Question

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

, and Cho's profit is

.

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

per gallon. Given Cho and Bob's production levels, Bob's profit becomes

and Cho's profit becomes

.

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

After Cho increases her production, Bob's profit becomes

, Cho's profit becomes

, and total profit (the sum of the profits of Bob and Cho) is now

.

Answer 1

Blanks-

1) 3

2) 270

3) 810/2 = 405

4) 810/2 = 405

5) decreases

6) 2.50

7) [270/2 + 45]*2.5 = 450

8) 270/2 * 2.5 = 337.50

9) 180*2 = 360

10) 180*2 = 360

11) 360+360 = 720