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Assume that: Consumers' preferences are uniformly distributed on the unit interval. Prices are fixed such that (p-c) 1 and the number of consumers has been normalized to one. Firms enter sequentially and incur a startup cost of 1/6. Suppose that startup costs are not sunk-firms can costlessly relocate. What is the free-entry number and location of firms? [Hint: The equilibrium to the game in which firms enter sequentially, but fixed costs are not sunk, is the same as an alternative game in which firms simultaneously choose their locations but fixed startup costs are sunk. In the simultaneous-location-and-entry game, we can find the Nash equilibrium by separating the location and entry decisions. First find the equilibrium to the location game with a fixed number of firms. The outcome of the location decisions and game determines the profitability of entry.]

Assume that: Consumers' preferences are uniformly distributed on the unit interval. Prices are fixed such that (p-c) 1 and the number of consumers has been normalized to one. Firms enter sequentially and incur a startup cost of 1/6. Suppose that startup costs are not sunk-firms can costlessly relocate. What is the free-entry number and location of firms? [Hint: The equilibrium to the game in which firms enter sequentially, but fixed costs are not sunk, is the same as an alternative game in which firms simultaneously choose their locations but fixed startup costs are sunk. In the simultaneous-location-and-entry game, we can find the Nash equilibrium by separating the location and entry decisions. First find the equilibrium to the location game with a fixed number of firms. The outcome of the location decisions and game determines the profitability of entry.]

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 1 Assume that: Consumers' preferences are uniformly distributed on the unit interval. Prices are fixed such that (p-c) 1 and the number of consumers has been normalized to one. Firms enter sequentially and incur a startup cost of 1/6. Suppose that startup costs are not sunk-firms can costlessly relocate. What is the free-entry number and location of firms? [Hint: The equilibrium to the game in which firms enter sequentially, but fixed costs are not sunk, is the same as an alternative game in which firms simultaneously choose their locations but fixed startup costs are sunk. In the simultaneous-location-and-entry game, we can find the Nash equilibrium by separating the location and entry decisions. First find the equilibrium to the location game with a fixed number of firms. The outcome of the location decisions and game determines the profitability of entry.]
Transcribed Image Text:Problem 1 Assume that: Consumers' preferences are uniformly distributed on the unit interval. Prices are fixed such that (p-c) 1 and the number of consumers has been normalized to one. Firms enter sequentially and incur a startup cost of 1/6. Suppose that startup costs are not sunk-firms can costlessly relocate. What is the free-entry number and location of firms? [Hint: The equilibrium to the game in which firms enter sequentially, but fixed costs are not sunk, is the same as an alternative game in which firms simultaneously choose their locations but fixed startup costs are sunk. In the simultaneous-location-and-entry game, we can find the Nash equilibrium by separating the location and entry decisions. First find the equilibrium to the location game with a fixed number of firms. The outcome of the location decisions and game determines the profitability of entry.]
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