2. A firm has a cost function that satisfies the following: (i) PS (y) - II (y) = 2 for all y, (ii) SMC (0) = AVC(0) = 1 and (iii) AVC() = (20 pts) a) Derive the firm's cost function C (y), marginal cost function SMC (y), average cost SAC (y), and average variable cost function AVC (y). Show AVC, SMC and SAC on a graph. b) Suppose the market price is 11. How many units would the firm produce? Determine the associated profit and producer surplus for the firm. 3. For the cost function given in question 2 above, determine the firm's short run supply func- tion giving its output as a function of market price, P. At what set of prices would the firm choose to shut down? Explain. (20 pts)