Question

Consider an economy with two sectors: manufacturing and services. Demand for labor in manufacturing and services are described by the following equations

Lm=200-6Wm

Ls=100-4Ws

Where L is labor, W is the wage 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 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 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 dollars= that is, rather than taking a job at a wage below 15 dollars, they would rather wait for a 25 dollar union job to open up. Calculate the wage and employment in each sector. What is the economy’s unemployment rate?

Answer 1

Step-by-step explanation:

If workers are free to move between sectors, the wages in each sector will be equal. If wages are not equal, the workers will be motivated to move to sectors with higher wages and this will make a higher salary reduction, and lower wages will increase until they equal.

b. Since there are 100 workers in total,we have:

• Ls =100- Lm = 100 -4w
• Lm = 4w

Now set this equal to the labor demand for manufacturing equation and solve for w:

• 4w = 200 - 6w
• w = $20.

Substitute w =20 into the two labor demand equations, we have LM = 80 and LS i= 20

c. If the wage in manufacturing is equal to $25 then

• Lm=200-6(25) = 50

d. There are now Ls = 50 workers employed in the service sector and the wage:

• Ls=100-4Ws

<=> 50 = 100 -4Ws

<=> Ws = 12.5

e. Wages in the manufacturing sector will remain at 25 dollars and jobs will remain at 50. If wages are reserved for the service sector is 15 dollars, then jobs in the service sector will be 40. Therefore 10 unemployed and the unemployment rate is 10%.