1. In this exercise, we examine the partial equilibrium model of a competitive market. Suppose we have a market with a linear demand function given by Q = 57500 p, where Q is the total amount exchanged by the market. The number of firms in the market is n. Every firm has total cost function given by C(q) = 10000q 100q^2 + q^3 . (Notice that there are no fixed costs here. There are two differences between the short and long runfixed costs can be adjusted in the latter but not in the former, and firms can enter and exit in the latter but not the former. Since there are not fixed costs here, we are focusing on the long-run effects of entry and exit. ) We assume that all of the firms are identical, which shows up in the fact that every firm has this cost function. Hence, the market quantity Q will equal n q, where q is the output per firm.

1.1 Plot the demand curve, with quantity on the horizontal axes and price on the vertical axes.

1.2 Find the necessary condition for (long-run) profit maximization for a firm in this market. Remember that the firms are perfectly competitive, so they take price as fixed when they solve their profit maximization problem.

1.3 Rewrite the demand in terms of n and q rather than Q. This is the market balance condition.

1.4 Write the expression for profits for a firm, and set this equal tot zero. This is the (long-run) equilibrium entry condition, since firms would enter the market (increasing n) if this is positive, and exist (decreasing n) if it is negative.

1.5 Parts 1.2-1.4 give you three equations in three variables, p, q, and n. Solve these equations to find the equilibrium price, quantity per firm, number of firms, and quantity sold in the market. Show that each firm earns zero profits in this equilibrium. 1.6 Let compare this with the short run. Suppose that n = 1200, i.e., there are 1200 firms in this market. Since this is the short run, this number is fixed, and hence n is no longer a variable. You thus have two variables to determine, p and q, and two conditions (the counterparts of 1.2-1.3). Find the short-run equilibrium market price and the quantity produced by each firm (the calculation are not quite as convenient as they have been). Are profits for a firm positive or negative? What adjustment we expect to occur as this market moves to its long-run equilibrium?