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Chapter 6: Q6. (page 236)

A firm has a production process in which the inputs to production are perfectly substitutable in the long run. Can you tell whether the marginal rate of technical substitution is high or low, or is further information necessary? Discuss.

Short Answer

Expert verified

Some information regarding the marginal productivity of the inputs is required to calculate the value of MRTS and to conclude whether MRTS is high or low.

Step by step solution

01

The definition of MRTS 

The marginal rate of technical substitution is a concept that indicates substitution or exchange between inputs. It depends on the marginal productivity of each input. The value of MRTS defines the slope of isoquant.

02

The conclusion regarding MRTS

In this case, the inputs used by the firm are perfect substitutes. So the isoquant faced by the firm is linear, and the value of MRTS should be constant. However, to calculate the slope of the isoquant or the value of MRTS, it is important to know the marginal product of each input. Hence, to conclude whether the value of MRTS is high or low, some information regarding the marginal productivity is required.

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Most popular questions from this chapter

Fill in the gaps in the table below.

Quantity of variable input
Total output
Marginal product of variable input
Average product of variable input
00

1225

2

300
3
300
41140

5
225
6

225

The production function for the personal computers of DISK, Inc., is given by

q = 10K0.5L0.5

where q is the number of computers produced per day, K is hours of machine time, and L is hours of labor input.

DISK’s competitor, FLOPPY, Inc., is using the production function

q = 10K0.6L0.4

a. If both companies use the same amounts of capital and labor, which will generate more output?

b. Assume that capital is limited to 9 machine-hours, but labor is unlimited in supply. In which company is the marginal product of labor greater? Explain.

The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/4. What is the marginal product of capital?

Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor held constant?

a. q = 3L + 2K

b. q = (2L + 2K)1/2

c. q = 3LK2

d. q = L1/2K1/2

e. q = 4L1/2 + 4K

Suppose a chair manufacturer is producing in the short-run (with its existing plant and equipment). The manufacturer has observed the following levels of production corresponding to different numbers of workers:

Number of workers
Number of chairs
110
218
324
428
530
628
725

a. Calculate the marginal and average product of labor for this production function.

b. Does this production function exhibit diminishing returns to labor? Explain.

c. Explain intuitively what might cause the marginal product of labor to become negative.
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