3. Breakdown of a cartel agreement

Consider a town in which only two residents, Amrit and Aideen, own wells that produce water safe for drinking. Amrit and Aideen 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)
6.00	0	0
5.50	45	$247.50
5.00	90	$450.00
4.50	135	$607.50
4.00	180	$720.00
3.50	225	$787.50
3.00	270	$810.00
2.50	315	$787.50
2.00	360	$720.00
1.50	405	$607.50
1.00	450	$450.00
0.50	495	$247.50
0	540	0

Suppose Amrit and Aideen 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, Amrit and Aideen agree to split production equally. Therefore, Amrit's profit is

, and Aideen's profit is

.

Suppose that Amrit and Aideen 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, Amrit says to himself, "Aideen 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 Amrit implements his new plan, the price of water to

per gallon. Given Aideen and Amrit's production levels, Amrit's profit becomes

and Aideen's profit becomes

.

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

After Aideen increases her production, Amrit's profit becomes

, Aideen's profit becomes

, and total profit (the sum of the profits of Amrit and Aideen) is now

.

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

True

False

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

This behavior is an example of .