Consider a town in which only two residents, Hubert and Kate, own wells that produce water safe for drinking. Hubert and Kate 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.
(a.) Suppose Hubert and Kate form a cartel and behave as a monopolist. What is the profit-maximizing price per gallon and total output in gallons? As part of their cartel agreement, Hubert and Kate agree to split production equally. What is Hubert's profit and Kate's profit?
(b.) Suppose that Hubert and Kate 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 Hubert says to himself, "Kate 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. After Hubert implements his new plan, what is the price of water per gallon? Given Kate's and Hubert's production levels, what are their profits now?
(c.) Because Hubert has deviated from the cartel agreement and increased his output of water to 35 gallons more than the cartel amount, Kate decides that she will also increase her production to 35 gallons more than the cartel amount. After Kate increases her production, what are Hubert?s, Kate?s and total profits now?