2 Production with fixed costs A firm produces a single output from two inputs. Suppose the price of output is 1 and input prices are w1, W2 > 0. The firm's production function is f ( 21, 2 2 ) = 27 , 22 2 1 , 22 0. Input 2 captures fixed factors of production, such as buildings and equipment; input 1 captures the materials used to make the output good using the fixed factors. 1. Calculate the firm's cost function. (Be careful to include the case q = 0!) 2. Suppose a > 1. Does the firm have a profit-maximizing output level? Why or why not? 3. Suppose o = 1. What is the firm's profit-maximizing output level when w1 2 1? What about when wi