Question

Consider a town in which only two residents, Dmitri and Frances, own wells that produce water safe for drinking. Dmitri and Frances 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 Dmitri and Frances 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, Dmitri and Frances agree to split production equally. Therefore, Dmitri's profit is_________, and Frances's profit is_________.

Suppose that Dmitri and Frances 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, Dmitri says to himself, "Frances 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 Dmitri implements his new plan, the price of water (Increases or decreases?) to _______ per gallon. Given Frances and Dmitri's production levels, Dmitri's profit becomes_________ and Frances's profit becomes__________.

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

After Frances increases her production, Dmitri's profit becomes_________, Frances's profit becomes___________, and total profit (the sum of the profits of Dmitri and Frances) is now____________.

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

True

False

Dmitri and Frances have each cheated on their cartel agreement and increased production by 45 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 Dmitri's profit when he produces 90 gallons more than the cartel amount compared to his profit when he produces 45 gallons more than the cartel amount.)

Neither Dmitri nor Frances has an incentive to further increase output, nor does either have an incentive to decrease output. This outcome is an example of   .

A) resale price maintenance

B) predatory pricing

C) a Nash equilibrium

D) tying

Answer 1

Suppose Dmitri and Frances form a cartel and behave as a monopolist. The profit-maximizing price is $3 per gallon, and the total output is 270 gallons.
It is so because at this price and quantity the total revenue is maximum and for them total revenue is equal to profit.

As part of their cartel agreement, Dmitri and Frances agree to split production equally. Therefore, Dmitri's profit is 810/2 = $405, and Frances's profit is also $405.
It is so because the total revenue is 810 and both of them spilt production equally it means profit will also split equally.

After Dmitri implements his new plan, the price of water decreases to $2.50 per gallon. Given Frances and Dmitri's production levels, Dmitri's profit becomes (270/2 + 45)*2.50 =$ 450 and Frances's profit becomes 270/2 *2.50 = $337.5.
It is so because after Dmitri increases the production the gallons of water rises to 315 and at this quantity the price is $2.50 means price decreases.
Dmitri new quantity is now 270/2 +45 = 180 so his profit is 180*2.50 =$450 and France's profit become 135*2.50 =$337.5

After Frances increases her production, Dmitri's profit becomes 180*2 =$360, Frances's profit becomes 180*2 =$360 and total profit (the sum of the profits of Dmitri and Frances) is now 360+360 =$720.
As now they total gallon of water increases to 360 and at this quantity price will decreases to $2 so the new profit of each of them will be $360.

Yes it is true that ouptut effect was larger than the price effect.

The output effect refers to the fact that increasing production yields additional revenue from the sale of those units. This positively affects profits when price is above marginal cost because selling one more unit yields greater revenues than costs. The price effect refers to the fact that increasing production means higher total output and a lower price per unit. This lowers the profit on all previous units sold. Thus, producers choose to increase output when the output effect is greater than the price effect, and to reduce output when the price effect is greater than the output effect.

This output is an example of Nash equilibrium.

It is so because  A Nash equilibrium is a situation in which each economic entity chooses the best strategy to maximize his or her payoff, given the actions of other entities. Each party sees no gain from changing his or her strategy if the actions of the other parties remain fixed. And in this case this condition is applicable.