Deborah can pump and sell as much water as they want at no cost. For them, total

Question

Deborah 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. Suppose Carlos and Deborah 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, Carlos and Deborah agree to split production equally. Therefore, Carlos's profit is $________, and Deborah's profit is $__________. Suppose that Carlos and Deborah 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, Carlos says to himself, "Deborah 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 Carlos implements his new plan, the price of water________to $________per gallon. Given Deborah and Carlos's production levels, Carlos's profit becomes $__________and Deborah's profit becomes $_________. Because Carlos has deviated from the cartel agreement and increased his output of water to 45 gallons more than the cartel amount, Deborah decides that she will also increase her production to 45 gallons more than the cartel amount. After Deborah increases her production, Carlos's profit becomes $__________, Deborah's profit becomes $_________, and total profit (the sum of the profits of Carlos and Deborah) is now $_________.

Explanation / Answer

Suppose Carlos and Deborah form a cartel and behave as a monopolist. Since, these two are behaving like monopolist, they will charge as price at which their total revenue is at maximum. The given table shows that total revenue is maximum when $3 per gallon is charged. So, the profit maximizing price is $3 per gallon and total output is 270 gallons.

As part of their cartel agreement, Carlos and Deborah agree to split production and thereby revenue or profit equally. Therefore, Carlos’s profit is $405 and Deborah’s profit is $405.

Now, Carlos has decided to increase his production by 45 gallons. If he does so, total production will become (270 + 45) 315 gallons. The provided table shows that 315 gallons are demanded at $2.50 per gallon.

So, after Carlos implements his new plan, the price of water decreases to $2.50 per gallon. Given the Deborah and Carlos’s production level, Carlos’s profit becomes (180 * $2.50) $450 and Deborah’s profit becomes (135 * $2.50) $337.5.

Now, Deborah also increases the production by 45 gallons. Total production becomes 360 gallons. This production translates into total revenue or profit of $720. As both split profit equally, each will get $360.

So, after Deborah increases her production, Carlos’s profit becomes $360, Deborah’s profit becomes $360, and the total profit is now $720.

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