Question

6. Breakdown of a cartel agreement Consider a town in which only two residents, Tim and Alyssa, own wells that produce water safe for drinking. Tim and Alyssa 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 (Gallons of water) Total Revenue (Dollars) (Dollars per gallon) 6.00 0 0 5.50 45 248 5.00 90 450 4.50 135 608 4.00 180 720 3.50 225 788 3.00 270 810 2.50 315 788 2.00 360 720 1.50 405 608 1.00 450 450 0.50 495 248 0 540 o

6. Breakdown of a cartel agreement

Consider a town in which only two residents, Tim and Alyssa, own wells that produce water safe for drinking. Tim and Alyssa 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	248
5.00	90	450
4.50	135	608
4.00	180	720
3.50	225	788
3.00	270	810
2.50	315	788
2.00	360	720
1.50	405	608
1.00	450	450
0.50	495	248
0	540	0

Suppose Tim and Alyssa 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, Tim and Alyssa agree to split production equally. Therefore, Tim's profit is

, and Alyssa's profit is

.

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

per gallon. Given Alyssa and Tim's production levels, Tim's profit becomes

and Alyssa's profit becomes

.

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

After Alyssa increases her production, Tim's profit becomes

, Alyssa's profit becomes

, and total profit (the sum of the profits of Tim and Alyssa) is now

.

Tim and Alyssa 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 Tim'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 Tim nor Alyssa has an incentive to increase output further, nor does either have an incentive to decrease output. This outcome is an example of   .

Answer 1

Tim and Alyssa has formed a cartel. They will produce that quantity corresponding to which total revenue is maximum. The total revenue is maximized when 270 gallons of water is produced and price is $3 per gallon.

Thus,

The profit-maximizing price is $3 per gallon, the total output is 270 gallons. As part of their cartel agreement, Tim and Alyssa agree to split production equally. Therefore, Tim's profit is $405, and Alyssa's profit is $405.

The cartel is producing 270 gallons of water. Now, Tim cheats on the cartel agreement and produces extra 45 gallons of water. This means Tim is now producing 180 gallons of water and Alyssa is producing 135 gallons of water. The total production is 315 gallons of water. The price at which 315 gallons of water is demanded is $2.50 per gallon. The profit of Tim would be ($2.50 * 180) $450 and the profit of Alyssa would be ($2.50 * 135) $337.5.

After Tim implements his new plan, the price of water decreases to $2.50 per gallon. Given Alyssa and Tim's production levels, Tim's profit becomes $450 and Alyssa's profit becomes $337.50.

Now, Alyssa also increases her production of water by 45 gallons. Total production is now 360 gallons and price becomes $2 per gallon and total revenue is $720.

After Alyssa increases her production, Tim's profit becomes $360, Alyssa's profit becomes $360, and total profit (the sum of the profits of Tim and Alyssa) is now $720.

Neither Tim nor Alyssa has an incentive to increase output further, nor does either have an incentive to decrease output.

This outcome is an example of Nash equilibrium.