Question

6. Suppose you have a job analyzing a perfectly competitive market. The aggregate demand is 0(p)98 p and the cost function for the firms is Ca)735. 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 cach individual shop and then also for aggregate quantity in equilibrium when the number of firms is fixed at N 42. Show your work. (Leave quantiry, price, profit, and number of firms in fractiovdecimai form. Do not round your answers.) (6 points) e) Will these firms shutdown in the short nun? Explain. (2 points) (d) Define the short run competitive equilibrium. Compare this definition to your answer from part b (5 points) (c) What will be the long-run (free entry) equilibrium in this market where the number of firms is flexible? Solve for the equilibrium price, individual quantity, aggregate quantity, number of firms, and individual firm profit. (Leave quantity, price, profit, and number of firms in fractionvdecimal form. Do not round your answers.) (6 points) () Define a free entry competitive equilibrium. Compare this definition to your answer from the previous part (6 points) (g) Graph the equilibrium in the short run and in the long run on the graph below. That is, graph the aggregate demand, the short run aggregate supply, and the long run aggregate supply curves and then plot the long run cquilibrium point and the short run equilibrium point. Aggregate quantity is on the horizontal axis and price is on the vertical axis. 3 points) 300 250 200 150 50

Answer 1

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