Suppose that there is a town in which only two of the residents, Dmitri and Kris

Question

Suppose that there is a town in which only two of the residents, Dmitri and Kristen, own wells that produce water safe for drinking, and suppose that Dmitri and Kristen 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 Dmitri and Kristen form a cartel and behave as a monopolist. Now, the profit-maximizing price is per litre, and the total output is litres. As part of their cartel agreement, Dmitri and Kristen agree to split production equally. Therefore, Dmitri's profit is , and Kristen's profit is Suppose that Dmitri and Kristen 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, Dmitri says to himself, "Kristen and I aren't the best of friends anyway. If I increase my production to 250 litres more than the cartel amount, I can increase my profit, even though her profit goes down. I will do that starting tomorrow." After Dmitri implements his new plan, the price of water decreases to per litre. Given Kristen's and Dmitri's production levels, Dmitri's profit becomes , Kristen's profit becomes. Because Dmitri has deviated from the cartel agreement and increased his output of water to 250 litres more than the cartel amount, Kristen decides that she will also increase her production to 250 litres more than the cartel amount. After Kristen increases her production, Dmitri's profit becomes , and Kristen's profit becomes and total profit (the sum of the profits of Dmitri and Kristen) is now.

Explanation / Answer

If Dmitri sells 1000 litres and Kristen sells 750 litres, total output becomes 1750 litres. New prices fall down to $5/ litre. Dmitri’s profit becomes 1000*5 = $5000 and Kristen’s profit becomes 750 *5 = $ 3750.

Now if Kristen increases her production too, the total production becomes 1750 + 250 = 2000 litres, then the prices $4, and Kristen profit becomes 1000*4 = $4000 And the total profit is nor 4000 + 4000 = $8000.

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