Question

3. 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)
3.00	0	0
2.75	50	$137.50
2.50	100	$250.00
2.25	150	$337.50
2.00	200	$400.00
1.75	250	$437.50
1.50	300	$450.00
1.25	350	$437.50
1.00	400	$400.00
0.75	450	$337.50
0.50	500	$250.00
0.25	550	$137.50
0	600	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 50 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 50 gallons more than the cartel amount, Teresa decides that she will also increase her production to 50 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

.

True or False: Based on the fact that both Sam and Teresa increased production from the initial cartel quantity, you know that the output effect was larger than the price effect at that quantity.

True

False

Note that Sam and Teresa started by behaving cooperatively. However, once Sam decided to cheat, Teresa decided to cheat as well. In other words, Teresa's output decisions are based on Sam's actions.

This behavior is an example of   .

Answer 1

From the table in the question the “total revenue” is maximum at “P=$1.5 per gallon” and output production is “Q=300 gallon”. If Sam and Teresa form a cartel and behave as a monopolist, then the profit maximizing price is “P=$1.5 per gallon”, and the total output is “Q=300 gallons”.

As part of their cartel agreement, Sam and Teresa agree to split production equally, => both will produce “300/2 = 150 gallon water”. Therefore, Sam's profit is “450/2 = $225”, and Teresa's profit is “$225”.

After Sam implements his new plan, the total production increases to “Q=300+50 = 350 gallon”, => the price of water “decreases” to “$1.25 per gallon”. Given Teresa and Sam's production levels, Sam's profit becomes “P*q1 = 1.25*(150+50) = $250” and Teresa's profit becomes “P*q2 = 1.25*150 = $187.5”, and the total profit is now “$250+$187.5 = $437.5.

Here as the Sam increases its production that will increase the total production and decrease the market price, where total revenue also decreases to “$437.5” from “$450”. So, here the price effect is larger than the output effect, => the given statement is FALSE.

Sam and Teresa started by behaving cooperatively. However, once Sam decided to cheat, Teresa decided to cheat as well. In other words, Teresa's output decisions are based on Sam's actions.

This behavior is an example of “tit-for-tat strategy”.