A firm is a monopoly in the output market and a perfect competitor in the input market. The price of the input is w = 2. The demand curve for the output y is y = 10 p.

1. If the production function is y = x, find the quantity of input the firm will hire, the quantity of output it will produce, and the price it will charge for the output.

2. Same questions as in 1. for the production function y = x/2.