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Chapter 6

Production

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Chapter 6 Slide 2

Topics to be Discussed

The Technology of Production

Isoquants

Production with One Variable Input

(Labor)

Production with Two Variable Inputs

Returns to Scale

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Chapter 6 Slide 3

Introduction

Our focus is the supply side.

The theory of the firm will address:

How a firm makes cost-minimizingproduction decisions

How cost varies with output

Characteristics of market supply

Issues of business regulation

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Chapter 6 Slide 4


The Production Process

Combining inputs or factors of production

to achieve an output

Categories of Inputs (factors ofproduction)

Labor

Materials

Capital

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Chapter 6 Slide 5


Production Function:

Indicates the highest output that a firm can

produce for every specified combination ofinputs given the state of technology.

Shows what is technically feasible when

the firm operates efficiently.

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Chapter 6 Slide 6


The production function for two inputs:

Q = F(K,L)

Q = Output, K = Capital, L = Labor

For a given technology

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Isoquants

Assumptions

Food producer has two inputs

Labor (L) & Capital (K)

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Isoquants

Observations:

1) For any level of K, output increases

with more L.

2) For any level of L, output increases

with more K.

3) Various combinations of inputs

produce the same output.

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Isoquants

Isoquants

Curves showing all possible combinations

of inputs that yield the same output

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Production Function for Food

1 20 40 55 65 75

2 40 60 75 85 90

3 55 75 90 100 105

4 65 85 100 110 115

5 75 90 105 115 120

Capital Input 1 2 3 4 5

Labor Input

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Production with Two Variable Inputs (L,K)

Labor per year

1

2

3

4

1 2 3 4 5

5

Q1=55

The isoquants are derived

from the productionfunction for output of

of 55, 75, and 90.A

D

B

Q2=75Q3=90

C

ECapitalper year The Isoquant Map

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Chapter 6 Slide 12

Isoquants

The isoquants emphasize how different

input combinations can be used to

produce the same output.

This information allows the producer to

respond efficiently to changes in themarkets for inputs.

Input Flexibility

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Chapter 6 Slide 13

Isoquants

Short-run:

Period of time in which quantities of one ormore production factors cannot be

changed.

These inputs are called fixed inputs.

The Short Run versus the Long Run

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Chapter 6 Slide 14

Isoquants

Long-run

Amount of time needed to make allproduction inputs variable.

The Short Run versus the Long Run

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Chapter 6 Slide 15

Amount Amount Total Average Marginal

of Labor (L ) of Capital (K) Output (Q) Product Product

Production withOne Variable Input (Labor)

0 10 0 --- ---

1 10 10 10 10

2 10 30 15 20

3 10 60 20 30

4 10 80 20 20

5 10 95 19 15

6 10 108 18 13

7 10 112 16 4

8 10 112 14 0

9 10 108 12 -4

10 10 100 10 -8

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Chapter 6 Slide 16

Observations:

1) With additional workers, output (Q)

increases, reaches a maximum, andthen decreases.


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Chapter 6 Slide 17

Observations:

2) The average product of labor (AP),

or output per worker, increases andthen decreases.

LQ

InputLaborOutputAP


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Chapter 6 Slide 18

Observations:

3) The marginal product of labor (MP),

or output of the additional worker,increases rapidly initially and then

decreases and becomes negative..

L

Q

InputLabor

OutputMPL


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Chapter 6 Slide 19

Total Product

A: slope of tangent = MP (20)

B: slope of OB = AP (20)

C: slope of OC= MP & AP

Labor per Month

Outputper

Month

60

112

0 2 3 4 5 6 7 8 9 101

A

B

C

D


P d ti ith

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Chapter 6 Slide 20

Average Product


8

10

20

Output

perMonth

0 2 3 4 5 6 7 9 101 Labor per Month

30

E

Marginal Product

Observations:

Left of E: MP > AP & AP is increasing

Right of E: MP < AP & AP is decreasing

E: MP = AP & AP is at its maximum

P d ti ith

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Chapter 6 Slide 21

Observations:

When MP = 0, TPis at its maximum

When MP > AP, APis increasing

When MP < AP, AP is decreasing

When MP = AP, APis at its maximum


P d ti ith

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Laborper Month

Outputper

Month

60

112

0 2 3 4 5 6 7 8 9 101

A

B

C

D

8

10

20E

0 2 3 4 5 6 7 9 101

30

Outputper

Month

Laborper Month

AP =slope of line from origin to a point on TP, lines b, & c .MP =slope of a tangent to any point on the TPline, lines a & c.

P d ti ith

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Chapter 6 Slide 23

As the use of an input increases in

equal increments, a point will bereached at which the resulting additions

to output decreases (i.e. MPdeclines).


The Law of Diminishing Marginal Returns

P d ti ith

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Chapter 6 Slide 24

When the labor input is small, MP

increases due to specialization.

When the labor input is large, MP

decreases due to inefficiencies.



P d ti ith

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Chapter 6 Slide 25

Can be used for long-run decisions to

evaluate the trade-offs of different plantconfigurations

Assumes the quality of the variable

input is constant



P d ti ith

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Chapter 6 Slide 26

Explains a declining MP, not necessarily

a negative oneAssumes a constant technology



The Effect of

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Chapter 6 Slide 27

The Effect ofTechnological Improvement

Labor pertime period

Outputpertime

period

50

100

0 2 3 4 5 6 7 8 9 101

A

O1

C

O3

O2

B

Labor productivitycan increase if thereare improvements in

technology, even thoughany given production

process exhibitsdiminishing returns to

labor.

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Chapter 6 Slide 28

Malthus predicted mass hunger and

starvation as diminishing returns limited

agricultural output and the population

continued to grow.

Why did Malthus prediction fail?

Malthus and the Food Crisis

Index of World Food

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Chapter 6 Slide 29

Index of World FoodConsumption Per Capita

1948-1952 100

1960 115

1970 123

1980 128

1990 137

1995 135

1998 140

Year Index

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Chapter 6 Slide 30


The data show that production

increases have exceeded population

growth.

Malthus did not take into consideration

the potential impact of technology which

has allowed the supply of food to growfaster than demand.

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Chapter 6 Slide 31


Technology has created surpluses and

driven the price down.

Question

If food surpluses exist, why is there

hunger?

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Chapter 6 Slide 32


Answer

The cost of distributing food from

productive regions to unproductive regions

and the low income levels of the non-

productive regions.

Production with

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Chapter 6 Slide 33

Labor Productivity

InputLaborTotal

OutputTotaltyProductiviAverage


Production with

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Chapter 6 Slide 34

Labor Productivity and the Standard of

Living

Consumption can increase only ifproductivity increases.

Determinants of Productivity

Stock of capitalTechnological change


Labor Productivity in

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Chapter 6 Slide 35

Labor Productivity inDeveloped Countries

1960-1973 4.75 4.04 8.30 2.89 2.36

1974-1986 2.10 1.85 2.50 1.69 0.71

1987-1997 1.48 2.00 1.94 1.02 1.09

United United

France Germany Japan Kingdom States

Annual Rate of Growth of Labor Productivity (%)

$54,507 $55,644 $46,048 $42,630 $60,915

Output per Employed Person (1997)

Production with

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Chapter 6 Slide 36

Trends in Productivity

1) U.S. productivity is growing at a

slower rate than other countries.

2) Productivity growth in developed

countries has been decreasing.


Production with

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Chapter 6 Slide 37

Explanations for Productivity GrowthSlowdown

1) Growth in the stock of capital is theprimary determinant of the growth inproductivity.


Production with

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Chapter 6 Slide 38

Explanations for Productivity GrowthSlowdown

2) Rate of capital accumulation in theU.S. was slower than otherdeveloped countries because theothers were rebuilding after WWII.


Production with

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Chapter 6 Slide 39

Explanations for Productivity Growth

Slowdown

3) Depletion of natural resources

4) Environment regulations


Production with

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Chapter 6 Slide 40

Observation

U.S. productivity has increased in recent

years

What Do You Think?

Is it a short-term aberration or a new long-run trend?


Production with

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Chapter 6 Slide 41

Production withTwo Variable Inputs

There is a relationship between

production and productivity.

Long-run production K& L are variable.

Isoquants analyze and compare the

different combinations ofK & L and

output

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Chapter 6 Slide 42

The Shape of Isoquants

Labor per year

1

2

3

4

1 2 3 4 5

5

In the long run both

labor and capital arevariable and both

experience diminishingreturns.

Q1=55

Q2=75Q3=90

Capitalper year

A

D

B C

E

Production with

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Chapter 6 Slide 43

Reading the Isoquant Model

1) Assume capital is 3 and laborincreases from 0 to 1 to 2 to 3.

Notice output increases at a decreasing

rate (55, 20, 15) illustrating diminishingreturns from labor in the short-run and

long-run.


Diminishing Marginal Rate of Substitution

Production with

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Chapter 6 Slide 44

Reading the Isoquant Model

2) Assume labor is 3 and capitalincreases from 0 to 1 to 2 to 3.

Output also increases at a decreasing

rate (55, 20, 15) due to diminishingreturns from capital.

Diminishing Marginal Rate of Substitution


Production with

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Chapter 6 Slide 45

Substituting Among Inputs

Managers want to determine what

combination if inputs to use.

They must deal with the trade-off between

inputs.


Production with

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Chapter 6 Slide 46


The slope of each isoquant gives the trade-

off between two inputs while keeping

output constant.


Production with

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Chapter 6 Slide 47


The marginal rate of technical substitution

equals:

inputlaborinangecapital/ChinChange-MRTS

)oflevelfixeda(for QLKMRTS


Marginal Rate of

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Chapter 6 Slide 48

Marginal Rate ofTechnical 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

2/3

1/3

Q1=55

Q2=75

Q3

=90

Production with

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Chapter 6 Slide 49

Observations:

1) Increasing labor in one unit

increments from 1 to 5 results in adecreasing MRTS from 1 to 1/2.

2) Diminishing MRTS occurs because

of diminishing returns and implies

isoquants are convex.


Production with

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Chapter 6 Slide 50

Observations:

3) MRTS and Marginal Productivity

The change in output from a change in

labor equals:

L))((MPL


Production with

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Chapter 6 Slide 51

Observations:


The change in output from a change in

capital equals:


K))((MPK

Production with

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Chapter 6 Slide 52

Observations:


If output is constant and labor is

increased, then:

0K))((MPL))((MP KL MRTSL)K/(-))(MP(MP KL


Isoquants When Inputs are

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Chapter 6 Slide 53

Isoquants When Inputs arePerfectly Substitutable

Laborper month

Capitalper

month

Q1 Q2 Q3

A

B

C

Production with

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Chapter 6 Slide 54

Observations when inputs are perfectly

substitutable:

1) The MRTS is constant at all points on

the isoquant.


Perfect Substitutes

Production with

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Chapter 6 Slide 55

Observations when inputs are perfectly

substitutable:

2) For a given output, any combination of

inputs can be chosen (A, B, or C) to

generate the same level of output(e.g. toll booths & musical

instruments)


Perfect Substitutes

Fixed-Proportions

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Chapter 6 Slide 56

ed opo t o sProduction Function

Laborper month

Capitalper

month

L 1

K1Q

1

Q2

Q3

A

B

C

Production with

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Chapter 6 Slide 57

Observations when inputs must be in a

fixed-proportion:

1) No substitution is possible.Each

output requires a specific amount of

each input (e.g. labor andjackhammers).

Fixed-Proportions Production Function

Two Variable Inputs

Production with

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Chapter 6 Slide 58

Observations when inputs must be in a

fixed-proportion:

2) To increase output requires more

labor and capital (i.e. moving fromA

to B to Cwhich is technicallyefficient).

Fixed-Proportions Production Function

Two Variable Inputs

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Chapter 6 Slide 59

A Production Function for Wheat

Farmers must choose between a capital

intensive or labor intensive technique of

production.

Isoquant Describing the

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Chapter 6 Slide 60

q gProduction of Wheat

Labor(hours per year)

Capital(machinehour per

year)

250 500 760 1000

40

80

120

100

90Output = 13,800 bushels

per year

A

B

10-K

260L

Point A is morecapital-intensive, and

Bis more labor-intensive.


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Chapter 6 Slide 61

Observations:

1) Operating atA:

L = 500 hours and K = 100machine hours.



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Chapter 6 Slide 62

Observations:

2) Operating at B

Increase L to 760 and decrease K to 90the MRTS < 1:

04.0)260/10(

LK-MRTS



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Chapter 6 Slide 63

Observations:

3) MRTS < 1, therefore the cost of labor

must be less than capital in order forthe farmer substitute labor for capital.

4) If labor is expensive, the farmer would

use more capital (e.g. U.S.).



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Chapter 6 Slide 64

Observations:

5) If labor is inexpensive, the farmer

would use more labor (e.g. India).


Returns to Scale

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Chapter 6 Slide 65

Returns to Scale

Measuring the relationship between the

scale (size) of a firm and output

1) Increasing returns to scale: outputmore than doubles when all inputs

are doubled

Larger output associated with lower cost (autos)

One firm is more efficient than many (utilities)

The isoquants get closer together

Returns to Scale

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Chapter 6 Slide 66

Returns to Scale

Labor (hours)

Capital(machine

hours)

10

20

30

Increasing Returns:

The isoquants move closer together

5 10

2

4

0

A

Returns to Scale

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Chapter 6 Slide 67

Returns to Scale



2) Constant returns to scale: outputdoubles when all inputs are doubled

Size does not affect productivity

May have a large number of producers

Isoquants are equidistant apart

Returns to Scale

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Chapter 6 Slide 68

Returns to Scale

Labor (hours)

Capital(machine

hours)

Constant Returns:Isoquants areequally spaced

10

20

30

155 10

2

4

0

A

6

Returns to Scale

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Chapter 6 Slide 69

Returns to Scale



3) Decreasing returns to scale: outputless than doubles when all inputs are

doubled

Decreasing efficiency with large sizeReduction of entrepreneurial abilities

Isoquants become farther apart

Returns to Scale

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Chapter 6 Slide 70

Returns to Scale

Labor (hours)

Capital(machine

hours)

Decreasing Returns:Isoquants get furtherapart

1020

30

5 10

2

4

0

A

Returns to Scale

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Chapter 6 Slide 71

in the Carpet Industry

The carpet industry has grown from a

small industry to a large industry with

some very large firms.

Returns to Scale

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Chapter 6 Slide 72


Question

Can the growth be explained by the

presence of economies to scale?

The U S Carpet Industry

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Carpet Shipments , 1996(Mil l ion s o f Dollars p er Year)

The U.S. Carpet Industry

1. Shaw Industries $3,202 6. World Carpets $475

2. Mohawk Industries 1,795 7. Burlington Industries 450

3. Beaulieu of America 1,006 8. Collins & Aikman 418

4. Interface Flooring 820 9. Masland Industries 380

5. Queen Carpet 775 10. Dixied Yarns 280

Returns to Scalei th C t I d t

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Chapter 6 Slide 74


Are there economies of scale?

Costs (percent of cost)

Capital -- 77%

Labor -- 23%


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Chapter 6 Slide 75


Large Manufacturers

Increased in machinery & labor

Doubling inputs has more than doubled

output

Economies of scale exist for large

producers


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Chapter 6 Slide 76


Small Manufacturers

Small increases in scale have little or no

impact on output

Proportional increases in inputs increase

output proportionally

Constant returns to scale for smallproducers

Summary

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Chapter 6 Slide 77

Summary

Aproduction function describes the

maximum output a firm can produce for

each specified combination of inputs.

An isoquantis a curve that shows all

combinations of inputs that yield a given

level of output.

Summary

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Chapter 6 Slide 78

Summary

Average product of labormeasures the

productivity of the average worker,

whereas marginal product of labor

measures the productivity of the lastworker added.

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Summary

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Chapter 6 Slide 80

Summary

Isoquants always slope downward

because the marginal product of all

inputs is positive.

The standard of living that a country can

attain for its citizens is closely related to

its level of productivity.

Summary

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Chapter 6 Slide 81

Summary

In long-run analysis, we tend to focus

on the firms choice of its scale or size

of operation.

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End of Chapter 6

Production

chap6-ev

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