Question

2. Breakdown of a cartel agreement Consider a town in which only two residents, Manuel and Poornima, own wells that produce water safe for drinking. Manuel and Poornima 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. Total Revenue Price Quantity Demanded (Dollars per gallon) (Gallons of water) (Dollars) 3.60 0 3.30 35 $115.50 3.00 70 $210.00 105 $283.50 2.70 2.40 140 $336.00 175 $367.50 2.10 1.80 210 $378.00 1.50 245 $367.50 280 1.20 $336.00 0.90 315 $283.50 0.60 350 $210.00 $115.50 0.30 385 420 Suppose Manuel and Poornima form cartel and behave as a monopolist. The profit-maximizing price is per gallon, and the total gallons. As part of their cartel agreement, Manuel and Poornima agree to split production equally. Therefore, Manuel's profit is output is and Poornima's profit is Suppose that Manuel and Poornima 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, Manuel says to himself, "Poornima 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 Manuel implements his new plan, the price of water to $ per gallon. Given Poornima and Manuel's production levels, Manuel's profit becomes and Poornima's profit becomes $ Because Manuel has deviated from the cartel agreement and increased his output of water to 35 gallons more than the cartel amount, Poornima decides that she will also increase her production to 35 gallons more than the cartel amount.

Answer 1

Cartel:

Profit maximizing price = $ 1.8

Total Output = 210 gallons

Manuel's profit = 105 x 1.8 = $ 189

Poornima's profit = 105 x 1.8 = $ 189

Manuel cheats:

The price of water decreases to $ 1.5 per gallon

Manuel's profit = 140 x 1.5 = $ 210

Poornima's profit = 105 x 1.5 = $ 157.5

Poornima increases production:

New price = $ 1.2 per gallon

Manuel's profit = 140 x 1.2 = $ 168

Poornima's profit = 140 x 1.2 = $ 168

Total Profit = $ 336

The statement is false (output effect > price effect , as total revenue increased)

This outcome is an example of a Nash equilibrium (tit-for-tat strategy)