6. Breakdown of a cartel agreement 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.
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 Lorenzo and Neha 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, 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 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 Lorenzo implements his new plan, the price of water to
$
per gallon. Given Neha and Lorenzo's production levels, Lorenzo's profit becomes
$
and Neha's profit becomes
$
.
Because Lorenzo has deviated from the cartel agreement and increased his output of water to 35 gallons more than the cartel amount, Neha decides that she will also increase her production to 35 gallons more than the cartel amount.
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 .