Consider a town in which only two residents, Nick and Rosa, own wells that produ
ID: 2495367 • Letter: C
Question
Consider a town in which only two residents, Nick and Rosa, own wells that produce water safe for drinking. Nick and Rosa 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 Nick and Rosa 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, Nick and Rosa agree to split production equally. Therefore, Nick's profit is, and Rosa's profit is. Suppose that Nick and Rosa 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, Nick says to himself, "Rosa 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 Nick implements his new plan, the price of water to per gallon. Given Rosa and Nick's production levels, Suppose that Nick and Rosa 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, Nick says to himself, "Rosa 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 Nick implements his new plan, the price of water to per gallon. Given Rosa and Nick's production levels, Nick's profit become and Rosa's profit becomes. Because Nick has deviated from the cartel agreement and increased his output of water to 45 gallons more than the cartel amount, Rosa decides that she will also increase her production to 45 gallons more than the cartel amount. After Rosa increases her production, Nick's profit becomes $, Rosa's profit becomes, and total profit (the sum of the profits of Nick and Rosa) is now. True or False: Based on the fact that both Nick and Rosa increased production from the initial cartel quantity, you know that the output effect was smaller than the price effect at that quantity. True False Nick and Rosa have each cheated on their cartel agreement and increased production by 45 gallons more than the cartel amount. However, they both realize that if they continue to increase output beyond this amount, they'll each suffer a decrease in profit. (To see this for yourself, consider Nick's profit when he produces 90 gallons more than the cartel amount compared to his profit when he produces 45 gallons more than the cartel amount.) Neither Nick nor Rosa has an incentive to further increase output, nor does either have an incentive to decrease output. This outcome is an example of.Explanation / Answer
The profit maximizing price (revenue maximzing) is $3 per gallon and the total output is 270 gallons. Nick’s profit is 405 and Rosa’s profit is $405.
The total output now is 270+45 = 315 gallons
The price of water decreases to $2.5 per gallon. Nick now produces 135+45 =180 gallons and Rosa produces same 135 gallons
Nick’s profit = 180x2.5 = $450
Rosa = 135x2.5= $337.5
Total output after Rosa increases her production =315+45 = 360
Both produce 180 gallons at $2
Rosa profit = 180x2 =360
Nick=180x2-360
True the output effect is greater than price effect
The outcome is an example of Nash equilibrium of game theory.