Question 5:
Suppose that the production technology is fully characterized by the Cobb-Douglas production function q = f (L,K) = ALαKβ with α+β < 1 and A,α,and β all greater than zero.
MPL = AαLα-1Kβ and MPK = AβLαKβ-1 .
(a) Does this production process have increasing, decreasing or constant returns to scale?
(b) Set up the cost minimization problem and solve for the conditional labor and capital demands.
(c) Derive the cost function and simplify the function as much as you can.
Question 3.
A manufacturing firm's production function is Q = KL + K +L. For this production function, MPL = K + 1 and MPK = L + 1. Suppose that the price r of capital services is equal to 1, and let w denote price of the labour services. If the firm is required to produce 5 units of output, for what values of w would a cost-minimizing firm use
a) only labour?
b) only capital?
c) both labour and capital?