Suppose you have a job analyzing a perfectly competitive market. The aggregate demand is C) = 72- and the cost function for the identical) firms is Cla-29 +32 (a) Consider first a short run scenario, and setup and solve the profit maximization problem over quantity Write the quantity an individual firm will produce as a function of the sale price (Points: 5) Answer: (6) For now on, take as given that the equilibrium price in the short run is P48 Solve for the quantity, and profits for each individual firm. Find the number of firms that are in the market in the short run 2 (Points: 10) Answer: (c) Write the Average Variable Cost as a function of the quantities 4. Considering the equilibrium price in the short-ran from item (b). will these firms shutdown in the short run? Explain. (Points: 5) Answer: (d) Imagine now that that we are in the long run. What will be the equilibrium in this market if the free entry assumption holds? Solve for the equilibrium price, individual quantity, aggregate quantity, number of firms, and individual firm profit (Points: 10)