Consider production function y = x if x<5, and y =0.5 x + 2.5 otherwise.

a. What is the profit maximizing input (and output) given prices p and w for the output and input respectively? Given these levels what is the total profit.

b. Suppose if the firm produces 0 output, it faces 0 costs. But to produce any output at all, it must pay a fixed cost of 5. What is the profit maximizing input (and output) given prices p and w for the output and input respectively? Given these levels what is the total profit