3. Breakdown of a cartel agreement
Consider a town in which only two residents, Musashi and Rina, own wells that produce water safe for drinking. Musashi and Rina 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 Musashi and Rina 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, Musashi and Rina agree to split production equally. Therefore, Musashi's profit is
$
, and Rina's profit is
$
.
Suppose that Musashi and Rina 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, Musashi says to himself, "Rina 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 Musashi implements his new plan, the price of water to
$
per gallon. Given Rina and Musashi's production levels, Musashi's profit becomes
$
and Rina's profit becomes
$
.
Because Musashi has deviated from the cartel agreement and increased his output of water to 45 gallons more than the cartel amount, Rina decides that she will also increase her production to 45 gallons more than the cartel amount.
After Rina increases her production, Musashi's profit becomes
$
, Rina's profit becomes
$
, and total profit (the sum of the profits of Musashi and Rina) is now
$
.
True or False: Based on the fact that both Musashi and Rina increased production from the initial cartel quantity, you know that the output effect was larger than the price effect at that quantity.

True
False
Musashi and Rina 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 Musashi'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 Musashi nor Rina has an incentive to increase output further, nor does either have an incentive to decrease output. This outcome is an example of .