Answer to Question #300104 in Microeconomics for Lolah

Question

5. In a particular industry, labor supply is L

S = 10+W and labor demand is L

D = 40−4W,

where L is the level of employment and W is the hourly wage.

(a) What are the equilibrium wage and employment if the labor market is competitive?

What is the unemployment rate? [7]

(b) Suppose the government sets a minimum hourly wage of M8.

(i) How many workers would lose their jobs? [4]

(ii) How many additional workers would want a job at the minimum wage? [2]

(iii) What is the unemployment rate? [2]

(c) Suppose the hourly wage is M10 and the price of each unit of capital is M25. The

price of output is constant at M50 per unit. The production function is

f(L, K) = L

1/2K1/2

so that the marginal product of labor is

MPL = (1/2)(K/L)

1/2

If the current capital stock is fixed at 1,600 units, how much labor should the firm

employ in the short run? How much profit will the firm earn?

Answer 1

$Ls=10+W$

$Ld=40-4W$

At equilibrium $Ld=Ls$

$10+W=40-4W$

$W=6$

$L=10+6=16$

Demand change:

$Ld=16-(40-4×8)$

$= 8$ people would loose their jobs.

Supply change:

$Ls=(10+8)-16$

$=2$ more people will be willing to supply their labour.

$f(L,K)=L^{\frac{1}{2}}K^{\frac{1}{2}}$

$MPL=\frac{K^{\frac{1}{2}}}{L^{\frac{1}{2}}}$

Isocost:

$1600=10L+50K$

Optimum combinations is when slope of isocost is equal to MPL

Slope of isocost$=\frac{-10}{25}$

$\frac{K^{\frac{1}{2}}}{L^{\frac{1}{2}}}=\frac{-10}{25}$

$25K^{\frac{1}{2}}=-10L^{\frac{1}{2}}$

$K=2L^{\frac{1}{2}}$

Replacing K in the isocost:

$1600=10L+50×2L^{\frac{1}{2}}$

$1600=20L$

$L=80$

$K=2×80^{\frac{1}{2}}=17.9$