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Chapter 6: Problem 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?

Short Answer

Expert verified
The marginal product could be higher for the second and third workers because the division of labor allows workers to specialize, and this improves service efficiency. However, the marginal product of additional workers might eventually diminish due to the shortage of resources, which may hamper movement and service, illustrating the principle of diminishing returns.

Step by step solution

01

Concept of Marginal Product

Define the concept of a marginal product. In simple terms, it can be defined as the extra output (in this case, served customers) that can be derived from an additional unit of input (here, worker).
02

Increase in Marginal Product

Explain the reason behind the possible increase in marginal product with additional workers. In this case, the increase in efficiency can be attributed to division of labor and specialization. The first worker may have to juggle all tasks alone, but when the second and third workers are hired, they can all specialize in specific tasks. This can improve service efficiency and lead to more customers served, increasing the marginal product of the second and third workers.
03

Diminishing Marginal Product

Demonstrate why the marginal product might eventually diminish with more workers. This is mainly due to the law of diminishing returns, which states that at some point, employing additional units of an input will lead to smaller increases in output. This could be because all workers start to compete for limited resources like kitchen tools or because the coffee shop becomes crowded to a point where movement and service are hampered.

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

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?

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 \(1 ?\)

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.
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