Question

Given an economy with a MPN = 100-(.125)N, and a labor supply of NS=40+30w, where w is the real wage, what:

a) would be the quantity of (whole) laborers demanded if w=37?

b) is the equilibrium w?

c) is the equilibrium quantity of labor?

Answer 1

a) We will get the quantity of laborers demanded by setting w = MPN = 100-(.125)N
So, 37 = 100-(.125)N
So, 0.125N = 100-37 = 63
So, N = 63/0.125 = 504

The quantity of (whole) laborers demanded if w=37 is 504.

b) At equilibrium, labor demand = labor supply
We solve labor demand equation first as a function of w.
MPN = 100-(.125)N = w
So, 0.125N = 100-w
So, N = (100-w)/0.125
So, N = (100/0.125) - (w/0.125)
So, N = 800 - 8w

Now, equating labor demand and labor supply, we get,
800-8w = 40+30w
So, 30w+8w = 800-40
So, 38w = 760
So, w = 760/38 = 20

The equilibrium w is 20.

(c) N = 800 - 8w = 800 - 8(20) = 800 - 160 = 640
The equilibrium quantity of labor is 640.