Question

3. Breakdown of a cartel agreement Consider a town in which only two residents, Sam and Teresa, own wells that produce water safe for drinking. Sam and Teresa 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. Price Quantity Demanded Total Revenue (Dollars per gallon) (Gallons of water) (Dollars) 3.00 0 0 2.75 50 $137.50 2.50 100 $250.00 2.25 150 $337.50 2.00 200 $400.00 1.75 250 $437.50 1.50 300 $450.00 1.25 350 $437.50 1.00 400 $400.00 0.75 450 $337.50 0.50 500 $250.00 0.25 550 $137.50 0 600 0 Suppose Sam and Teresa 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, Sam and Teresa agree to split production equally. Therefore, Sam's profit is $ , and Teresa's profit is $ . Suppose that Sam and Teresa 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, Sam says to himself, "Teresa 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 Sam implements his new plan, the price of water to $ per gallon. Given Teresa and Sam's production levels, Sam's profit becomes $ and Teresa's profit becomes $ . Because Sam has deviated from the cartel agreement and increased his output of water to 50 gallons more than the cartel amount, Teresa decides that she will also increase her production to 50 gallons more than the cartel amount. After Teresa increases her production, Sam's profit becomes $ , Teresa's profit becomes $ , and total profit (the sum of the profits of Sam and Teresa) is now $ . True or False: Based on the fact that both Sam and Teresa increased production from the initial cartel quantity, you know that the output effect was larger than the price effect at that quantity. True False Note that Sam and Teresa started by behaving cooperatively. However, once Sam decided to cheat, Teresa decided to cheat as well. In other words, Teresa's output decisions are based on Sam's actions.

This behavior is an example of

Answer 1

1)The profit maximizing price is $1.50 per gallon and the total output is 300 gallons. Sam’s profit is $225 and Teresa’s profit is $225.

There is no cost involved in the production of drinking water. The revenue is the highest ($450) when the price is $1.50 per gallon and quantity produced at this price is 300 gallons. Since the profit is shared equally between Sam and Teresa, Sam’s profit share is $450/2=$ 225 and Teresa’s profit share is $450/2=$225.

2) If Sam increases production by 50 gallons, the price of water decreases to $1.25 per gallon. Sam’s profit becomes $250 and Teresa’s profit becomes $187.50.

The original production was 300 gallons and Sam’s share was 300/2=150 gallons and Teresa’s share was also 150 gallons. Now Sam wants to increase his production by 50 gallons. The new production will be 150 + 50= 200 gallons for Sam. The total production will be 200+150=350 gallons.

The price when quantity is 350 gallons is $1.25 per gallon. Sam’s share of profit will be $1.25x 200 gallons=$250. Teresa’s share will be $1.25x 150=$187.50.

3) After Teresa increases her production by 50 gallons, Sam’s profit becomes $200 and Teresa’s profit becomes $200 and total profit is now $400 .

The new output is Sam’s production is 200 gallons and Teresa’s production is 150 + 50 gallons=200 gallons. The new output is 400 gallons. At this quantity, the price per gallon is $1.00. Sam’s profit will be 200 gallons x $1.00 =$ 200 and Teresa’s profit will be 200 gallons x $1.00 =$ 200.

Total profit is $200 + $200=$400.

4) True. Output effect is larger than the price effect.

5) Tit-for-tat.