平狄克微观经济学第六版第十四章课后答案(9)

平狄克微观经济学第六版课后答案

Substituting into either the labor supply or labor demand equations, we find the

equilibrium quantity of labor is 800:

LS = (20)(40) = 800,

and

LD = 1,200 - (10)(40) = 800.

Economic rent is the summation of the difference between the equilibrium wage and

the wage given by the labor supply curve. Here, it is the area above the labor supply

curve up to L = 800 and below the equilibrium wage. This triangle’s area is

(0.5)(800)($40) = $16,000.

9. This exercise is a continuation of Exercise 8. Suppose now that the only labor available is controlled by a monopolistic labor union that wishes to maximize the rent earned by union members. What will be the quantity of labor employed and the wage rate? How does your answer compare with your answer to Exercise 8? Discuss. (Hint: The union’s marginal revenue curve is given by L = 1200 - 20w.)

Recall that the monopolist chooses output by setting marginal revenue equal to the

marginal cost of supplying one more unit of output, as opposed to the competitive firm

which chooses output by setting price equal to marginal cost, or in other words

producing where supply intersects demand. The monopolistic labor union acts in the

same way. To maximize rent in this case, the union will choose the number of workers

hired so that the marginal revenue to the union (the additional wages earned) is equal

to the extra cost of inducing the worker to work. This involves choosing the quantity of

labor at the point where the marginal revenue curve crosses the supply curve of labor.

Note that the marginal revenue curve has twice the slope of the labor demand curve.

Marginal revenue is less than the wage, because when more workers are hired, all

workers receive a lower wage.

Setting the marginal revenue curve equal to the supply curve for labor, we find:

1200 - 20w = 20w, or w* = 30.

At w*, we may determine the number of workers who are willing to work by

substituting w* into the labor supply equation:

L* = (20)(30) = 600.

Therefore, if the union wants to maximize the rent that the union members earn, the

union should limit employment to 600 members.

To determine the wage the members will earn, substitute L* into the labor demand

equation:

600 = 1,200 - 10w, or w = 60.

The total rent the employed union members will receive is equal to:

Rent = (60 - 30)(600) + (0.5)(30)(600) = $27,000.

Notice that the wage is higher and the number of workers employed is lower than in Exercise (8).

*10. A firm uses a single input, labor, to produce output q according to the production function q . The commodity sells for $150 per unit and the wage rate is $75 per hour.

a. Find the profit-maximizing quantity of L.

There are two (equivalent) methods of solving this problem. Most generally, define

the profit function, where revenues and costs are expressed in terms of the input,

calculate the first order necessary condition (the first derivative of the profit function),

and solve for the optimal quantity of the input. Alternatively, use the rule that the