Consider the linear city model. Suppose that firm 1 is located at point a 0...

 

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Consider the linear city model. Suppose that firm 1 is located at point a ≥ 0 and firm 2 is at point 1-b, where bz0 and1-bza. (Firm1 is to the left of firm2.) Both firms have the same marginal cost of production c. Transportation costs (borne by the consumer) are quadratic: a consumer at point x incurs a cost of t(x-a)2 to go to store 1 and a cost of t(x-(1-b))2 to go to store 2. (a) Solve for the indifference point, where a consumer is indifferent between purchasing from either firm. (b) What are the demand functions faced by each firm? (You may assume that prices are such that 0 ≤ Di < 1 for each Di, where Di is the demand for firm i. You may also assume that the gross consumer surplus is high enough that every consumer purchases the good, i.e. the entire market is covered.) Simplify your answer (c) What are the equilibrium prices charged under Bertrand competition? Consider the linear city model. Suppose that firm 1 is located at point a ≥ 0 and firm 2 is at point 1-b, where bz0 and1-bza. (Firm1 is to the left of firm2.) Both firms have the same marginal cost of production c. Transportation costs (borne by the consumer) are quadratic: a consumer at point x incurs a cost of t(x-a)2 to go to store 1 and a cost of t(x-(1-b))2 to go to store 2. (a) Solve for the indifference point, where a consumer is indifferent between purchasing from either firm. (b) What are the demand functions faced by each firm? (You may assume that prices are such that 0 ≤ Di < 1 for each Di, where Di is the demand for firm i. You may also assume that the gross consumer surplus is high enough that every consumer purchases the good, i.e. the entire market is covered.) Simplify your answer (c) What are the equilibrium prices charged under Bertrand competition?

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