Question

The nation of Ectenia has 80 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:

QQ	=  =	80L−L280L−L2
MPLMPL	=  =	80−2L80−2L

where QQ is the number of apples produced in a day, LL is the number of workers, and MPLMPL is the marginal product of labor.

Suppose the world price of apples doubles to $4 per apple.

What is each orchard's labor demand as a function of the daily wage W ? L=80−2W L=40−0.125W L=3,200−10W L=40−0.25W

What is the market's labor demand? L=40−0.125W L=3,200−20W L=80−20W L=3,200−10W

Ectenia has 1,200 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

Given, Q = 80L - L²

MP_L = 80 - 2L

Labor demand function can be derived as follows

VMP_L = P × MP_L = 80P - 2PL = 160 - 4L (Since P = $ 2)

W = VMP_L

W = 160 - 4L

L = 40 - 0.25W (At world price = $ 2) kindly ignore just for reference

Markets Labor demand function

L = 3,200 - 20W (At world price = $ 2) ignore just for reference.

Solution:

When we assume price to be $ 4

Each firms labor demand function

VMPL = 320 - 8L

W = 320 - 8L

(At a price = $ 4)

Total kabir demand function

(At a price = $ 4)

Labor = 1200

1200 = 3200 - 10W

10 W = 2000

W = $ 200 per worker per day

Number of labor hired = 1200/80 = 15 labor per day

Profit = PQ - TC

Profit = 4 ×(80×15 -15² ) - 200 × 15

Profit = $ 900

What is each orchard's labor demand as a function of the daily wage W ?

Answer

What is the market's labor demand?

Ectenia has 1,200 workers who supply their labor inelastically. The equilibrium wage is $ 200 per worker per day. Each orchard hires workers and makes a profit of $ 900 per day.