Homework #5 1. Slick Willies produces Soul Glo hair product by employing labor and capital according to the production function: q = 3421Ki. a) What are the returns to scale for Slick Willies? b) If r = $40/unit of capital and w = $10/worker, what is the optimal input bundle for 9 = 100? c) What is Slick Willies total cost function with respect to q, w and r? 2. A firm that competes in a perfectly competitive industry has a short run cost function: C(q) = 30g - 8q' + q' (1) a) For this firm, what are: FC, VC, MC, ATC, AVC, and AFC? b) If this industry is in equilibrium (recall the conditions for equilibrium), what will be the profit maximizing output for our firm and what will be profits? 3. A perfectly competitive firm has short run total cost function of the form: C(q) = 1000 + 50g - q2 + 0.01q3 (2) a) Define this firm's supply curve (Hint: it will be defined by a price). 4. A firm has the following production function: 9 = LiKi (3) a) What is the firm's total cost function? b) What is the firm's short run total cost function when capital is fixed at K = 16? c) What are the answers to a) and b) when w = $10 and r = $15