This document discusses key concepts around production functions and firm behavior, including: 1) Production functions relate inputs like capital and labor to outputs. Marginal product is the change in output from an additional unit of input. Total and average product are also discussed. 2) Isoquant maps show the combinations of inputs that produce the same output level. The slope of the isoquant is the rate of technical substitution, which diminishes as more of one input is used. 3) Returns to scale describe how output changes when all inputs change proportionally. Constant, increasing, and decreasing returns to scale are defined. 4) Technological progress shifts the production function upward, allowing more output from fewer inputs.

1. Walter Nicholson
1
Amherst College
Christopher Snyder
Dartmouth College
PowerPoint Slide Presentation | Philip Heap, James Madison University
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

2. ©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
CHAPTER
2
6
Production

3. Chapter Preview
Ch. 6 • 3
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• We now want to turn to firm behavior, and answer three main
questions.
1. What happens to output as a firm increases the number of
input(s) it uses?
2. To what degree is a firm able to substitute one input for
another?
3. What happens to production as a result of technological
change?

4. Production Functions
Ch. 6 • 4
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• A firm is any organization that turns inputs into outputs.
• A production function is a mathematical relationship between
inputs and outputs.
– q = f( K, L, M, ...)
– q = f( K, L )

5. Marginal Product
Ch. 6 • 5
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Marginal product:
– The additional output that can be produced by adding one
more unit of some input, holding all other inputs constant.
• What happens to output as we add one more unit of one input
(labor) to a fixed amount of another input (capital).

6. T
otal Product and Marginal Product
Labor input
per week
Labor input
per week
Output
per week MPL
L* L*
As labor increases output
increases but at a diminishing
rate.
Ch. 6 • 6
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
So marginal product decreases
as labor increases.

7. Average Product
Ch. 6 • 7
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Average product is equal to total output divided by the number
of workers.
• Average product tells you how productive all your workers are on
average. It does not tell you how productive an extra worker is.
• Practical difficulty in applying the marginal product concept.

8. Isoquant Maps
Ch. 6 • 8
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• How can a firm combine different amounts of capital and labor to
produce output?
• Isoquant:
– A curve that shows the various combinations of inputs that
will produce the same (a particular) amount of output.
– How does this compare to an indifference curve?
• Isoquant map is a contour map of a firm’s production function.

9. Capital
per
week
K
A
A
B q = 10
K
B
Labor
per
week
L
B
LA
q=30
q=20
Ch. 6 • 9
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Isoquant Map

10. Rate of Technical Substitution
Ch. 6 • 10
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Marginal rate of technical substitution (RTS):
– The amount by which one input can be reduced when one
more unit of another input is added while holding output
constant.
• If you used one more worker how much less capital could you use
and still produce the same level of output.
• RTS = - slope of the isoquant
• RTS = - (change in capital) / (change in labor)

11. Capital
per
week
K
A
q = 10
K
B
Labor
per
week
L
B
LA
The amount of capital that can be given up
when one more unit of labor is employed
Ch. 6 • 11
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
gets smaller and smaller
Rate of Technical Substitution
At point A, the slope of the isoquant =
RTS = ΔK / ΔL
A
Along the isoquant. the slope gets flatter
and the RTS diminishes
ΔK
A
A
ΔL
At point B, the slope of the isoquant =
B
RTS = ΔK / ΔL
ΔKB
B ΔL

12. The RTSand Marginal Product
Ch. 6 • 12
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Why must the slope of the isoquant be negative or the RTS
positive?
– RTS = MP /MP
L K
– If RTS was < 0 either MP or the MP would also have to be < 0.
L K
– But then a firm would be paying for an input that reduced
output.
– Since no firm would do that MP’s > 0 and the RTS > 0.

13. The RTSand Marginal Product
Ch. 6 • 13
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Why does the slope of the isoquant get flatter or why does the
RTS diminish?
– The less (more) labor is used relative to capital, the more (less)
able labor is able to replace capital in production.
– As the firm uses more and more labor, the MP falls.
L
– Therefore, to maintain the same level of output, the firm
would only be able to give up smaller and smaller amounts of
capital.

14. Returns to Scale
Ch. 6 • 14
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• What would happen to production if a firm increased the number
of all inputs?
• Returns to scale:
– The rate at which output increases in response to a
proportional increases in all inputs.
• Two opposing effects at work as scale increases:
– Greater division of labor (specialization).
– Managerial inefficiencies and coordination problems

15. Returns to Scale
Ch. 6 • 15
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Constant returns to scale:
– If inputs increase by a factor of X, output increases by a factor
equal to X.

16. Capital
per
week
1
q = 10
Labor
per
week
q=20
q=30
2
1
4
3
2
3
4
q=40
Ch. 6 • 16
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Output increases at the same
proportion as inputs
Constant Returns to Scale

17. Returns to Scale
Ch. 6 • 17
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Constant returns to scale
– If inputs increase by a factor of X, output increases by a factor
equal to X.
• Increasing returns to scale
– If inputs increase by a factor of X, output increases by a factor
greater than X.

18. Capital
per
week
1
q = 10
Labor
per
week
q=20
q=30
2
1
4
3
2
3
4
Output increases at a rate
greater than the increase in
inputs
Ch. 6 • 18
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Or to increase output by some
factor X, inputs would only need to
increase by a factor less than X.
q=40
Increasing Returns to Scale

19. Returns to Scale
Ch. 6 • 19
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Constant returns to scale
– If inputs increase by a factor of X, output increases by a factor
equal to X.
• Increasing returns to scale
– If inputs increase by a factor of X, output increases by a factor
greater than X.
• Decreasing returns to scale
– If inputs increase by a factor of X, output increases by a factor
less than X.

20. Capital
per
week
1
q = 10
Labor
per
week
q=20
q=30
2
1
4
3
2
3
4
Output increases at a rate less
than the increase in inputs
Ch. 6 • 20
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Decreasing Returns to Scale

21. Input Substitution
Ch. 6 • 21
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• How is the shape of the isoquant related to how easy it is to
substitute one input for another?
• Fixed proportions production function:
– A production function in which the inputs must be used in a
fixed ratio to one another.
– Mowing a lawn: one worker and one lawnmower.
– There is no way to substitute one input for another.

22. Capital
per
week
L
0
Labor
per
week
L
1
K
0
K
1
q0
Ch. 6 • 22
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
q1
If you only have K0 machines would
only need L0 workers to produce q0.
If you used L1 workers your output
would remain the same.
Fixed Proportions Production

23. Input Substitution
Ch. 6 • 23
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Why does the degree to which a firm can substitute one input for
another matter?
– Suppose the price of one of the firm’s inputs increases.
– The firm will want to use less of the relatively more expensive
input and more of the relatively less expensive input.
– A firm that is able to substitute one input for another will be
able to keep its costs from rising as much.

24. Changes in Technology
Ch. 6 • 24
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• A production function or isoquant reflects a firm’s current
technological knowledge.
• What happens to the production function if there is technological
progress?
• Technical progress:
– a shift in the production function that allows a given output
level to be produced using fewer inputs.

25. Capital
per
week
q0
q0’
Labor
per
week
Changes in Technology
Ch. 6 • 25
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

26. Capital
per
week
q0’
Labor
q0
K
0
per
week
1 0
Ch. 6 • 26
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
L
With technological change the firm can
produce the same level of output, q0, with K0
but less labor.
L
Changes in Technology vs. Input
Substitution

27. Capital
per
week
q0
q0’
Labor
per
week
K
0
L
0
Ch. 6 • 27
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
With input substitution the firm would need to
use K1 units of capital with L1 units of labor.
L
1
K
1
Changes in Technology vs. Input
Substitution

28. A Numerical Production Example
Ch. 6 • 28
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Production of burgers at Hamburger Heaven
– Hamburgers per hour: q = 10 x (KL) ½
– There are constant returns to scale.
• K, L = 1, q = 10
• K, L = 2, q = 20

29. Constant Returns at Hamburger Heaven
Ch. 6 • 29
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Grills Workers Hamburgers
1 1 10
2 2 20
3 3 30
4 4 40
5 5 50
6 6 60
7 7 70
8 8 80
9 9 90
10 10 100

30. Average and Marginal Product at
Hamburger Heaven
Ch. 6 • 30
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Suppose that Hamburger Heaven uses 4 units of capital
– q = 10(KL)½
– q = 10(4L) ½
– q = 20L½

31. Q, AP and MP at Hamburger Heaven
q = 10 x (4 x 2)1/2 = 28.3 APL = 28.3/2 = 14.1
MPL = 28.3 - 20 = 8.3
Ch. 6 • 31
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

32. Isoquant for Hamburger Heaven
Ch. 6 • 32
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Suppose Hamburger Heaven wants to make 40 burgers.
– q = 40 = 10(KL)½
– 4 = (KL) ½
– 16 = KL
– So if K = 2 and L = 8, q = 40

33. Isoquant for Hamburger Heaven
Ch. 6 • 33
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

34. Grill
s
8
q = 40
2
Workers
8
2
Isoquant for Hamburger Heaven
Ch. 6 • 34
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

35. RTSat Hamburger Heaven
RTS = - change in K / change in L = -(4-5.3)/(4-3) = 1.3
RTS = - change in K / change in L = -(1.8-2)/(9-8) = 0.2
Ch. 6 • 35
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
shani
2022-10-18 10:44:48
--------------------------------------------
Rate of Technical Sustitution

36. RTSat Hamburger Heaven
Ch. 6 • 36
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• As HH uses more and more workers, the RTS falls.
– From L =3 to L =4, RTS = 1.3
– From L = 8 to L = 9, RTS = 0.2
• As more and more workers are used, the firm is less able to
reduce the number of grills it uses.

37. Technological Progressat Hamburger
Heaven
Ch. 6 • 37
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• Suppose that due to genetic engineering hamburgers can flip
themselves.
• Old production function: q = 10(KL) ½
• New production function: q = 20(KL) ½
• If HH still wants to make 40 burgers
– 40 = 20(KL) ½
– 4 = KL
– With old technology: 16 = KL

38. Grill
s
q = 40
4
Workers
4
With the old technology: 16 = KL
1
q = 40
With the new technology: 4 = KL
Technological Progressat Hamburger
Heaven
Ch. 6 • 38
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

39. Summary
Ch. 6 • 39
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• A production function, q = (K,L) shows the relationship between
output and inputs.
• Marginal product is the additional output that can be produced
by adding one more unit of some input, holding all other inputs
constant.
• An isoquant shows the possible input combinations that a firm
can use to produce a given level of output.
• The absolute value of the isoquant’s slope is the RTS – the rate at
which one input can be substituted for another.

40. Summary
Ch. 6 • 40
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
• The RTS falls as the firm uses more and more of one input.
• Production may exhibit constant, decreasing, or increasing
returns to scale.
• With fixed proportions production a firm will not be able to
substitute one input for another.
• With technological progress a firm can produce a given level of
output with fewer inputs: the isoquant shifts in.