3 Breakdown of a cartel agreement Consider a town in which o

3. Breakdown of a cartel agreement Consider a town in which only two residents, Jake and Latasha, own wells that produce water safe for drinking. Jake and Latasha 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 Quantity Demanded (Gallons of water) Price Total Revenue (Dollars per gallon) (Dollars) 5.40 4.95 4.50 4.05 3.60 3.15 2.70 2.25 1.80 1.35 0.90 0.45 40 80 120 160 200 240 280 320 360 400 440 480 S198.00 S360.00 S486.00 S576.00 S630.00 $648.00 S630.00 S576.00 S486.00 S360.00 S198.00 Suppose Jake and Latasha form a cartel and behave as a monopolist. The profit-maximizing price is$ per gallon, and the total output is gallons. As part of their cartel agreement, Jake and Latasha agree to split production equally. Therefore, Jake\'s profit is and Latasha\'s profit is Suppose that Jake and Latasha 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, Jake says to himself, \"Latasha and I aren\'t the best of friends anyway. If I increase my production to 40 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow.\" After Jake implements his new plan, the price of water tos per gallon. Given Latasha and Jake\'s production levels, Jake\'s profit becomes and Latasha\'s profit becomes

Solution

1. $ 2.70

2. 240 gallons

3. Each profit = $ 648/2 = $ 324. Therefore, Jake\'s profit is $ 324 each

4. Latasha\'s profit = $ 324 or (120 units X 2.70)

5. New production will be 280 units so price of water decreases to $ 2.25

6. Profit of Jake = (120 + 40) units X 2.25 = $ 360

7. Latasha\'s profit = 120units X 2.25 = $ 270

If Latasha also increases the production by seeing the action of Jake by 40 units then price will become 1.80

In this case,

8. Jake\'s profit = 160 units X 1.80 = $ 288

9. Latasha\'s profit = 160 units X 1.80 = $ 288

10. Total profit = $ 288 + $ 288 = $ 576

11. False effect of both are same.

12. Pareto optimal