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Chapter 6: Problem 2

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: $$\begin{array}{|cc|} \hline \text { NUMBER OF WORKERS } & \text { NUMBER OF CHAIRS } \\ \hline 1 & 10 \\ \hline 2 & 18 \\ \hline 3 & 24 \\ \hline 4 & 28 \\ \hline 5 & 30 \\ \hline 6 & 28 \\ \hline 7 & 25 \\ \hline \end{array}$$ 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.

Short Answer

Expert verified
The MPL first increases from 10 to 8 when going from one to two workers, then diminishes with each additional worker thereafter, turning negative from 5 to 6 workers employed. Hence, this production function exhibits diminishing returns. The APL also exhibits a similar pattern, reaching a peak at 4 workers, followed by a decline. Finally, when too many workers are employed, the productivity of each worker gets impacted negatively leading to a decrease in total output; hence MPL can turn negative.

Step by step solution

01

- Calculate Marginal Product of Labor

To calculate the Marginal Product of Labor (MPL), subtract the number of chairs produced with one less worker from the number produced with the current number, and repeat this for each worker. For the first worker, the MPL is the same as the total product, which equals to 10.
02

- Calculate Average Product of Labor

To calculate the Average Product of Labor (APL), divide the total number of chairs produced by the number of workers employed. Repeat this for each number of workers.
03

- Verify Diminishing Returns

Analyse the calculated MPL values. A production function is said to exhibit diminishing returns if the MPL starts to fall after a certain point.
04

- Explain Negative Marginal Product

The Marginal Product of Labor can become negative when an additional worker decreases the total output. This situation can occur when too many workers are employed that they negatively impact the productivity of others.

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Most popular questions from this chapter

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?

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?

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?

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.

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 \(L=\mathrm{c} H^{0.8} N^{0.2}\) a. Beginning with a health input of \(\$ 400\) per year \((H=4)\) and a nutrition input of \(\$ 4900\) per year \((N=49),\) show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. 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 \(1 ?\)
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