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Homework answers / question archive / Consider a town in which only two residents, Rajiv and Simone, own wells that produce water safe for drinking
Consider a town in which only two residents, Rajiv and Simone, own wells that produce water safe for drinking. Rajiv and Simone 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 Rajiv and Simone form a cartel and behave as a monopolist. The profit-maximizing price isper gallon, and the total output isgallons. As part of their cartel agreement, Rajiv and Simone agree to split production equally. Therefore, Rajiv's profit is, and Simone's profit is.
Suppose that Rajiv and Simone 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, Rajiv says to himself, "Simone 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 Rajiv implements his new plan, the price of water toper gallon. Given Simone and Rajiv's production levels, Rajiv's profit becomes and Simone's profit becomes.
Because Rajiv has deviated from the cartel agreement and increased his output of water to 45 gallons more than the cartel amount, Simone decides that she will also increase her production to 45 gallons more than the cartel amount.
After Simone increases her production, Rajiv's profit becomes, Simone's profit becomes, and total profit (the sum of the profits of Rajiv and Simone) is now.
True or False: Based on the fact that both Rajiv and Simone increased production from the initial cartel quantity, you know that the output effect was larger than the price effect at that quantity.
True
False
Rajiv and Simone 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 Rajiv'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 Rajiv nor Simone has an incentive to increase output further, nor does either have an incentive to decrease output. This outcome is an example of .
1. Suppose Rajiv and Simone form a cartel and behave as a monopolist. The profit-maximizing price is 3.00 per gallon, and the total output is 270 gallons. As part of their cartel agreement, Rajiv and Simone agree to split production equally. Therefore, Rajiv's profit is 405, and Simone's profit is 405.
explanation:
TR column tells that the maximum revenue = 810 when quantity = 270; price = 3.00. As marginal cost = 0, TR = profit. So, Rajiv's profit = 405; Simone's rofit = 405
2. After Rajiv implements his new plan, the price of water decreases to 2.50 per gallon. Given Simone and Rajiv's production levels, Rajiv's profit becomes 450 and Simone's profit becomes 337.50.
explanation:
When Rajiv increases his output by 45, total production = 270+45 = 315. As per teh table, price will be 2.50.
Rajiv's profit = (135 + 45) *2.50 = 450
Simone's profit = 135*2.50 = 337.50.
Total profit = 787.50
3. After Simone increases her production, Rajiv's profit becomes 360, Simone's profit becomes 360, and total profit (the sum of the profits of Rajiv and Simone) is now 720.
Explanation:
When Simone increases her output by 45, total production = 315+45 = 360. As per the table, price will be 2.00. Total revenue (or, profit) = 720.
Rajiv's profit = 180*2 = 360
Simone's profit = 180*2 = 360
Or, each gets half of the total profit (720/2 = 360)
4. True or False: Based on the fact that both Rajiv and Simone increased production from the initial cartel quantity, you know that the output effect was larger than the price effect at that quantity.
False
reason: Price effect = (3-2)*270 = 270
Output effect =(360 - 270) 8 2 = 180
Price effect is larger. Also, a decrease in price decreases revenue. So, we know that the demand is inelastic. When demand is inelastic, price effect is larger than the output effect. This can be represented in the following graph:
Rajiv and Simone 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 Rajiv'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.)
Rajiv's profit when he increases his output by 90 units = 450 (which is the same as when he increased his output by 45 gallons).
Explanation: When Rajiv increases his output by 90 units, his output will be 135+90 = 225; total output will be 225+135 = 360. Rajiv's profit = 225*2 = 450, which is the same as when he increased his output by 45 = 450. So, he does not gain anyhting by increasing his output, but the total profit declines by 810 - 720 = 90.
5. Neither Rajiv nor Simone has an incentive to increase output further, nor does either have an incentive to decrease output. This outcome is an example of Nash equilibrium .
Nash equilibrium is an outcome where neither player has an incentive to change their strategy given the srategy of the other player. Here neither Rajiv nor Simone would want to change their output as it will lead to a decrease in their profits.
please see the attached file for the complete solution.
