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)
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 Bob and Cho 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, 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 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 Bob implements his new plan, the price of water toper 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 40 gallons more than the cartel amount, Cho decides that she will also increase her production to 40 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.

Suppose Bob and Cho form a cartel and behave as a monopolist. The profit-maximizing price is 2.10  per gallon, and the total output is 240 gallons. As part of their cartel agreement, Bob and Cho agree to split production equally. Therefore, Bob's profit is $252 and Cho's profit is $252.

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 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 Bob implements his new plan, the price of water  decreases to 1.75     per gallon. Given Cho and Bob's production levels, Bob's profit becomes  280 and Cho's profit becomes  210 . Because Bob has deviated from the cartel agreement and increased his output of water to 40 gallons more than the cartel amount, Cho decides that she will also increase her production to 40 gallons more than the cartel amount. After Cho increases her production, Bob's profit becomes 224 , Cho's profit becomes 224 , and total profit (the sum of the profits of Bob and Cho) is now 448.

Explanation:

Suppose Bob and Cho form a cartel and behave as a monopolist. The profit-maximizing price is 2.10  per gallon, and the total output is 240 gallons. As part of their cartel agreement, Bob and Cho agree to split production equally. Therefore, Bob's profit is $252 and Cho's profit is $252.

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 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 Bob implements his new plan, the price of water  decreases to 1.75     per gallon. Given Cho and Bob's production levels, Bob's profit becomes  280 and Cho's profit becomes  210 . Because Bob has deviated from the cartel agreement and increased his output of water to 40 gallons more than the cartel amount, Cho decides that she will also increase her production to 40 gallons more than the cartel amount. After Cho increases her production, Bob's profit becomes 224 , Cho's profit becomes 224 , and total profit (the sum of the profits of Bob and Cho) is now 448.