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. Assume that outside water cannot be transported into the town for sale. The following questions will walk you through how to compute the Cournot quantity competition outcome for these duopolists.
Price Quantity Demanded Total Revenue
(Dollars per gallon) (Gallons of water) (Dollars)
3.60 0 0
3.30 35 $115.50
3.00 70 $210.00
2.70 105 $283.50
2.40 140 $336.00
2.10 175 $367.50
1.80 210 $378.00
1.50 245 $367.50
1.20 280 $336.00
0.90 315 $283.50
0.60 350 $210.00
0.30 385 $115.50
0 420 0
Suppose Kenji and Lucia 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, 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 35 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 (increases/decreases) to per 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 35 gallons more than the cartel amount, Lucia decides that she will also increase her production to 35 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 .