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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

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The marginal product of second and third workers might be higher than the first because they can share the responsibilities, improving efficiency and serving more customers. However, eventually, the marginal product of workers might diminish because when the number of workers is beyond the roles available, it might create inefficiency, leading to diminishing marginal returns.

Step by step solution

01

Understanding Marginal Product

\'Marginal Product\' in economics refers to the additional output resulting from adding an extra unit of input, in this case, a worker. Here, it is defined as the number of customers served by a particular worker in a given time period.
02

Explaining Higher Marginal Productiveness of Second and Third Workers

The marginal product of the second and third workers could be higher than the first one due to several reasons. For instance, the first worker might need to handle all tasks, from taking orders, prepping food, serving customers to cleaning. When a second worker is hired, tasks can be divided. This division could increase efficiency and thus, more customers can be served in the same amount of time. The same applies when a third worker is hired.
03

The Law of Diminishing Marginal Returns

In economics, the Law of Diminishing Marginal Returns suggests that as a company continues to add more units of a certain input (like labor), at some point, the additional output from each extra unit of input will start to decrease. After hiring a certain number of workers, further hires may not increase customer service significantly as there are only so many roles to perform. Also, more workers could lead to overcrowding and less efficiency.
04

Example for Diminishing Marginal Returns

For example, if Joe hires a fourth worker who takes over cash handling, while the other three perform tasks like taking orders, preparing food, and cleaning respectively. Now, if Joe hires a fifth worker, they may only marginally improve efficiency, ensuring that queues move faster. However, this additional efficiency will certainly be less compared to the addition of the second or third worker who were able to add much greater value by taking over significantly larger roles.

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Most popular questions from this chapter

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

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 \(L=c H^{0.8} N^{0.2}\) 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 \(1 ?\)

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.

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?

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