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1. (25 pts) A competitive firm has a cost function given by: C (y)-y2 +y+4. (a) Derive the firms marginal cost function MC (y), average variable cost function AVC(y), and average cost function AC (y) and show them on a graph. (5 pts) (b) At what output is the average cost AC (y) minimized? (5 pts) (c) Determine the short-run supply curve for this firm and show this curve on your graph. (5 pts) (d) Assume that the market price is p 13. Show on a graph the producers surplus using the three alternative methods covered in class. Use one of these methods to calculate the producers surplus. (5 pts 5 pts) 2. (30 pts) A competitive firm has a cost function that satisfies the following: (i) PS (y) 11 (y)-4 for all y, (ii) MC(0) = AVC(0) = 2 and (iii) AVC(y) = y-2 (a) Derive the firms total cost function C (y), marginal cost function MC (y), average variable cost function AVC(y), and average cost function AC (y). (5 pts) (b) Show MC, AVC, and AC functions on a graph. (5 pts) (c) Derive the short-run supply curve for this firm. (5 pts) (d) If the market price is p 12. How many units will the firm produce? (5 pts) (e) Determine the associated profit and producer surplus for the firm. (5 pts) (f) How do the maximum profit related to the producers surplus? (5 pts)I also need help with the drawings of the graphs!

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