Reference no: EM1311659
Q. Consider a linear-city model in which consumers are uniformly located on a line from 0 to
1. Suppose that firm 1 is located at 0 also produces product 1, while firm 2 is located at 1 also produces product
2. Firms are competing by choosing prices. Suppose that every firm's marginal cost is zero.
A consumer pays pi + tx to buy product i (i = 1, 2), where pi is the price of product i also x is the distance among the consumer also firm i also t is the transportation cost to be paid for every distance traveled. Every consumer purchases only one product that minimizes her cost.
(1) Find a critical consumer located at x who is indifferent among product 1 also product 2.
(2) Illustrate what is the demand for firm 1? Also, illustrate what is the demand for firm 2?
(3) Illustrate what is the profit function for firm 1? Find firm 1's best response function for p1 given p2.
(4) Illustrate what is the profit function for firm 2? Find firm 1's best response function for p2 given p1.
(5) Find a Nash equilibrium (p∗1,p∗2). Illustrate what is the equilibrium profit for every firm?
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