Consider the Salop circular city model with population density Son a circle of unit perimeter. Identical firms equidistantly locate on the circle, each having one location, and produce a physically identical good. Consumers are located uniformly on the circle. Each con- sumer buys exactly one unit of the product, and always chooses the lowest sum of transportation cost and price of the product. The transportation cost is td where d is the distance of travel. Each firm's costs consist of an entry cost f and a marginal cost of pro- duction & Consider the following two-stage game: In the first stage

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Chapter1: Making Economics Decisions
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Consider the Salop circular city model with population density S on
a circle of unit perimeter. Identical firms equidistantly locate on the
circle, each having one location, and produce a physically identical
good. Consumers are located uniformly on the circle. Each con-
sumer buys exactly one unit of the product, and always chooses the
lowest sum of transportation cost and price of the product. The
transportation cost is td where d is the distance of travel. Each
firm's costs consist of an entry cost f and a marginal cost of pro-
duction c. Consider the following two-stage game: In the first stage,
potential entrants simultaneously choose whether or not to enter.
In the second stage, then entering firms compete in prices.
(a) Determine the price level in a symmetric equilibrium of the
second-stage subgame. How does the price change with n?
Transcribed Image Text:Consider the Salop circular city model with population density S on a circle of unit perimeter. Identical firms equidistantly locate on the circle, each having one location, and produce a physically identical good. Consumers are located uniformly on the circle. Each con- sumer buys exactly one unit of the product, and always chooses the lowest sum of transportation cost and price of the product. The transportation cost is td where d is the distance of travel. Each firm's costs consist of an entry cost f and a marginal cost of pro- duction c. Consider the following two-stage game: In the first stage, potential entrants simultaneously choose whether or not to enter. In the second stage, then entering firms compete in prices. (a) Determine the price level in a symmetric equilibrium of the second-stage subgame. How does the price change with n?
How does the parameter t affect the relationship between price
and n? Interpret your results intuitively.
(b) Determine the number of firms in a pure strategy equilibrium of
first-stage entry game. Discuss how the parameters t, f, and S
affect n respectively. Interpret your results intuitively.
(c) What happens to n if t → ? What happens to n and price if
→ ∞? Interpret your results intuitively.
f
Transcribed Image Text:How does the parameter t affect the relationship between price and n? Interpret your results intuitively. (b) Determine the number of firms in a pure strategy equilibrium of first-stage entry game. Discuss how the parameters t, f, and S affect n respectively. Interpret your results intuitively. (c) What happens to n if t → ? What happens to n and price if → ∞? Interpret your results intuitively. f
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