Consider a town in which only two residents, Kenji and Lucia, own wells that pro

Question

Consider a town in which only two residents, Kenji and Lucia, own wells that produce water safe for drinking. Kenji and Lucia 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 Kenji and Lucia 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, Kenji and Lucia agree to split production equally. Therefore, Kenji's profit is _____ , and Lucia's profit is ______

Suppose that Kenji and Lucia 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, Kenji says to himself, "Lucia 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 Kenji implements his new plan, the price of water _______ (increases or decreases) to _____ per gallon. Given Lucia and Kenji's production levels, Kenji's profit becomes ______ and Lucia's profit becomes _____

Because Kenji has deviated from the cartel agreement and increased his output of water to 45 gallons more than the cartel amount, Lucia decides that she will also increase her production to 45 gallons more than the cartel amount.

After Lucia increases her production, Kenji's profit becomes ______ , Lucia's profit becomes _____, and total profit (the sum of the profits of Kenji and Lucia) is now _____

True or False: Based on the fact that both Kenji and Lucia increased production from the initial cartel quantity, you know that the output effect was smaller than the price effect at that quantity.

True

False

Note that Kenji and Lucia started by behaving cooperatively. However, once Kenji decided to cheat, Lucia decided to cheat as well. In other words, Lucia's output decisions are based on Kenji's actions.

This behavior is an example of ______ (tying, a tit for tat strategy, a dominant strategy, a prisoners' dilemma)

Price Quantity Demanded Total Revenue (Dollars per gallon) (Gallons of water) (Dollars) 6.00 0 0 5.50 45 $247.50 5.00 90 $450.00 4.50 135 $607.50 4.00 180 $720.00 3.50 225 $787.50 3.00 270 $810.00 2.50 315 $787.50 2.00 360 $720.00 1.50 405 $607.50 1.00 450 $450.00 0.50 495 $247.50 0 540 0

Explanation / Answer

Suppose Kenji and Lucia form a cartel and behave as a monopolist. The profit-maximizing price is $ 3 per gallon (where revenue is maximum), and the total output is 270 gallons. As part of their cartel agreement, Kenji and Lucia agree to split production equally. Therefore, Kenji's profit is $ 405 , and Lucia's profit is $ 405. ( = 135 x 3)

Kenji cheats:

After Kenji implements his new plan, the price of water decreases to $2.5 per gallon. Given Lucia and Kenji's production levels, Kenji's profit becomes $ 450 (=180 x 2.5) and Lucia's profit becomes $ 337.5.

After Lucia increases her production, Kenji's profit becomes $ 360 (=180 x 2) , Lucia's profit becomes $ 360, and total profit (the sum of the profits of Kenji and Lucia) is now $ 720.

The statement is false, output effect > price effect (this was the reason why Kenji's profit increased despite reduction in the price)

This behavior is an example of a tit for tat strategy

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