Question

orations 365 Discover hinking Online Consider an economy with two sectors: manufacturing and services. Demand for labor in manufacturing and services are described by these equations: LM = 200 - 4WM Ls = 100 - 4Ws whereLis labor (in number of workers),W is the wage (in dollars), and the subscripts denote the sectors. The economy has 222 workers who are willing and able to work in either sector. Assuming that workers are free to move between sectors, what is the equilibrium wage? Round to the nearest two decimal place. Mate

Answer 1

Solution:

We are given that there are total of 222 workers willing and able to work, so, Lm + Ls = 222.

Also, at equilibrium, the wages in two sectors with free movement of labor within two sectors, Wm = Ws (= W*, which is the equilibrium wage), that is wage must be same or equal across the two sectors.

Then, Lm + Ls = 222

(200 - 4*Wm) + (100 - 4*Ws) = 222

With Wm = Ws = W*, 200 - 4*W* + 100 - 4*W* = 222

300 - 8*W* = 222

8*W* = (300 - 222)

W* = (300 - 222)/8 = 9.75

Thus, equilibrium wage is $9.75.