Question

The nation of Ectenia has 40 competitive apple orchards, which sell apples at the world price of $2 per apple. The following equations describe the production function and the marginal product of labor in each orchard: Q = 120L−L2, MPL = 120−2L where Q is the number of apples produced in a day, L is the number of workers, and MPL is the marginal product of labor. What is each orchard’s labor demand as a function of the daily wage W?

L=60−0.25W

L=2,400−10W

L=120−2W

L=60−0.5W

What is the market’s labor demand?

L=2,400−10W

L=60−0.25W

L=2,400−0.25W

L=120−10W

Ectenia has 200 workers who supply their labor inelastically. The equilibrium wage is $__ per worker per day. Each orchard hires workers and makes a profit of $__ per day. (Note: Assume that wages are the firm’s only costs.)

Answer 1

The orchard's labor demand will be equal to the value of its marginal product. Therefore, w=VMP

w=VMP = P*MP_L = 2 (120-2L) = 240-4L

From the above equation we have

L= 60-0.25w

From the above equation we have

L= 60-0.25w

Therefore, each orchard's labor demand as a function of w is:

L= 60-0.25w

Therefore, the correct option is a.

The market demand curve for labor will be the horiontal summation of 40 orchard demand curves summed over L

From the above equation we have

L= 60-0.25w

Therefore the market demand curve will be

L= 40(60-0.25w)

L=2400-10w

Therefore, the correct option is a.

Ectenia has 200 workers who supply their labor inelastically. Then market equilibrium will be when

200=2400-10w

w=220

The equilibrium wage is 220 per worker per day.

Each orchard will have 200/40= 5 workers and will produce

Q= 120*5-(5)² = 575 apples

Total revenue of each orchard will be 575*2= $1150

If we assume that wages are the firm's only cost then total cost for each orchard will be 220*5=$1100.

Therefore, Profit for each orchard will be $1150-$1100 = $50

Therefore, each orchard hires and makes a profit of $50 per day.