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Chapter 6: Problem 7

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?

Short Answer

Expert verified
The marginal product of capital is 200 chips per hour.

Step by step solution

01

Understand the relation between the Marginal Product of Labor and Capital

The Marginal Rate of Technical Substitution (MRTS) is the amount of one input (like capital) that can be replaced by one unit of another input (like labor) while keeping output the same. Mathematically, it is equal to the ratio of the marginal product of one input to the marginal product of the other input, that is, MRTS = (Marginal Product of Labor) / (Marginal Product of Capital)
02

Plug the given values into the formula

In the problem, the Marginal Product of Labor (MPL) is given as 50 chips per hour and the MRTS is given as \(1/4\). Plugging these into the formula gives the following equation: \(1/4 = 50 / (Marginal Product of Capital)\)
03

Solve for Marginal Product of Capital

Solving the above equation for Marginal Product of Capital gives: Marginal Product of Capital = 50 / (1/4) = 200 chips per hour

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Most popular questions from this chapter

The production function for the personal computers of DISK, Inc., is given by $$q=10 K^{0.5} L^{0.5}$$ 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 $$q=10 K^{0.6} L^{0.4}$$ 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.

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.

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. \(q=3 L+2 K\) b. \(q=(2 L+2 K)^{1 / 2}\) c. \(q=3 L K^{2}\) \(\mathbf{d} . q=L^{1 / 2} K^{1 / 2}\) \(\mathbf{e} . q=4 L^{1 / 2}+4 K\)

In Example \(6.4,\) wheat is produced according to the production function $$q=100\left(K^{0.8} L^{0.2}\right)$$ 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?

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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