor-intensive.

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Slide 35

Returns to Scale

n Measuring the relationship between thescale (size) of a firm and output

1) Increasing returns to scale :output more than doubles when allinputs are doubled

u Larger output associated with lower cost

(autos)u One firm is more efficient than many

(utilities)u The isoquants get closer together

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Slide 36

Returns to Scale

Labor (hours)

Capital(machine

hours)

10

20

30

Increasing Returns:The isoquants move closer together

5 10

2

4

0

A

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Slide 37

Returns to Scale

n Measuring the relationship between thescale (size) of a firm and output

2) Constant returns to scale :output doubles when all inputs aredoubled

u Size does not affect productivityu May have a large number of

producersu Isoquants are equidistant apart

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Slide 38

Returns to Scale

Labor (hours)

Capital(machine

hours)

Constant Returns:Isoquants are

equallyspaced

10

20

30

155 10

2

4

0

A

6

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Returns to Scale

n Measuring the relationship between thescale (size) of a firm and output

3) Decreasing returns to scale :output less than doubles when allinputs are doubled

u Decreasing efficiency with largesize

u Reduction of entrepreneurialabilities