Homework: Monopolistic Competition and Oligopoly

$\backslash$table$[[3\mathrm{.}00,0,0],[2\mathrm{.}75,50,138],[2\mathrm{.}50,100,250],[2\mathrm{.}25,150,338],[2\mathrm{.}00,200,400],[1\mathrm{.}75,250,438],[1\mathrm{.}50,300,450],[1\mathrm{.}25,350,438],[1\mathrm{.}00,400,400],[0\mathrm{.}75,450,338],[0\mathrm{.}50,500,250],[0\mathrm{.}25,550,138],[0,600,0]]$

Suppose Lorenzo and Neha form a cartel and behave as a monopolist. The profit$-$maximizing price is $$ $$1\mathrm{.}50$ per gallon, and the total output s $300$ gallons. As part of their cartel agreement, Lorenzo and Neha agree to split production equally. Therefore, Lorenzo's profit is

Suppose that Lorenzo and Neha 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, Lorenzo says to himself, "Neha and I aren't the best of friends anyway. If I increase my production to $50$ gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow."

After Lorenzo implements his new plan, the price of water increases grad to $$ $$2\mathrm{.}00$ per gallon. Given Neha and Lorenzo's production levels, Lorenzo's profit becomes $$ and Neha's profit becomes $$

Because Lorenzo has deviated from the cartel agreement and increased his output of water to $50$ gallons more than the cartel amount, Neha decides that she will also increase her production to $50$ gallons more than the cartel amount.