Breakdown of a cartel agreement

Consider a town in which only two residents, Larry and Megan, own wells that produce water safe for drinking. Larry and Megan 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 Larry and Megan 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, Larry and Megan agree to split production equally. Therefore, Larry's profit is, and Megan's profit is.

Suppose that Larry and Megan 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, Larry says to himself, "Megan and I aren't the best of friends anyway. If I increase my production to 45 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow."

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

Because Larry has deviated from the cartel agreement and increased his output of water to 45 gallons more than the cartel amount, Megan decides that she will also increase her production to 45 gallons more than the cartel amount.

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

True or False: Based on the fact that both Larry and Megan increased production from the initial cartel quantity, you know that the output effect was larger than the price effect at that quantity.

True

False

Larry and Megan have each cheated on their cartel agreement and increased production by 45 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 Larry's profit when he produces 90 gallons more than the cartel amount compared to his profit when he produces 45 gallons more than the cartel amount.)

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