Question

6. Suppose you have a job analyzing a perfectly competitive market. The aggregate demand is CP(p) -98 - and the cost function for the firms is Cla) -79 +35. Suppose all firms use the same cost function. (a) Setup and solve the profit maximization problem over quantity. Write the quantity an individual firm will produce as a function of the sale price. (3 points) (b) Solve for the price, quantity, and profits for each individual shop and then also for aggregate quantity in equilibrium when the number of firms is fixed at N = 42. Show your work. (Remember: In short-run equilibrium, MC and Q-0') (6 points)

Answer 1

20 - 98-PIL Ca)=7q²+35 & Proft - Po-cco) a Pq - 2q2 +35 iyon me is supply cure Р= mc - - чa It - PJ - Since there are 42 foins os = 42q = 420P/4)= 3P am Oozos = 98-P = 3P 98 = 7 P = 9882 14x2=28 q=2 0 = 98-14=84 & T from = 2802) - 7 (2)-35 so- 28-35 No fair will produs in shortsun. d) Short son en & fim con carn proht & even is achieved when MatDD ass the economic profit, occonome negatie cui propt in shorsen