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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. $$\begin{array}{cc} \boldsymbol{q} & \boldsymbol{l} \\ \hline 0 & 0 \\ 20 & 1 \\ 35 & 2 \\ 47 & 3 \\ 57 & 4 \\ 65 & 5 \\ 70 & 6 \end{array}$$ 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
a. The profit-maximizing quantity of labor is X units. b. With a wage rate of $21 and price of $2, the profit-maximizing quantity of labor is Y units. c. When price of product is $3 and wage remains at $16 per hour, the profit-maximizing quantity of labor is Z units. d. With a technological breakthrough that increases output by 25%, and the price remaining at $2 and the wage at $16, the profit-maximizing quantity of labor is W units.

Step by step solution

01

Calculate the Marginal Product of Labor

First, compute the changes in output (q) per change in labor units (l). This gives the 'marginal product of labor'. Subtract each q value from the previous one in the table and do the same for l, then divide the difference in q by the difference in l. This results in a new 'marginal product of labor' for each l value.
02

Calculate the Marginal Revenue Product

Next, multiply the 'marginal product of labor' by the price of the product. This will give the 'marginal revenue product', which is the additional revenue that an extra unit of labor brings in.
03

Calculate the Marginal Cost

For each unit of labor, calculate the 'marginal cost', which is simply the wage rate as given in the problem statement.
04

Find where Marginal Revenue Product equals Marginal Cost

The labor unit that maximizes profit is where marginal revenue product equals marginal cost. Look for the l value where this condition is met. If it falls between two numbers, the smaller one is chosen as firms cannot hire fractions of workers. This is the profit-maximizing quantity of labor when the wage rate is $16 and price is $2.
05

Step 5, 6, 7: Repeat steps for different scenarios

Repeat Steps 1-4 for the different scenarios provided, i.e., when the wage rate changes to $21, price to $3, and when there is a technological breakthrough. The increase in output due to the technological breakthrough means that the 'marginal product of labor' increases by 25% at each level of labor.

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Most popular questions from this chapter

The only legal employer of military soldiers in the United States is the federal government. If the government uses its knowledge of its monopsonistic position, what criteria will it employ when determining how many soldiers to recruit? What happens if a mandatory draft is implemented?

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 A. Aluminum used for beverage cans

Suppose that a firm's production function is given by \(Q=12 L-L^{2},\) for \(L=0\) to \(6,\) where \(L\) is labor input per day and \(Q\) is output per day. Derive and draw the firm's demand for labor curve if the firm's output sells for \(\$ 10\) in a competitive market. How many workers will the firm hire when the wage rate is \(\$ 30\) per day? \(\$ 60\) per day? (Hint: The marginal product of labor is \(12-2 L\).)

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 \(L=20\) tw. What is the equilibrium wage rate and quantity of labor hired? What is the economic rent earned by workers?

Using your knowledge of marginal revenue product, explain the following: a. A famous tennis star is paid \(\$ 200,000\) for appearing in a 30 -second television commercial. The actor who plays his doubles partner is paid \(\$ 500\). b. The president of an ailing savings and loan is paid not to stay in his job for the last two years of his contract. c. A jumbo jet carrying 400 passengers is priced higher than a 250 -passenger model even though both aircraft cost the same to manufacture.
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