Q1. (10 points)

Imagine a small town in which only two residents, Rochelle and Alec, own wells that produce safe drinking water. Each week Rochelle and Alec work together to decide how many gallons of water to pump. They bring the water to town and sell it at whatever price the market will bear. To keep things simple, suppose that Rochelle and Alec can pump as much water as they want without any cost so that the total and marginal and total costs of water equal zero (TC=MC=0). The town 's market demand curve is Q_D = 1200 - 20*P_D and the potential monopolist's marginal curve corresponding to this demand curve is given as MR = 60 - (1/10)*Q. With this information, answer the questions Q1-A ~ Q1-G

Q1-A. What is the socially efficient quantity of water?

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Q1-B. If Rochelle and Alec operate as a profit-maximizing monopoly in the market for water, what will be the monopoly's equilibrium price and quantity?

Q1-C. If Rochelle and Alec operate as a profit-maximizing monopoly in the market for water, how much profit will each of them earn, assuming that the two producers split the market equally?

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Q1-D. Suppose the town enacts new antitrust laws that prohibit Rochelle and Alec from operating as a monopoly. Now Rochelle and Alec are in an oligopoly. Let's say Q is the water quantity Rochelle produces, while Q_A is the water quantity Alec produces. Then, fill the blanks to derive Rochelle's best response function against

Alec's producing water quantity, and Alec's best response function against

Rochelle's producing water quantity.

(Hint: Note that MR_R = 60 - (1/10)*Q_R - (1/20)*Q_A, MR_A = 60 - (1/10)*Q_A - (1/20)*Q_R)

(Hint: Use the Cournot model you learned)

Q_R = ( ) + ( )*Q_A

Q_A = ( ) + ( )*Q_R

Q1-E. What will be the oligopoly equilibrium price of water, once Rochelle and Alec

reach a Nash equilibrium in the oligopoly?

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Q1-F. How many gallons of water will be produced and sold in total in this town,

once Rochelle and Alec reach a Nash equilibrium in the oligopoly?

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Q1-G. Given the answers above, compare the efficiencies among the perfectly

competitive, monopoly, and oligopoly markets.