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(a) What is the relative price of xd in terms of xh from the prime ministers point of view? (b) Find the policy bundle that maximizes the prime ministers utility subject to the govern- ments budget constraint. (c) What is the share of the governments 1999 budget that the prime minister decides to spend on health care? (d) How would your answer to question (c) change if the prime ministers preferences were represented by the following utility function: v Workouts book; write your answers instead on a separate sheet to be handed in. Be sure to show your work.

Exercise #1. Consider a monopolist whose cost function is: c (y) = 2y, where y is the amount of output produced by the monopolist. The monopolist faces a market demand curve described by equation QD(p) = 11 p 2 , where QD is the quantity demanded when the price of a unit of output is equal to p. The monopolist's goal is to maximize its profits. (a) [10 pts.] Calculate the monopolist's optimal level of output. What price does the monopolist charge for its output? (b) [10 pts.] Calculate consumers' surplus given the monopolist's optimal choices for price and output. In addition, compute producer's surplus (i.e. the monopolist's profits). What is the total amount of surplus generated by this market? (c) [10 pts.] Suppose now that the government enacts regulatory legislation requiring the monopolist to behave competitively. That is, the government requires the monopolist to set the price of its output equal to marginal cost. How much output does the monopolist produce? What price does the monopolist charge? Calculate producer's surplus and consumers' surplus given the competitive values of price and output. Verify that total surplus is higher than in part (c). Calculate the deadweight loss of monopoly in this market. Exercise #2. The US pharmaceutical company Pharmacia holds a patent on drug P in the US and an analogous patent in Canada. Its marketing department has identified the following inverse demand curves for drug P by US and Canadian consumers: pUS = 1,000 yUS pCA = 500 yCA, where yUS and yCA denote the quantity demanded by US and Canadian consumers, while pUS and pCA denote the price (expressed in US $) at which the drug is sold in the US and Canada respectively. 1 The cost of producing y units of drug P is given by the cost function c (y) = 100y. (a) [10 pts.] Suppose that Pharmacia can sell drug P at different prices in the US and Canada (third degree price discrimination). What price will it charge in the US and which price will it charge in Canada in order to maximize its profits? (b) [10 pts.] Compute the profits that Pharmacia makes in the US market and in the Canadian market. Also compute the surplus of US consumers and the surplus of Canadian consumers. In a diagram (with y on the x-axis and p on the y-axis) illustrate the US inverse demand curve, the firm's cost function, the US equilibrium price, the profits that Pharmacia makes in the US, and the surplus of US consumers. Draw a second diagram for Canada. (c) [15 pts.] Suppose now that US consumers can buy the same drug P in Canada via internet at the Canadian price, without Pharmacia being able to stop these trades (assume also that shipping costs are zero). What price will Pharmacia set for its drug in Canada? [Hint: in this case the monopolist faces only one market with demand given by the sum of the US and Canadian demands. Therefore, the monopolist has to decide only one price at which to sell its drug. Be careful, when summing up the two demand curves, to remember that for pUS > 1,000, yUS = 0 and for pCA > 500, yCA = 0. See the class on aggregation of demand curves.] (d) [5 pts.] Compute the profits that Pharmacia makes and the surplus that US and Canadian consumers enjoy in (c). What has happened? Why? Exercise #3. Steel firm A is situated along the banks of the Allegheny river. Further downstream is fishery B. The cost function of A is given by cA(s, x) = 5s2 + (1 x)2 , where s denotes the quantity of steel produced by A in a year and x denotes the quantity of pollutants that A dumps into the Allegheny in a given year. Thus, A can decrease its production costs by dumping more pollutants into the river. Pollutants increase the cost of production for the fishery B, whose cost function is cB(f, x) = f2 + 2x,

(b) [10 pts.] Compute the profit maximizing quantity of fish f caught by B (assuming B behaves competitively in the output market, i.e., taking the price of fish as given). Notice that B does not choose x. Also, compute B's profits. (c) [10 pts.] Suppose now that the two firms A and B merge, creating A&B. The management of A&B now maximizes A&B's profits by appropriately choosing x,s, and f. Find the quantities of steel, fish, and pollutants that the new firm produces. Also, find the profits of A&B. 2

Exercise #1. Consider a monopolist whose cost function is: c (y) = 2y, where y is the amount of output produced by the monopolist. The monopolist faces a market demand curve described by equation QD(p) = 11 p 2 , where QD is the quantity demanded when the price of a unit of output is equal to p. The monopolist's goal is to maximize its profits. (a) [10 pts.] Calculate the monopolist's optimal level of output. What price does the monopolist charge for its output? (b) [10 pts.] Calculate consumers' surplus given the monopolist's optimal choices for price and output. In addition, compute producer's surplus (i.e. the monopolist's profits). What is the total amount of surplus generated by this market? (c) [10 pts.] Suppose now that the government enacts regulatory legislation requiring the monopolist to behave competitively. That is, the government requires the monopolist to set the price of its output equal to marginal cost. How much output does the monopolist produce? What price does the monopolist charge? Calculate producer's surplus and consumers' surplus given the competitive values of price and output. Verify that total surplus is higher than in part (c). Calculate the deadweight loss of monopoly in this market. Exercise #2. The US pharmaceutical company Pharmacia holds a patent on drug P in the US and an analogous patent in Canada. Its marketing department has identified the following inverse demand curves for drug P by US and Canadian consumers: pUS = 1,000 yUS pCA = 500 yCA, where yUS and yCA denote the quantity demanded by US and Canadian consumers, while pUS and pCA denote the price (expressed in US $) at which the drug is sold in the US and Canada respectively. 1 The cost of producing y units of drug P is given by the cost function c (y) = 100y. (a) [10 pts.] Suppose that Pharmacia can sell drug P at different prices in the US and Canada (third degree price discrimination). What price will it charge in the US and which price will it charge in Canada in order to maximize its profits? (b) [10 pts.] Compute the profits that Pharmacia makes in the US market and in the Canadian market. Also compute the surplus of US consumers and the surplus of Canadian consumers. In a diagram (with y on the x-axis and p on the y-axis) illustrate the US inverse demand curve, the firm's cost function, the US equilibrium price, the profits that Pharmacia makes in the US, and the surplus of US consumers. Draw a second diagram for Canada. (c) [15 pts.] Suppose now that US consumers can buy the same drug P in Canada via internet at the Canadian price, without Pharmacia being able to stop these trades (assume also that shipping costs are zero). What price will Pharmacia set for its drug in Canada? [Hint: in this case the monopolist faces only one market with demand given by the sum of the US and Canadian demands. Therefore, the monopolist has to decide only one price at which to sell its drug. Be careful, when summing up the two demand curves, to remember that for pUS > 1,000, yUS = 0 and for pCA > 500, yCA = 0. See the class on aggregation of demand curves.] (d) [5 pts.] Compute the profits that Pharmacia makes and the surplus that US and Canadian consumers enjoy in (c). What has happened? Why? Exercise #3. Steel firm A is situated along the banks of the Allegheny river. Further downstream is fishery B. The cost function of A is given by cA(s, x) = 5s2 + (1 x)2 , where s denotes the quantity of steel produced by A in a year and x denotes the quantity of pollutants that A dumps into the Allegheny in a given year. Thus, A can decrease its production costs by dumping more pollutants into the river. Pollutants increase the cost of production for the fishery B, whose cost function is cB(f, x) = f2 + 2x, where f denotes the quantity of fish caught in a given year. Notice that the cost of fishing f fish increases with x. Suppose that the unit price of fish is $1 and that the unit price of steel is $10. (a) [10 pts.] Compute the profit maximizing quantity of steel s and pollutant x produced by A (assuming A behaves competitively in the output market, i.e., taking the price of steel as given). Also, compute A's profits. (b) [10 pts.] Compute the profit maximizing quantity of fish f caught by B (assuming B behaves competitively in the output market, i.e., taking the price of fish as given). Notice that B does not choose x. Also, compute B's profits. (c) [10 pts.] Suppose now that the two firms A and B merge, creating A&B. The management of A&B now maximizes A&B's profits by appropriately choosing x,s, and f. Find the quantities of steel, fish, and pollutants that the new firm produces. Also, find the profits of A&B. 2

Consider a competitive industry consisting of a large number of identical price-taking firms, each of which has the cost function: c(y) = 4y2 + 16 if y > 0 c(y) = 0if y = 0, where y is the output of a typical firm. The market demand curve in this industry is described by the equation: QD(p) = 200 2p, where QD(p) is the quantity demanded when the market price is p. (a) Suppose that there are N firms in the industry. Derive the equation of the industry supply curve (i.e. express total industry supply as a function of N and p). (b) Determine the long-run equilibrium number of firms in this industry. What is the equilibrium price of the good? How much output does a typical firm produce? What is the total amount of output produced in this market? What are the profits earned by a typical firm? What is the surplus of consumers? (c) Suppose now that the government decides to subsidize this industry by rebating to consumers 50% of the sales price of the good. That is, if the market price of the good is p, then consumers pay only 0.5p in order to obtain a unit of the good. Assuming that the number of firms remains fixed (in the short-run) at the value determined in part (b), compute the new equilibrium price (i.e., the price received by firms). What price do consumers pay? How much output does a typical firm produce? What is the total amount of output produced in the market? What are the profits earned by a typical firm? (d) After the imposition of the subsidy, what is the new long-run equilibrium number of firms in this industry? How many new firms enter the industry as a result of the government subsidy? (e) Suppose that, instead of being competitive, the industry is a monopoly. The monopolist has the same cost function as one of the typical firms above. What is the price chosen by the monopolist? What is the quantity of the good produced? What are the profits of the monopolist? What is the surplus of consumers? (f) Repeat the subsidy exercise of point (c) for the monopolist. How does the subsidy affect the price of the good received by the monopolist? How does it affect the quantity produced? 1

Consider a competitive industry consisting of a large number of identical price-taking firms, each of which has the cost function: c(y) = 4y2 + 16 if y > 0 c(y) = 0if y = 0, where y is the output of a typical firm. The market demand curve in this industry is described by the equation: QD(p) = 200 2p, where QD(p) is the quantity demanded when the market price is p. (a) Suppose that there are N firms in the industry. Derive the equation of the industry supply curve (i.e. express total industry supply as a function of N and p). (b) Determine the long-run equilibrium number of firms in this industry. What is the equilibrium price of the good? How much output does a typical firm produce? What is the total amount of output produced in this market? What are the profits earned by a typical firm? What is the surplus of consumers? (c) Suppose now that the government decides to subsidize this industry by rebating to consumers 50% of the sales price of the good. That is, if the market price of the good is p, then consumers pay only 0.5p in order to obtain a unit of the good. Assuming that the number of firms remains fixed (in the short-run) at the value determined in part (b), compute the new equilibrium price (i.e., the price received by firms). What price do consumers pay? How much output does a typical firm produce? What is the total amount of output produced in the market? What are the profits earned by a typical firm? (d) After the imposition of the subsidy, what is the new long-run equilibrium number of firms in this industry? How many new firms enter the industry as a result of the government subsidy? (e) Suppose that, instead of being competitive, the industry is a monopoly. The monopolist has the same cost function as one of the typical firms above. What is the price chosen by the monopolist? What is the quantity of the good produced? What are the profits of the monopolist? What is the surplus of consumers? (f) Repeat the subsidy exercise of point (c) for the monopolist. How does the subsidy affect the price of the good received by the monopolist? How does it affect the quantity produced? 1