Question

Consider a profit maximizing competitive firm with the following production function: y=L^α+K^β where
0 <α< 1 and 0 <β< 1. The firm can purchase labor (L) and capital (K) it wants in competitive input market at unit prices of w and r, respectively. The market price of the firm’s output is p.

a) Find the profit maximizing quantities of labor, L* and capital, K* and output, Y*.

b) Is Y* an increasing function of output price?

c) How does the profit maximizing level of output change when the rental rate of capital is decreased?