1) Suppose that a monopolist has zero marginal cost and faces two consumers. The first is Antonio. Antonio has an inverse demand function given by the following schedule: p(1) = 5 p(2) = 4 p(3) = 3 p(4) = 2 p(5) = 1 p(6) = 0
a) What would Antonio be willing to pay for one unit of the monopolist's good?
b) What would Antonio be willing to pay for a second unit of the monopolist's good?
c) How much would Antonio be willing to pay for 5 units of the monopolist's good?
The second customer is Bianca. Bianca has the following inverse demand function: p(1) = 8 p(2) = 7.5 p(3) = 7 . . . p(15) = 1 p(16) = 0.5 p(17) = 0
d) How much would Bianca be willing to pay for 18 units of the monopolist's good?
e) Suppose the monopolist offered two ways to purchase its good - you can buy 5 units for the amount you answered in part c), or 18 units for the amount you answered in part d). Which offer would Antonio take? Which offer would Bianca take?
f) What is the most Bianca would pay for 18 units of the monopolist's good if she were also able to buy 5 units for the amount you answered in part c)?
g) Suppose the monopolist were to offer 5 units for the amount you answered in part c) and 18 units for the amount you answered in part f). How much profit could the monopolist make? Could the monopolist change the packages she offers and make still more money?
h) What are the packages the monopolist could offer that would earn the most money?
1) Suppose that a monopolist has zero marginal cost and faces two consumers. The first is Antonio. Antonio has an inverse demand function given by the following schedule: p(1) = 5 p(2) = 4 p(3) = 3 p(4) = 2 p(5) = 1 p(6) = 0
a) What would Antonio be willing to pay for one unit of the monopolist's good?
b) What would Antonio be willing to pay for a second unit of the monopolist's good?
c) How much would Antonio be willing to pay for 5 units of the monopolist's good?
The second customer is Bianca. Bianca has the following inverse demand function: p(1) = 8 p(2) = 7.5 p(3) = 7 . . . p(15) = 1 p(16) = 0.5 p(17) = 0
d) How much would Bianca be willing to pay for 18 units of the monopolist's good?
e) Suppose the monopolist offered two ways to purchase its good - you can buy 5 units for the amount you answered in part c), or 18 units for the amount you answered in part d). Which offer would Antonio take? Which offer would Bianca take?
f) What is the most Bianca would pay for 18 units of the monopolist's good if she were also able to buy 5 units for the amount you answered in part c)?
g) Suppose the monopolist were to offer 5 units for the amount you answered in part c) and 18 units for the amount you answered in part f). How much profit could the monopolist make? Could the monopolist change the packages she offers and make still more money?
h) What are the packages the monopolist could offer that would earn the most money?
Related textbook solutions
Related questions
Consider a town in which only two residents, Antonio and Caroline, own wells that produce water safe for drinking. Antonio and Caroline can pump and sell as much water as they want at no cost. For them, the 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) |
| 3.60 | 0 | 0 |
| 3.30 | 35 | $115.50 |
| 3.00 | 70 | $210.00 |
| 2.70 | 105 | $283.50 |
| 2.40 | 140 | $336.00 |
| 2.10 | 175 | $367.50 |
| 1.80 | 210 | $378.00 |
| 1.50 | 245 | $367.50 |
| 1.20 | 280 | $336.00 |
| 0.90 | 315 | $283.50 |
| 0.60 | 350 | $210.00 |
| 0.30 | 385 | $115.50 |
| 0 | 420 | 0 |
Suppose Antonio and Caroline form a cartel and behave as a monopolist. The profit-maximizing price is (1) $______ per gallon, and the total output is (2) ___ gallons.
As part of their cartel agreement, Antonio and Caroline agree to split production equally. Therefore, Antonio's profit is (3) $____, and Caroline's profit is (4) $_____.
Suppose that Antonio and Caroline 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, Antonio says to himself, "Caroline 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 Antonio implements his new plan, the price of water (5) (increases/decreases) to (6) $____per gallon. Given Caroline and Antonio's production levels, Antonio's profit becomes (7) $____ and Caroline's profit becomes (8) $______.
Because Antonio has deviated from the cartel agreement and increased his output of water to 35 gallons more than the cartel amount, Caroline decides that she will also increase her production to 35 gallons more than the cartel amount.
After Caroline increases her production, Antonio's profit becomes (9) $_____, Caroline's profit becomes (10) $_____ and total profit (the sum of the profits of Antonio and Caroline) is now (11) $_____
(12) True or False: Based on the fact that both Antonio and Caroline increased production from the initial cartel quantity, you know that the output effect was smaller than the price effect at that quantity.
Note that Antonio and Caroline started by behaving cooperatively. However, once Antonio decided to cheat, Caroline decided to cheat as well. In other words, Caroline's output decisions are based on Antonio's actions.
(13) This behavior is an example of (tying/ a dominant strategy/ a tit-for-tat strategy/ a prisoners' dilemma).
