Question

Consider a town in which only two residents, Kenji and Lucia, own wells that produce water safe for drinking. Kenji and Lucia 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	30	$115.50
3.50	60	$210.00
3.15	90	$283.50
2.80	120	$336.00
2.45	150	$367.50
2.10	180	$378.00
1.75	210	$367.50
1.40	240	$336.00
1.05	270	$283.50
0.70	300	$210.00
0.35	330	$115.50
0	360	0

Suppose Kenji and Lucia form a cartel and behave as a monopolist. The profit-maximizing price isper gallon, and the total output isgallons. As part of their cartel agreement, Kenji and Lucia agree to split production equally. Therefore, Kenji's profit is, and Lucia's profit is

.

Suppose that Kenji and Lucia 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, Kenji says to himself, "Lucia and I aren't the best of friends anyway. If I increase my production to 30 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow."

After Kenji implements his new plan, the price of water   toper gallon. Given Lucia and Kenji's production levels, Kenji's profit becomes and Lucia's profit becomes

.

Because Kenji has deviated from the cartel agreement and increased his output of water to 30 gallons more than the cartel amount, Lucia decides that she will also increase her production to 30 gallons more than the cartel amount.

After Lucia increases her production, Kenji's profit becomes, Lucia's profit becomes, and total profit (the sum of the profits of Kenji and Lucia) is now

.

True or False: Based on the fact that both Kenji and Lucia 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 Kenji and Lucia started by behaving cooperatively. However, once Kenji decided to cheat, Lucia decided to cheat as well. In other words, Lucia's output decisions are based on Kenji's actions.

This behavior is an example of   .

Answer 1

Both residents can draw water at zero cost.

So, total revenue indicates their total profit. Their total profit is maximum when 180 gallons of water is drawn. The maximum total profit is $378.

Both split production and profit equally.

So,

Kenji's profit is $189, and Lucia's profit is $189.

Now, Kenji increases his production by 30 gallons of water. Now, total production is 210 gallons. Price corresponding to 210 gallons is $1.75

After Kenji implements his new plan, the price of water decreases to $1.75 per gallon.

Given Lucia and Kenji's production levels, Kenji's profit becomes $210 and Lucia's profit becomes $157.50.

Now, Lucia also increases her production by 30 gallons of water.

After Lucia increases her production, Kenji's profit becomes $168, Lucia's profit becomes $168, and total profit is now $336.

Total profit has declined which means price effect is larger than output effect.

Thus, the given statement is False.

The given behavior is example of Tit-for-Tat Strategy.