6. The cartel

Consider a town in which only two residents, Lorenzo and Neha, own wells that produce water safe for drinking. Lorenzo and Neha 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.

PriceQuantity DemandedTotal Revenue(Dollars per gallon)(Gallons of water)(Dollars)6.00005.5045247.505.0090450.004.50135607.504.00180720.003.50225787.503.00270810.002.50315787.502.00360720.001.50405607.501.00450450.000.50495247.5005400

Suppose Lorenzo and Neha form a cartel and behave as a monopolist. The profit-maximizing price isper gallon, and the total output isgallons. As part of their cartel agreement, Lorenzo and Neha agree to split production equally. Therefore, Lorenzo's profit is, and Neha's profit is.

Suppose that Lorenzo and Neha 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, Lorenzo says to himself, "Neha and I aren't the best of friends anyway. If I increase my production by 45 gallons, I can increase my profit even though her profit goes down. I will do that starting tomorrow."

After Lorenzo implements his new plan, the price of water toper gallon. Given Neha and Lorenzo's production levels, Lorenzo's profit becomesand Neha's profit becomes.

Because Lorenzo has deviated from the cartel agreement and increased his output of water by 45 gallons, Neha decides that she will also increase her production by 45 gallons.

After Neha increases her production, Lorenzo's profit becomes, Neha's profit becomes, and total profit (the sum of the profits of Lorenzo and Neha) is now.

Note that Lorenzo and Neha started by behaving cooperatively. However, once Lorenzo decided to cheat, Neha decided to cheat as well. In other words, Neha's output decisions are based on Lorenzo's actions.

This behavior is an example of .

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