2. (10 points) Consider a competitive firm with cost function given by c(y) = 500 + 2y + 0.05y2. The price of the firms output is p > 0, and the firms profit function is (y) = py c(y). (a) (5 points) Find the formula for the profit-maximizing output level given p, namely y = y(p). (Remember to check the SOC.) (b) (5 points) Find the formula for the maximum-profit function, (p), and verify that (p) = y(p).

Q3. (10 points) Repeat problem (2) but using the following cost function: c(y) = 500 + 2y +( 1/300) y^3.