Question

7. Work It Out. Consider an economy with two sectors: manufacturing and services. Demand for labor in manufacturing and services are described by these equations: L Lm=200-6WmLs=100-4W L = 200 - 6W = 100 - 4W. where Lis labor (in number of workers), W is the wage (in dollars), and the subscripts denote the sectors. The economy has 100 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 WmW. and Ws?W.? 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 $25. 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 $15-that is, rather than take a job at a wage below $15, they would rather wait for a $25 union job to open up. Calculate the wage and employment in each sector. What is the economy's unemployment rate?

Answer 1

Answer:

Given that:

An economy with two sectors: manufacturing and services.

Demand for labor in these sectors is as follows:

L_m = 6W_m

L_s=100-4W_s

A) If workers are free to move between sectors, the wage in both sectors needs to be equal .

The only relationship that prevails is W_m =W_s

B) It is given that three are total 100 workers in the economy to be divided into both the sectors

.
_{Lg = 100 – Lm}

substitute the values of labor demand into above equation.

100 – 4W, = 100 - 200 +6Wm

100 – 4W, = -100 + 6W m

Assuming

W = Wm=W

100-4W =-100 + = 6W

=200=10W

$20=W

Thus the wage is S20

Substitute this value of wage into the labor demand equations:

Lm = 200 – 6(20)

=200-120

=80

L_s =100 -4 (20)

=100-80

=20

Thus the labor demand in manufacturing sector is 80 workers and labor demanded in service sector is 20 workers.

C) Suppose union pushes the manufacturing wage to the $25. Calculation of employment in manufacturing sector is as follows :

L_m =200-6W_m

=200-6(25)

=200-150

=50

Thus the manufacturing sector will employ 50 workers at S25 wage.

D)All the workers who cannot get the higher paid union jobs. shifts to services sector. Total workers in the economy are 100 and out of which 50 are employed in manufacturing sector. Thus the level of employment in service sector is 50 workers.

Calculation of wage under service sector is as follows :

L_s =100 -4W_s

50 =100 - 4W_s

50=4W_s

$125=W_s

Thus the wage in the service sector is $12.5