3- Suppose the hourly wage is $10 and the price of each unit of capital is $25.

Question

3- Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The production function is f(K, E) = K ^0.5 E^0.5 so that the marginal product of labor is MPE = 1/2 ( K^0.5/E ) a) 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? (10 points) b) Now, suppose the capital stock is not fixed (i.e. you can choose its quantity). How much workers and units of capital can the firm hire to sustain a cost of $2000? (10 points)

Explanation / Answer

The rato of marginal productivity of labor to capital shuld be equal to the ratio of priceof labor to capital.

(a) MPE/MPK = wage/ price of capital

K0.5 / 2E / E0.5 / 2K = 10/25

(K/E)1.5 = (2/5)

K=1600

E1.5 = 16000

E=2947units

(b) At the cost $2000 the budget equation will be:

10E+25K= 2000

2E+5K=400

(K/E)1.5 = (2/5)

k/E = 0.5428

K=0.5428E

Substitute this value in budget equation

10E +25x0.5428E = 2000

23.572E = 2000

E = 84.846=84 labor

K=45units

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