1. A competitive firm has a cost function given by C (y) = 9+ y + . (20 pts) a) Derive the SAC, SMC and AV C functions and show them on a graph. At what output is SAC minimized? Determine the short run supply function for this firm and show it on your graph. Why is SMC (y) = AVC (y) aty = 07 b) Assume that the market price is p = 11. Compute the producer surplus at p = 11 using the following twe methods: (i) [p AVC (y)]y and (ii} the area to the left of the supply curve under the price. Show these measures on your graph. 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) 22%CM = 1 (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 funec- 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) 4. Consider three firms out of a competitive industry. They have the following technologies: Ci(y) = v*+y; Ca(y) = 2+2y; C3(y) = y*+3y. Show these firms' individual supply functions on a graph. Construct an aggregate supply function for these three firms on your graph. (20 pts) 5. Again consider three firms out of a competitive industry. They have the following technolo- gies: C1 = y2 +16; Cy = y + y + 16; C3 = y2 + 2y + 16. (20 pts) a) For cach firm derive the SAC, SMC, and AVC. Show these curves on three graphs, one for each firm. b) Suppose that in the short run the market price is 9. Show each firm's profit on your graphs. Should all of these firms produce? Explain