Question

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

L_m = 400 – 12W_m

L_s = 200 – 8W_s

where L is labor (in number of workers), W is wage (in dollars), and the scripts denote the sectors. The economy has 200 workers who are willing and able to work in either sector.

1. If workers are free to move between sectors, what relationship will there be between W_m and W_s?
2. 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.
3. Suppose a union establishes itself in manufacturing and pushes the manufacturing wage to $25. Calculate employment in manufacturing.
4. Also suppose that in addition to (c), workers have a reservation wage of $15 – that is, rather than take a job at a wage below $15, they would rather remain unemploye Calculate the wage and employment in each sector. What is the economy’s unemployment rate?

Answer 1

1. Free movement imply Ws = Wm. That is the wages in the two sectors will be equal. Otherwise workers will keep moving to the sector with higher wage rate and as a result the wage will increase in the sector with lower wage and will stop increasing only when the wages in the two sector are equalised.
2. Lm = 400 -12Wm

Ls = 200 – 8Ws

Now Wm = Ws = W

Lm = 400 -12W

Ls = 200 – 8W

Adding these demands:

Lm+Ls = L = 600 – 20W

Labour supply = 200.

AT equilibrium Labour Demand = Labour supply:

600 – 20W = 200

20W = 400

W = 20.

Employment in Manufacturing Lm = 400 – 12*20 = 160

Employment in Service sector Ls = 200 – 8*20 = 40

3. W = 25

Lm = 400 – 12*25 = 100.

4. Reservation wage = $15.

Lm = 400 – 12*15 = 220

Ls = 200 – 8*15 = 80

Labour demand at reservation wage = 220+ 80 = 300.

But labour supply = 200

There is excess demand for labour exist at reservation wage.

Therefore the wage will keep increasing until all the supply is exhausted. The equilibrium wage rate will be $20 and employment will be equal to 200. Unemployment rate will be zero.