. Consider a state, its economy is largely based on two sectors, e.g. manufacturing and services. Most of local labor forces are employed in automobile manufacturers and traditional service industries (catering, education, retail and state employees). At aggregate, total employment is two million (or 2000 thousand) in this state. Demand functions for labor force in manufacturing (M) and service (S) are as following.

Demand for labor in manufacturing (in thousand), with wage rate as W_m ($/week).

M = 4000 - 3 * W_m .

Demand for labor in service (thousand), with wage rate as W_s ($/week).

S = 2000 - 2 * W_s .

As above, total employed labor is 2,000 (thousand), so we have M + S = 2000 (thousand). Then finish the following questions.

a. If labor forces are free to move between manufacturing and service sectors, what relationship will there be between W_m and W_s? (Higher, lower or the same and why?)

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 (W_m, W_s, M and S).

c. Suppose in manufacturing sector, a considerable portion of labor force is unionized. After labor unions in manufacture raised wage to $1,000 per week. Then what would happen to wage and total employment in service sector (labor force is free to move across two sectors).