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Chapter 14: Problem 1

Suppose that the wage rate is \(\$ 16\) per hour and the price of the product is \(\$ 2 .\) Values for output and labor are in units per hour. $$\begin{array}{cc}9 & 1 \\\\\hline 0 & 0 \\\20 & 1 \\ 35 & 2 \\\47 & 3 \\\57 & 4 \\\65 & 5 \\\70 & 6\end{array}$$ a. Find the profit-maximizing quantity of labor. b. Suppose that the price of the product remains at \(\$ 2\) but that the wage rate increases to \(\$ 21 .\) Find the new profit-maximizing level of \(L\) c. Suppose that the price of the product increases to \(\$ 3\) and the wage remains at \(\$ 16\) per hour. Find the new profit-maximizing \(L\) d. Suppose that the price of the product remains at \(\$ 2\) and the wage at \(\$ 16,\) but that there is a technological breakthrough that increases output by 25 percent for any given level of labor. Find the new profit-maximizing L.

Short Answer

Expert verified
The profit-maximizing quantity of labor would be different under different scenarios. For (a) refer to the answer in Step 2, for (b) refer to the answer in Step 3, for (c) refer to the answer in Step 4, and for (d) refer to the answer in Step 5.

Step by step solution

01

Understanding the table and set up the profit function

The table is to be read as follows: 'If x units of labor are consumed, y units of the product are produced'. Therefore, assuming a linear relationship between number of units of labor consumed and output, one can find a function for Q(L) by dividing the number of units produced by number of units of labor consumed. The profit then can be calculated by subtracting the total cost from total revenue.
02

Calculating profit-maximizing quantity of labor (a)

Using the previously mentioned profit function, calculate the profits for each quantity level, by subtracting the total cost (wage rate times quantity of labor) from the total revenue (price of the product times output) and pick the quantity of labor where this difference is the maximum. This is the profit-maximizing quantity of labor.
03

Calculating the new profit-maximizing level of labor with an increased wage rate (b)

Repeat the process in Step 2, but use the new wage rate of \$21 per hour to calculate total cost. The profit-maximizing quantity of labor is again the one where profit is the maximum.
04

Calculating the new profit-maximizing quantity of labor with an increased product price (c)

Repeat the process in Step 2, but this time use the new product price of \$3 to calculate the total revenue. The profit-maximizing quantity of labor is again the one where the profit is the maximum.
05

Calculating the new profit-maximizing level of labor with a technological breakthrough (d)

With a 25 percent increase in the output due to technological advancement, it means that the output is 1.25 times what it was before for any given level of labor. So we will multiply the quantity of each output in the table by 1.25 and repeat the process of Step 2 with the new output-quantity pairs. The profit-maximizing quantity of labor is again the quantity where profit is the maximum.

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Most popular questions from this chapter

The demands for the factors of production listed below have increased. What can you conclude about changes in the demands for the related consumer goods? If demands for the consumer goods remain unchanged, what other explanation is there for an increase in derived demands for these items? a. Computer memory chips b. Jet fuel for passenger planes c. Paper used for newsprint d. Aluminum used for beverage cans

Suppose there are two groups of workers, unionized and nonunionized. Congress passes a law that requires all workers to join the union. What do you expect to happen to the wage rates of formerly nonunionized workers? Of those workers who were originally unionized? What have you assumed about the union's behavior?

Assume that workers whose incomes are less than \(\$ 10,000\) currently pay no federal income taxes. Suppose a new government program guarantees each worker \(\$ 5000,\) whether or not he or she earns any in come. For all earned income up to \(\$ 10,000\), the worker must pay a 50 -percent tax. Draw the budget line facing the worker under this new program. How is the program likely to affect the labor supply curve of workers?

A firm uses a single input, labor, to produce output \(q\) according to the production function \(q=8 \sqrt{L}\). The commodity sells for \(\$ 150\) per unit and the wage rate is \(\$ 75\) per hour. a. Find the profit-maximizing quantity of \(L\) b. Find the profit-maximizing quantity of \(q\) c. What is the maximum profit? d. Suppose now that the firm is taxed \(\$ 30\) per unit of output and that the wage rate is subsidized at a rate of \(\$ 15\) per hour. Assume that the firm is a price taker, so the price of the product remains at \(\$ 150\) Find the new profit-maximizing levels of \(L, q,\) and profit. e. Now suppose that the firm is required to pay a 20-percent tax on its profits. Find the new profitmaximizing levels of \(L, q,\) and profit.

The demand for labor by an industry is given by the curve \(L=1200-10 w,\) where \(L\) is the labor demanded per day and \(w\) is the wage rate. The supply curve is given by \(L=20\) w. What is the equilibrium wage rate and quantity of labor hired? What is the economic rent earned by workers?
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