Question

Consider a town in which only two residents, Kevin and Maria, own wells that produce water safe for drinking. Kevin and Maria 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)
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
Suppose Kevin and Maria 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, Kevin and Maria agree to split production equally. Therefore, Kevin's profit is $
––––– .

Suppose Kevin and Maria 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, Kevin and Maria agree to split production equally. Therefore, Kevin's profit is $
––––– , and Maria's profit is $
––––– .

Suppose that Kevin and Maria 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, Kevin says to himself, "Maria 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 Kevin implements his new plan, the price of water
–––––––––– to $
––––– per gallon. Given Maria and Kevin's production levels, Kevin's profit becomes $
––––– and Maria's profit becomes $
––––– .

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

After Maria increases her production, Kevin's profit becomes $
––––– , Maria's profit becomes $
––––– , and total profit (the sum of the profits of Kevin and Maria) is now $
––––– .

True or False: Based on the fact that both Kevin and Maria increase production from the initial cartel quantity, you know that the output effect was larger than the price effect at that quantity.

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

This behavior is an example of
–––––––––– .

Answer 1

Answer:

Monopolist profit maximizing price

A: $3 per gallon , total output =270 Kelvins profit = $810(801/7/2 = $405

Maria's profit = $405

B. $2.5 per gallon . Kelvin's profit =$450 Maria's profit = 337.5

C = False. At the same quantity , fall in price brings fall in revenue

Cournot Nash equilibrium

Explanation:

In a monopolist market system , price are set higher than the marginal cost as the producer enjoy the dominance of the market through the production of a unique good.

At the price of $3 , change in demand =(270-225) =45 , change in revenue = ($810-$787.50)22.5 and marginal revenue = (45/22,5) = 0.5. That forms the maximizing price for a monopolist.

On the new arrangement , price drops to $2.5 , Maria's profit =(315-45/2)2.5 = $337.5 and Kelvin's = ($787.5-337.5) = $450

Cournot Nash equilibrium is business model that explains the competition among rival companies producing similar product on the level of output produced independently.