1. Walter Nicholson Christopher Snyder
Amherst College
Christopher Snyder
Dartmouth College
PowerPoint Slide Presentation | Philip Heap, James Madison University
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2. CHAPTER 6
Production
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3. Chapter Preview
We now want to turn to firm behavior, and answer three main questions.
What happens to output as a firm increases the number of input(s) it uses?
To what degree is a firm able to substitute one input for another?
What happens to production as a result of technological change?
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4. Production Functions
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 )
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5. Marginal Product 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).
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6. Total Product and Marginal Product
As labor increases output increases but at a diminishing rate.
So marginal product decreases as labor increases.
Output
per week
MPL L* L*
Labor input
per week
Labor input
per week
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7. Average Product
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.
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8. Isoquant Maps
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.
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9. Isoquant Map Capital per week KA A q=30 q=20 KB B q = 10 LA LB Labor
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10. Rate of Technical Substitution
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)
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11. Rate of Technical Substitution
At point A, the slope of the isoquant = RTS = ΔKA/ ΔL
Capital
per week
Along the isoquant. the slope gets flatter and the RTS diminishes
At point B, the slope of the isoquant = RTS = ΔKB/ ΔL KA A
The amount of capital that can be given up when one more unit of labor is employed gets smaller and smaller
ΔKA ΔL KB
ΔKB B
q = 10 ΔL LA LB
Labor
per week
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12. The RTS and Marginal Product
Why must the slope of the isoquant be negative or the RTS positive?
RTS = MPL/MPK
If RTS was < 0 either MPL or the MPK would also have to be < 0.
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.
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13. The RTS and Marginal Product
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 MPL falls.
Therefore, to maintain the same level of output, the firm would only be able to give up smaller and smaller amounts of capital.
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14. Returns to Scale
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
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15. Returns to Scale Constant returns to scale:
If inputs increase by a factor of X, output increases by a factor equal to X.
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16. Constant Returns to Scale
Capital
per week
Output increases at the same proportion as inputs 4
q=40 3
q=30 2
q=20 1
q = 10 1 2 3 4
Labor
per week
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17. Returns to Scale 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.
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18. Increasing Returns to Scale
Capital
per week
Output increases at a rate greater than the increase in inputs 4
Or to increase output by some factor X, inputs would only need to increase by a factor less than X. 3
q=40 2
q=30 1
q=20
q = 10 1 2 3 4
Labor
per week
©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.

19. Returns to Scale 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.
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20. Decreasing Returns to Scale
Capital
per week
Output increases at a rate less than the increase in inputs 4
q=30 3 2
q=20 1
q = 10 1 2 3 4
Labor
per week
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21. Input Substitution
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.
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22. Fixed Proportions Production
If you only have K0 machines would only need L0 workers to produce q0.
Capital
per week
If you used L1 workers your output would remain the same. K1 q1 K0 q0 L0 L1
Labor
per week
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23. Input Substitution
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.
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24. Changes in Technology
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.
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25. Changes in Technology Capital per week q0 q0’ Labor per week
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26. Changes in Technology vs. Input Substitution
Capital
per week
With technological change the firm can produce the same level of output, q0, with K0 but less labor. K0 q0
q0’ L1 L0
Labor
per week
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27. Changes in Technology vs. Input Substitution
Capital
per week
With input substitution the firm would need to use K1 units of capital with L1 units of labor. K1 K0 q0
q0’ L1 L0
Labor
per week
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28. A Numerical Production Example
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
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29. Constant Returns at Hamburger Heaven
Grills
Workers
Hamburgers 1 10 2 20 3 30 4 40 5 50 6 60 7 70 8 80 9 90
100
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30. Average and Marginal Product at Hamburger Heaven
Suppose that Hamburger Heaven uses 4 units of capital
q = 10(KL) ½
q = 10(4L) ½
q = 20L ½
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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 = = 8.3
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32. Isoquant for Hamburger Heaven
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
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33. Isoquant for Hamburger Heaven
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34. Isoquant for Hamburger Heaven
Grills 8 2
q = 40 2 8
Workers
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35. RTS at 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
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36. RTS at Hamburger Heaven
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.
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37. Technological Progress at Hamburger Heaven
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
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38. Technological Progress at Hamburger Heaven
Grills
With the old technology: 16 = KL
With the new technology: 4 = KL 4
q = 40
q = 40 1 4
Workers
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39. Summary
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.
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40. Summary 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.
©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.