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Chapter 6: Q7. (page 236)
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?
The marginal product of capital is 250 chips.
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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.
Fill in the gaps in the table below.
| Quantity of variable input | Total output | Marginal product of variable input | Average product of variable input |
| 0 | 0 | ||
| 1 | 225 | ||
| 2 | 300 | ||
| 3 | 300 | ||
| 4 | 1140 | ||
| 5 | 225 | ||
| 6 | 225 |
For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case?
a. A firm can hire only full-time employees to produce its output, or it can hire some combination of fulltime and part-time employees. For each full-time worker let go, the firm must hire an increasing number of temporary employees to maintain the same level of output.
b. A firm finds that it can always trade two units of labor for one unit of capital and still keep output constant.
c. A firm requires exactly two full-time workers to operate each piece of machinery in the factory
In Example 6.4, wheat is produced according to the production function
q = 100(K0.8L0.2)
a. Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing.
b. Does this production function exhibit increasing, decreasing, or constant returns to scale?
The menu at Joe’s 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?
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