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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

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.

The menu at Joe鈥檚 coffee shop consists of a variety of coffee drinks, pastries, and sandwiches. The marginal product of an additional worker can be defined as the number of customers that can be served by that worker in a given time period. Joe has been employing one worker but is considering hiring a second and a third. Explain why the marginal product of the second and third workers might be higher than the first. Why might you expect the marginal product of additional workers to diminish eventually?

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鈥檚 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.

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

A political campaign manager must decide whether to emphasize television advertisements or letters to potential voters in a reelection campaign. Describe the production function for campaign votes. How might information about this function (such as the shape of the isoquants) help the campaign manager to plan strategy?
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