Box 1: Increase or Decrease

Box 2: A Nash equilibrium, Typing, Predatory Pricing, Resale Price Maintenance

6. Breakdown of a cartel agreement Consider a town in which only two residents, Andrew and Beth, own wells that produce water safe for drinking. Andrew and Beth 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 Andrew and Beth 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, Andrew and Beth agree to split production equally. Therefore, Andrew's profit is , and Beth's profit is Suppose that Andrew and Beth 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, Andrew says to himself, "Beth 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 Andrew implements his new plan, the price of water to per gallon. Given Beth and Andrew's production levels, Andrew's profit becomes and Beth's profit becomes Because Andrew has deviated from the cartel agreement and increased his output of water to 35 gallons more than the cartel amount, Beth decides that she will also increase her production to 35 gallons more than the cartel amount. After Beth increases her production, Andrew's profit becomes , Beth's profit becomes , and total profit (the sum of the profits of Andrew and Beth) is now Andrew and Beth have each cheated on their cartel agreement and increased production by 35 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 Andrew's profit when he produces 70 gallons more than the cartel amount compared to his profit when he produces 35 gallons more than the cartel amount.) Neither Andrew nor Beth has an incentive to increase output further, nor does either have an incentive to decrease output. This outcome is an example of