Question

* A firm produces output that can be sold at a price of $10. The Cobb-Douglas production function is given by Q = F(K,L) = K½ L½     

If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is $2?

* Given the Cobb-Douglas production function for Mabel’s factory

Q = (L0.4) * (K0.7)

a) Based on the function above, does Mabel’s factory experiencing economies or diseconomies of scale? Explain.

b) If the manager wished to raise productivity by 50% and planned to increase capital by 25%, how much would she have to increase her labor to reach that desired production level?

Answer 1

(Question 1)

Q = K^1/2L^1/2

When K = 1,

Q = L^1/2

MPL = dQ/dL = (1/2) / (L^1/2)

Hiring is optimized and profit is maximized when (Output price x MPL) = Wage rate

$10 x [(1/2) / (L^1/2)] = $2

(1/2) / (L^1/2) = 1/5

(L^1/2) = 5/2

Squaring,

L = 25/4 = 6.25

NOTE: As HOMEWORKLIB Answering Policy, 1st question has been answered.