Breakdown of a cartel agreement

Consider a town in which only two residents, Sam and Teresa, ownwells that produce water safe for drinking. Sam and Teresa can pumpand sell as much water as they want at no cost. For them, totalrevenue equals profit. The following table shows the town's demandschedule for water.

Price	Quantity Demanded	Total Revenue
(Dollars per gallon)	(Gallons of water)	(Dollars)
4.20	0	0
3.85	40	$154.00
3.50	80	$280.00
3.15	120	$378.00
2.80	160	$448.00
2.45	200	$490.00
2.10	240	$504.00
1.75	280	$490.00
1.40	320	$448.00
1.05	360	$378.00
0.70	400	$280.00
0.35	440	$154.00
0	480	0

Suppose Sam and Teresa 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, Sam and Teresa agreeto split production equally. Therefore, Sam's profit is

, and Teresa's profit is

.

Suppose that Sam and Teresa have been successfully operating asa cartel. They each charge the monopoly price and sell half of themonopoly quantity. Then one night before going to sleep, Sam saysto himself, \"Teresa and I aren't the best of friends anyway. If Iincrease my production to 40 gallons more than the cartel amount, Ican increase my profit even though her profit goes down. I will dothat starting tomorrow.\"

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

per gallon. Given Teresa and Sam's production levels, Sam'sprofit becomes

and Teresa's profit becomes

.

Because Sam has deviated from the cartel agreement and increasedhis output of water to 40 gallons more than the cartel amount,Teresa decides that she will also increase her production to 40gallons more than the cartel amount.

After Teresa increases her production, Sam's profit becomes

, Teresa's profit becomes

, and total profit (the sum of the profits of Sam and Teresa) isnow

.