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.
Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N) in hundreds of dollars per year. The production function is
L = c H0.8N0.2.
a. Beginning with a health input of
b. Does this production function exhibit increasing, decreasing, or constant returns to scale?
c. Suppose that in a country suffering from famine, N is fixed at 2 and that c = 20. Plot the production function for life expectancy as a function of health expenditures, with L on the vertical axis and H on the horizontal axis.
d. Now suppose another nation provides food aid to the country suffering from famine so that N increases to 4. Plot the new production function.
e. Now suppose that N = 4 and H = 2. You run a charity that can provide either food aid or health aid to this country. Which would provide a greater benefit: increasing H by 1 or N by 1?
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?
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?
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
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