Question

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

??=1321–20??

??=1204–22??

where L is labor (in number of workers), W is the wage (in pesos), and the subscripts denote the sector. The economy has 500 workers who are willing and able to work in either sector.

Since the number of workers employed cannot be fractions and must be whole numbers, round answers for the values of employment to the nearest whole number.

Round all other answers to two places after the decimal when necessary.

A. If workers are free to move between sectors, what relationship will there be between W_m and W_s?

a. W_m > W_s

b. W_m < W_s

c. W_m = W_s

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.

Equilibrium wage =

Employment in the manufacturing sector: _____

Employment in the service sector: _____ workers

Suppose a union establishes itself in manufacturing and pushes the manufacturing wage to 53.21 pesos.

C. Calculate employment in the manufacturing sector.

Employment in the manufacturing sector: _____ workers

In the aftermath of the unionization of manufacturing, all workers who cannot get the highly paid union jobs move to the service sector.

D. Calculate the employment and wage in the service sector.

Employment in the service sector: _____ workers

Wage in the service sector: _____ pesos

In addition, workers have a reservation wage of 49.21 pesos—that is, rather than taking a job at a wage below 49.21 pesos, they would rather wait for a 53.21 peso union job to open up.

E. Calculate the wage and employment in each sector. What is the economy’s unemployment rate?

Wage in the manufacturing sector: _____ workers

Wage in the service sector: _____ pesos

Employment in the manufacturing sector: _____ workers

Employment in the service sector: _____ workers

Unemployment Rate: _____ %

Answer 1

A.

If the workers are free to move between the sectors then the wages between the two sector must be equal, i,e, W_m=W_s.

This is because if the wages in both the sectors are not equal then the workers will freely shift to the sector offering yhem a higher wage and this way the other sector will either stop producing or producing less due to shortage of labour.

B.

Assuming that W_s=W_m, we have the following equations

W_s=W_m=W

L_s+L_m=L=500

L_s=1204-22W_s

L_m=1321-20W_m

Solving the above equations we have,

500-1321-1204=-22W-20W

2025=42W

Therefore, W=48.21

Employment in service sector = 143.38 or 143 workers

Employment in manufacturing sector = 356.8 or 357 workers

C)

Wage = 53.21

Employment in manufacturing sector = 256.8 or 257 workers

D)

The workers who do not get the highly paid manufacturing job fall into the service sector. Therefor the labour force in the service sector = 500-257=243 workers

Therefore the wage in the service sector is given by

243=1204-22W_s

W_s=43.68

E)

If there is a reservation wage at 49.21 pesos then the following would be the wages

W_m=53.21

W_s=49.21

Consequently the labour participation rates would also change

L_m=257

L_s=121

Therefore the total unemployed workers would be 500-257-121=122

Unemployment rate = 122/500=0.244 or 24.4%