Price Quantity Demanded Total Revenue Dollars per gallon) (Gallons of water) (Do

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Price Quantity Demanded Total Revenue Dollars per gallon) (Gallons of water) (Dollars) 3.60 3.30 3.00 2.70 2.40 2.10 1.80 1.50 1.20 0.90 0.60 0.30 0 0 35 70 105 140 175 210 245 280 315 350 385 420 0 $115.50 $210.00 $283.50 $336.00 $367.50 $378.00 $367.50 $336.00 $283.50 $210.00 $115.50 0 Suppose Alex and Becky form a cartel and behave as a monopolist. The profit-maximizing price is $ IS and Becky's profit is $ per gallon, and the total output gallons. As part of their cartel agreement, Alex and Becky agree to split production equally. Therefore, Alex's profit is $ Suppose that Alex and Becky 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, Alex says to himself, "Becky 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."

Explanation / Answer

From the beginning: a cartel means that they maximize the profits by looking at the entire demand schedule. It is easy to see that profits are maximized at a price of $1.80. At that price, output is 210 (and total profits are $378). Since they split production equally, divide these numbers by 2. Each will have a profit of $189.

When alex, by himself, increases production by 35, and before Becky changes her production, total production will increase by 35 from the previous level of 210. That would be a total production of 245, and at that level, the market price would be $1.5. So the market price decreases. At a price of $1.5, with Alex increasing his share of production from 105 to 140, he would earn a profit of $210. Becky's profit would be the new price of $1.50 times her (unchanged) output of 105, or $157.5. The total profit is the sum of $210 and $157.5, or $367.5. This matches the total profit in the table for a price of $1.50.

Now, when Becky responds and also raises her output, the answers depend on how much she raises output. I will assume she increases output by 35, same as Alex. This means that total output will increase by another 35, to 280, with each having the same output of 140. At an output level of 280, the market price lowers to $1.2, and with each having an output of 140, the profit for each will be $168. If Becky's output increased by a different amount than 35, you would need to find the market price from the total output level of the two, and figure profits based on that price times each person's quantity

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