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3. (25 points-5 each) Consider the Circular City Model in which 71 rms have entered and located equidistance 'om each other in a Circular City of circumference 1 mile. Consumers buy exactly one product 'om exactly one rm. The consumers will buy from the rm 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 $25 per mile traveled. Therefore, if a consumer travels a distance of d, total transportation costs are $25d. There are 100 consumers. Note: you can use the general results from the notes to check your work, but you should derive the results yourself for this numeric example. All rms are identical paying a constant marginal cost of $5 per good and a xed entry cost of $100. (i) Derive the distance om rm i of the marginal consumer who is indifferent from buying om rm i and 1' 's nearest neighbor, i-I. Call this distance x. This term should be a function of the price rm i-I offers (PM) and the number of rms. (ii) Derive the demand for rm i assuming rm iI and rm i+1 offer the same price P. (iii) Derive the prot maximizing price rm i should charge as a function of p and 14. (iv) Derive the prot maximizing price all rms charge in the symmetric equilibrium as a function of n. (v) Derive the long run equilibrium number of rms and the price per rm