Question

Suppose the production function of a firm is: Q =100L^0.5K^0.5
The price per unit of capital (r) and labor (w) are $40 and $50, respectively.

a) Determine the type of returns to scale.

b) If the firm is contracted to produce 1118 units of output, determine the quantity of
capital and labor that the firm should use to minimize the total costs.

c) Using bordered Hessian, prove that the second-order conditions for minimum is
satisfied.

d) Prove that the combination of capital and labor inputs derived in (b) is the efficient
combination of capital and labor [Hint: Efficient combination of K and L is achieved
when MPL/MPK= w/r].