PART 2 OPTION 3 (CIRCULAR CITY) Consider the Circular City Model in which n firms have entered and located equal distance from each other in a Circular City of circumference 1 mile. Consumers buy exactly one product from exactly one firm. The consumers will buy from the firm that offers the product at least cost to the consumer, where the cost includes the price of the product plus the transportation costs of traveling to get the good. Transportation costs are $16 per mile traveled. Therefore, if a consumer travels a distance of d total transportation costs are $16d. There are 900 consumers. All firms are identical paying a constant marginal cost of $36 per good and a fixed entry cost of $400. (1) Derive the distance from firm i of the marginal consumer who is indifferent from buying from firm i and i's nearest neighbor, i-1. Call this distance x. This term should be a function of the price firm i-1 offers (P-1) and the number of firms. (ii) Derive the demand for firm i assuming firm i-1 and firm i+1 offer the same price. (iii) Derive the profit maximizing price firm i should charge as a function of and the profit maximizing price all firms charge in the symmetric equilibrium (where all firms charge the same price) as a function of n. (iv) Derive the long run equilibrium number of firms and the price per firm when there is free entry and exit in the long run.
PART 2 OPTION 3 (CIRCULAR CITY) Consider the Circular City Model in which n firms have entered and located equal distance from each other in a Circular City of circumference 1 mile. Consumers buy exactly one product from exactly one firm. The consumers will buy from the firm that offers the product at least cost to the consumer, where the cost includes the price of the product plus the transportation costs of traveling to get the good. Transportation costs are $16 per mile traveled. Therefore, if a consumer travels a distance of d total transportation costs are $16d. There are 900 consumers. All firms are identical paying a constant marginal cost of $36 per good and a fixed entry cost of $400. (1) Derive the distance from firm i of the marginal consumer who is indifferent from buying from firm i and i's nearest neighbor, i-1. Call this distance x. This term should be a function of the price firm i-1 offers (P-1) and the number of firms. (ii) Derive the demand for firm i assuming firm i-1 and firm i+1 offer the same price. (iii) Derive the profit maximizing price firm i should charge as a function of and the profit maximizing price all firms charge in the symmetric equilibrium (where all firms charge the same price) as a function of n. (iv) Derive the long run equilibrium number of firms and the price per firm when there is free entry and exit in the long run.
Chapter1: Making Economics Decisions
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Transcribed Image Text:PART 2 OPTION 3 (CIRCULAR CITY) Consider the Circular City Model in which n firms have
entered and located equal distance from each other in a Circular City of circumference 1 mile.
Consumers buy exactly one product from exactly one firm. The consumers will buy from the firm
that offers the product at least cost to the consumer, where the cost includes the price of the
product plus the transportation costs of traveling to get the good.
Transportation costs are $16 per mile traveled. Therefore, if a consumer travels a distance of d
total transportation costs are $16d.
There are 900 consumers.
All firms are identical paying a constant marginal cost of $36 per good and a fixed entry cost of
$400.
(1) Derive the distance from firm i of the marginal consumer who is indifferent from buying from
firm i and i's nearest neighbor, i-1. Call this distance x. This term should be a function of the price
firm i-1 offers (P.1) and the number of firms.
(ii) Derive the demand for firm i assuming firm i-1 and firm i+1 offer the same price.
(iii) Derive the profit maximizing price firm i should charge as a function of and the profit
maximizing price all firms charge in the symmetric equilibrium (where all firms charge the same
price) as a function of n.
(iv) Derive the long run equilibrium number of firms and the price per firm when there is free entry
and exit in the long run.
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