Consider the linear city model that has length 1. Firm 1 is
located at .25 miles from the left end and Firm 2 is located .75 miles from the left end. Consumers are uniformly distributed throughout the city. Assume that consumers buy one product from the firm from which it is able to buy at the lowest cost where cost includes the price the firm charges and transportation costs. Transportation costs are quadratic such that traveling a distance of d would cost the consumerd2*t. Assumemarginalcost=ATC=2andt=2.
-(i) Derive the demand for firm 1.
-(ii) Derive the demand for firm 1.
-(iii) Solve for the optimal price firm 1 should charge given firm 2’s price.
-(iv) Solve for the optimal price firm 2 should charge given firm 1’s price.
-(v) Solve for the Nash equilibrium prices each firm would charge.
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