1. The demand and cost curves for a monopoly firm are as follows:
Q = 750 - 5P
TC = 2000 + 70Q
TC= Q x P
TC = QP = 2000 +70Q
Q=750 - 5P
(a) At what output and price will the firm maximize total revenue? Price- $75.36, Quantity = 750 - 5(75.36) = 373
(b) At what output and price will the firm maximize total profit? Price- $70, Quantity- 750-5(70) = 400
(c) Compare the maximum profit obtainable with the profit that the firm would have if it chose a revenue-maximizing strategy.
A $5 decrease in price correlates to a 27 decrease in quantity (400 - 373 = 27), therefore it would be more profitable to go with maximizing total profit of the firm. Essentially, our costs will still need to be paid, and if we utilize our time to maximize our money, it would do more than simply maximizing our revenue.
2. (a) Considera perfectly competitive firm with the following total cost function in the short run:
STC = 100 + 100Q + 5Q2 + 1/3Q3
Given the market price of its product is P=$300 per unit, determine its profit-maximizing output and profit for the short run.
(b) Now suppose its long-run total cost is:
LTQ = 54Q
Indicate the firm's long-run price, quantity sold, and profit, assuming the industry is in long-run equilibrium.
3. In the following one-shot game, if you advertise and your rival does not, you will make $20 million in profits and your rival will make $6 million. If your rival advertises and you do not, you will make $2 million and your rival will make $6 million. If you advertise and your rival advertises, you will each earn $10 million. If neither of you advertise, your rival will make $8 million and you will make $4 million.
(a) Write the above game in normal form.
(b) Do you have a dominant strategy?
(c) Does your rival have a dominant strategy?
(d) What is the Nash equilibrium for the one-shot game?
(e) How much would you be willing to bribe your rival not to advertise?
4. A firm (You) has to decide whether or not to enter a market which is serviced by a monopolist. Currently the monopolists earns $6 economic profits, while you earn $0. If you enter the market and the monopolist doesn't engage in a price war, you will each earn profits of $3. If the monopolistengages in a price war, you will lose $6 and the monopolist will earn $2.
(a) Write out the extensive form of the above game.
(b) What is the Nash equilibrium (equilibria) for this game? Explain.
(c) Is there a subgame perfect equilibrium? Explain.
(d) If you were the potential entrant, would you enter? Explain why or why not.
5. Suppose you are a manager of a firm that produces products X, Y and Z.You know that there are two different types of consumers, type 1 and type 2, who value your products differently. You also know that there 10,000 type1 consumers and 50,000 type 2 consumers with the following valuations for the three products:
|
Consumer Type
|
Product X
|
Product Y
|
Product Z
|
|
1
|
$250
|
$150
|
$100
|
|
2
|
$200
|
$75
|
$250
|
(a) If you price each product separately (i.e., using a standard pricing strategy), what prices should youcharge to maximize revenues and what are the revenues?
(b) If you adopt a first-degree price discrimination policy, what prices should you charge to maximize revenues and what are the revenues?
(c) If you use a commodity-bundle strategy such that the products are sold as one item (i.e., you market product X, product Y, and product Z together), what price should you charge to maximize revenuesand what are the revenues?