Question

Problem 1: Consider an economy with two sectors: manufacturing and services. Demand for labor in manufacturing and services are described by these equations:

Lm = 200 - 6Wm

Ls = 100 - 4Ws where L is labor (in number of workers), W is the wage (in dollars), and the subscripts denote the sectors. The economy has 150 workers who are willing and able to work in either sector.

a. If workers are free to move between sectors, what relationship will there be between Wm and Ws?

b. Suppose that the condition in part (a) holds and wages adjust to equilibrate labor supply and labor demand. Calculate the wage and employment in each sector.

c. Suppose a union establishes itself in manufacturing and pushes the manufacturing wage to $20. Calculate employment in manufacturing.

d. In the aftermath of the unionization of manufacturing, all workers who cannot get the highly paid union jobs move to the service sector. Calculate the wage and employment in services.

e. Now suppose that workers have a reservation wage of $10—that is, rather than taking a job at a wage below $10, they would rather wait for a $20 union job to open up. Calculate the wage and employment in each sector. What is the economy’s unemployment rate?

Answer 1

Given : Lm = 200 - 6Wm Ls = 100 - 4Ws

(a) If the worker are free to move between sectots, the wage in both sector needs to be equal.Hence The only relationship that prevails is Wm=Ws

(b) It is given that there are total 150 workers in the economy to be divided into both the sectors.

  Lm = 200 - 6Wm Ls = 100 - 4Ws

   Lm+ Ls = 100

100-Ls =200-6W

100-100+4W=200-6W   

The wage W = 20

Then Lm= 80    Ls = 20

(C) Suppose Unions pushes the manufacturing wage to the $20. Calculation of employment in manufacturing sector is as follows

Lm=200-6Wm

=200-6(20)

=80

Hence the manufacturing sector will employ 80 workers at $20 wage

(d) All the worker who cannot get higher paid union jobs shifts to services sector.Total workers in the economy are 150 and out of which 80 are employed in manufacturing sector. Hence the level of emplyment in service sector is 70 workers.

Calculation of wage under service sector is as follows

Ls=100-4Ws

70=100-4Ws

30=4Ws

Ws=$7.5

(e)   workers have a reservation wage of $10 ,Ws =10

Ls =100-4Ws= 100-4*10=60

unemployment (Lm+ Ls)=100-90=10

unemployment rate =10/100 = 0.1=10 %