Question

Breakdown of a cartel agreement

Consider a town in which only two residents, Sam and Teresa, own wells that produce water safe for drinking. Sam and Teresa 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)
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 agree to split production equally. Therefore, Sam's profit is

, and Teresa's profit is

.

Suppose that Sam and Teresa 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, Sam says to himself, "Teresa and I aren't the best of friends anyway. If I increase my production to 40 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow."

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

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

and Teresa's profit becomes

.

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

.

Answer 1

Suppose Sam and Teresa form a cartel and behave as a monopolist. The profit is maximized to the level of $ 504 at price= $ 2.10. The profit-maximizing price is $ 2.10 per gallon, and the total output is 240 gallons. As part of their cartel agreement, Sam and Teresa agree to split production equally. Therefore, Sam's profit is $ 252 (504/2), and Teresa's profit is $ 252.

Suppose that Sam and Teresa 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, Sam says to himself, "Teresa and I aren't the best of friends anyway. If I increase my production to 40 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow."

After Sam implements his new plan, the total production rises to 240+40= 280 gallons. The price corresponding to 280 gallons is $ 1.75. The price of water decreases to $ 1.75 per gallon. Given Teresa and Sam's production levels, Sam's profit becomes ($ 1.75 X (120+40 gallons))= $280 and Teresa's profit becomes ( $ 1.75 X 120) $210. Total profit becomes 280+210= $490.

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

After Teresa increases her production,total production becomes 280+40= 320 gallons. The price further decreases to $1.40 and profit becomes $448. Profit will be split equally since both are producing equal quantities again. Sam's profit becomes ($1.40 X 160) $ 224 and Teresa's profit becomes ($1.40 X 160) $224. Total profit (the sum of the profits of Sam and Teresa) is now $448.

.