Consider a firm that uses two inputs to produce one output. The firm's production technology can be described by the production function y = f(21, 22) = (z1-2) (22 + 1) +2 Suppose the input prices are w = 4 per unit of input 1 and w = 1 per unit of input 2. 1. Find the firm's conditional factor demands (i.e. cost-minimizing input choices) z (y; 4, 1) and z (y; 4, 1) as functions of the target output level y > 0. Use your answer to find the firm's (long-run) cost function C(y) =W1' z(y) + w z(y) at the given input prices. 2. In the short run, the firm's second input is fixed at 2 = 9. Find the firm's short-run conditional factor demand for input 1 and the short-run cost function.