Answered: Consider a town in which only two…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider a town in which only two residents, Hubert and Kate, own wells that produce water safe for drinking. Hubert and Kate can pump and sell as much water as they want at no cost. For them, total revenue equals profit. The following table shows the town's demand schedule for water.

Price	Quantity Demanded	Total Revenue
(Dollars per gallon)	(Gallons of water)	(Dollars)
3.60	0	0
3.30	35	116
3.00	70	210
2.70	105	284
2.40	140	336
2.10	175	368
1.80	210	378
1.50	245	368
1.20	280	336
0.90	315	284
0.60	350	210
0.30	385	116
0	420	0

Suppose Hubert and Kate form a cartel and behave as a monopolist. The profit-maximizing price is

per gallon, and the total output is

gallons. As part of their cartel agreement, Hubert and Kate agree to split production equally. Therefore, Hubert's profit is

, and Kate's profit is

Suppose that Hubert and Kate have been successfully operating as a cartel. They each charge the monopoly price and sell half of the monopoly quantity. Then one night before going to sleep, Hubert says to himself, "Kate and I aren't the best of friends anyway. If I increase my production to 35 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow."

After Hubert implements his new plan, the price of water to

per gallon. Given Kate and Hubert's production levels, Hubert's profit becomes

and Kate's profit becomes

Because Hubert has deviated from the cartel agreement and increased his output of water to 35 gallons more than the cartel amount, Kate decides that she will also increase her production to 35 gallons more than the cartel amount.

After Kate increases her production, Hubert's profit becomes

, Kate's profit becomes

, and total profit (the sum of the profits of Hubert and Kate) is now

Hubert and Kate have each cheated on their cartel agreement and increased production by 35 gallons more than the cartel amount. However, they both realize that if they continue to increase output beyond this amount, they'll each suffer a decrease in profit. (To see this for yourself, consider Hubert's profit when he produces 70 gallons more than the cartel amount compared to his profit when he produces 35 gallons more than the cartel amount.)

Neither Hubert nor Kate has an incentive to increase output further, nor does either have an incentive to decrease output. This outcome is an example of .

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