THE DISCOVERY OF PRODUCTION AND ITS TECHNOLOGY CHAPTER 8

THE DISCOVERY OF PRODUCTION

AND ITS TECHNOLOGY

CHAPTER 8

DISCOVERING PRODUCTION

• Primitive society• Fruit and land• Accidental discovery: jam

• Opportunity cost• Cost of engaging in any activity• Opportunity forgone - particular activity

• Normal profit• Just sufficient to recover opportunity cost

• Extra-normal profit• Return above normal profit

2

PRODUCTION FUNCTION AND TECHNOLOGY

• Technology • Set of technological constraints

• On production• Combine inputs into outputs

3


• No free lunch assumption• Production process

• Need inputs to produce outputs

• Non reversibility assumption• Cannot run a production process in reverse

• Free disposability assumption• Combination of inputs

• Certain output• Or strictly less output

4


• Additivity assumption• Produce output x

• One combination of inputs

• Produce output y• Another combination of inputs

• Feasible: produce x+y

5


• Divisibility assumption• Feasible input combination y• Then, λy – feasible input combination

• 0≤ λ ≤ 1

6


• Convexity assumption• Production activity: y

• Output: z• Particular amounts of inputs

• Production activity: w• Output: z• Different amounts of inputs

• Produce: at least z• Mix activities y (λ time) and w(1- λ time)

7


• Production function• Maximum amount of output• Given a certain level of inputs

• Output=f (input1, input2)

• Marginal product of input1

• the increase in output as a result of a marginal increase in input1 holding input2 constant

• diminishing

8

ISOQUANT

• Isoquant • Set of bundles

• Given production function• Produce same output• Most efficiently

ISOQUANT

10

All combinations of inputs along the same isoquant yield the same output.

Labor0

Capital

I100

II200

III

ISOQUANT

• Isoquants • Never cross each other• Farther from the origin greater outputs• Slope

• Marginal rate of technical substitution

11

MARGINAL RATE OF TECHNICAL SUBSTITUTION

12

The absolute value of the isoquant’s slope measures the rate at which one input can be substituted for the other while keeping the output level constant.

Labor (x1)0

Capital (x2)

4

7

α

β

3

9

2

11


• Marginal rate of technical substitution (MRTS)• Rate of substitution• One input for another• Constant output

13

THE PRODUCTION FUNCTION

14

The level of output is a function of the levels of capital and labor used.

Capital (x2)

21

Labor (x1)

0

3

6

WW

Output (y)

4

y1

y2


• Marginal product of input x2 at point α

• MRTS of x2 for x1 at point α

15

2)(

xy

12 xgiven xinput of use the in (changeoutput) in change

2

1

xyxy

2

1

xof product Marginal xof product Marginal

DESCRIBING TECHNOLOGIES

• Returns to scale – ratio of• Change in output• Proportionate change in all inputs

• Constant returns to scale• All inputs - increase by λ• Output - increases by λ

16

DESCRIBING TECHNOLOGIES

• Increasing returns to scale• All inputs - increase by λ• Output - increases by more than λ

• Decreasing returns to scale• All inputs - increase by λ• Output - increases by less than λ

• Elasticity of substitution• Substitute one input for another• Given level of output

17

RETURNS TO SCALE

18

Constant returns to scale. Doubling the levels of labor (from 3 to 6) and capital (from 2 to 4) also doubles the level of output (from 4 to 8)

Labor (x1)

0

Capital (x2)

4

6

2

12

1

3

4

CA 8

B

D

p1

p2

(a)

Increasing returns to scale. Doubling the levels of both inputs more than doubles the output level

Labor (x1)

0

Capital (x2)

6

2

12

1 4A 10

B p1

(b)

Decreasing returns to scale. Doubling the levels of both inputs less than doubles the output level

Labor (x1)

0

Capital (x2)

6

2

12

1 4A 6

B p1

(c)

TIME CONSTRAINTS

• Immediate run• Period of time• Cannot vary inputs

• Fixed factor of production• Cannot be adjusted

• Given period of time

• Variable factor of production• Can be adjusted

19

TIME CONSTRAINTS

• Short run• Time period• At least one factor of production – fixed

• Long run• Time period• All factors of production – variable

20

TIME CONSTRAINTS

• Long-run production function• All inputs – variable

• Short-run production function• Some inputs – variable

• Capital – fixed• Labor – variable

21

FIGURE 8.5

Short-run production function

22

With the level of capital fixed at x2, the output level is a function solely of the level of labor.

Capital (x2)Labor (x1)

0

C

B

x2

TIME CONSTRAINTS• Total product curve

• Amount of output• Add more and more units of variable input• Hold one input constant

• Output – as we add more variable input• First: increase at increasing rate• After a point: Increase at decreasing rate• Later: decrease

23

FIGURE 8.6

Short-run production function in labor-output space

24

The level of the fixed input, capital, is suppressed.

Labor0

Output

8

30

D

1615

G

10

E

1

A

2

8 14

12

121

+1+1

TIME CONSTRAINTS• Decreasing returns to factor

• Rate of output growth: decreasing• Increase one input• Other inputs – constant

• Marginal product curve• Marginal product

• Factor of production

25

FIGURE 8.7

Marginal product

26

The slope of the short-run production function measures the change in the output level resulting from the introduction of 1 additional unit of the variable input - labor.

Labor (x1)0

Marginal product

30101

12

e

d


• Cobb-Douglas production functionQ=AKαLβ

• A – positive constant• 0<α<1; 0<β<1• K – amount of capital• L – amount of labor• Q – output

27


• Returns to scale = (α+β)• For λ K and λL: Q’= A(λK)α(λL)β =λ α+β Q• If α+β=1

• Linearly homogeneous• Constant returns to scale Q=AKαL1-α

• If α+β>1 • Increasing returns to scale

• If α+β<1 • Decreasing returns to scale

28


• MRTS: dQ=0

• Elasticity of substitution

29

LK

dLdK

1

1)ln()/ln(

MRTSdLKd

KL


• Q=AKαLβ; α+β=1

30

1

1

;)1(

;

AkKQ

MPK

AkLQ

MPL

AkKQ

APKAkLQ

APL

LK

kLQ

q

:products Marginal

:products Average

; :Define


• Q=AKαLβ; α+β=1 • Share of capital in output: K∙MPK/Q=α• Share of labor in output: L∙MPL/Q=1-α• Elasticity of output

31

1LQ

LQ

KQ

KQ

QL

QK

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THE DISCOVERY OF PRODUCTION AND ITS TECHNOLOGY CHAPTER 8