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Chapter 19: Problem 2

Marty's Frozen Yogurt has the production function per day shown in the accompanying table. The equilibrium wage rate for a worker is \(\$ 80\) per day. Each cup of frozen yogurt sells for \(\$ 2\). a. Calculate the marginal product of labor for each worker and the value of the marginal product of labor per worker. b. How many workers should Marty employ?

Short Answer

Expert verified
#Question# Based on the given production function for frozen yogurt and the equilibrium wage rate, calculate the marginal product of labor (MPL) and value of marginal product of labor (VMPL) for each worker, and determine the optimal number of workers that Marty should employ.

Step by step solution

01

Calculate the Marginal Product of Labor (MPL)

We will find the MPL for each worker by finding the difference in output between a worker and the previous worker in the table. The MPL formula is as follows: MPL = (Output with n workers) - (Output with n-1 workers) Calculate the MPL for each worker in the table.
02

Calculate the Value of Marginal Product of Labor (VMPL)

Next, we calculate the VMPL for each worker, by multiplying the marginal product of labor (MPL) obtained in step 1 by the price of each cup of frozen yogurt ($2). The VMPL formula is as follows: VMPL = MPL * Price of frozen yogurt Calculate the VMPL for each worker.
03

Determine the optimal number of workers

Now, we'll compare the VMPL for each worker to the equilibrium wage rate ($80) to determine the optimal number of workers to employ. Marty should employ workers as long as VMPL is greater than or equal to the wage rate. Once the VMPL drops below the wage rate, Marty should stop hiring more workers. Compare the VMPL of each worker to the wage rate and determine the optimal number of workers that Marty should employ. For part a, we have calculated MPL and VMPL for each worker employing the steps above. For part b, we have determined the optimal number of workers by comparing VMPL to the wage rate. This complete the exercise.

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Most popular questions from this chapter

Greta is an enthusiastic amateur gardener and spends a lot of her free time working in her yard. She also has a demanding and well-paid job as a freelance advertising consultant. Because the advertising business is going through a difficult time, the hourly consulting fee Greta can charge falls. Greta decides to spend more time gardening and less time consulting. Explain her decision in terms of income and substitution effects.

A New York Times article observed that the wage of farmworkers in Mexico was \(\$ 11\) an hour but the wage of immigrant Mexican farmworkers in California was \(\$ 9\) an hour. a. Assume that the output sells for the same price in the two countries. Does this imply that the marginal product of labor of farmworkers is higher in Mexico or in California? Explain your answer, and illustrate with a diagram that shows the demand and supply curves for labor in the respective markets. In your diagram, assume that the quantity supplied of labor for any given wage rate is the same for Mexican farmworkers as it is for immigrant Mexican farmworkers in California. b. Now suppose that farmwork in Mexico is more arduous and more dangerous than farmwork in California. As a result, the quantity supplied of labor for any given wage rate is not the same for Mexican farmworkers as it is for immigrant Mexican farmworkers in California. How does this change your answer to part a? What concept best accounts for the difference between wage rates for Mexican farmworkers and immigrant Mexican farmworkers in California? c. Illustrate your answer to part b with a diagram. In this diagram, assume that the quantity of labor demanded for any given wage rate is the same for Mexican employers as it is for Californian employers.

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Jameel runs a driver education school. The more driving instructors he hires, the more driving lessons he can sell. But because he owns a limited number of training automobiles, each additional driving instructor adds less to Jameel's output of driving lessons. The accompanying table shows Jameel's production function per day. Each driving lesson can be sold at \(\$ 35\) per hour. Determine Jameel's labor demand schedule (his demand schedule for driving instructors) for each of the following daily wage rates for driving instructors: \(\$ 160, \$ 180,\) \(\$ 200, \$ 220, \$ 240,\) and \(\$ 260\)

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