Homework #5
1. Suppose that there is a market for peanuts. The market demand is given by QD = 20 - 2P. Monopolist's costs are given by TC = 16 + 4Q.
a. Suppose a single price monopolist controls the market for peanuts. Find the monopolist's optimal price and quantity choice. Find the profit.
c. Using your answer from the previous question find the deadweight loss and consumer surplus in the market.
d. Now suppose that the market for this good is controlled by a perfectly price discriminating monopolist. What are the perfectly price discriminating monopolist's profits? Calculate the deadweight loss and consumer surplus.
2. Tandem paragliding is a fun sport where you paraglide on a tandem paraglider with an experienced and qualified tandem instructor as your pilot. Assume that Sky Sports is a monopolist firm and offers a tandem paragliding experience to its customers. Old and young people who are potential customers for this firm have different demand functions for tandem paragliding (the firms considers ages above 60 as old). Specifically, the demand function for young people is given by QD =100-P; for old people, the demand is given by QD =80-P. The cost function for Sky Sports is TC=10Q.
a) Derive the aggregate demand curve in the market for tandem paragliding flights and graph it. (Hint: this is the horizontal summation of the two demand curves for P<=80, and it is just the demand curve for young people for P>80. Can you explain why?)
b) What is the aggregate marginal revenue curve for P<=80? Using this marginal revenue curve, find the profit-maximizing quantity and price for Sky Sports as well as its profit.
c) Now assume that Sky Sports charges a different price to old people and young people, i.e. it acts as a third-degree price discriminator (this just means the monopolist treats each demand curve as separate and equates marginal revenue with marginal cost in the old people's market and the young people's market separately). Find the profit-maximizing quantity and price as well as the firm's profit in each separate market.
d) Add the two profit totals you found in (c) to get the total profit under price discrimination. Compare this with profit found in (b). What do you notice? In the real world, what might keep Sky Sports from charging a different price to young people and old people?
3. This is a price competition game between two firms, each of which produces Haggis (a rather foul meat concoction). MacEwan's Haggis, Inc. has a marginal cost per kilo of $11. Highlander's Awful Offal, Llp has a marginal cost of $16 per kilo. Further, suppose a monopolist in the Haggis market would set a price of $20 per kilo.
a. What is equilibrium price in this market?
b. Give brief intuitive argument why $20 cannot be equilibrium under price competition.
4. Consider the following table. In this game Jenny decides whether to play Left or Right, and Andy decides whether to play Up or Down. In each cell you have the payoff of each player if the game ends in such a position (the first value is Andy's payoff and the second value is Jenny's payoff)
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Jenny
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Andy
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Left
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Right
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Up
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(4, 3)
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(-4, 0)
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Down
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(0, -1)
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(0,0)
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a) Find the equilibrium (or equilibria) of the game.
b) Does Andy have a dominant strategy? Does Jenny have a dominant strategy?