Name:_______________________ Quiz #4 – EconS 425 (March 25th, 2015) Question #1 (50 Points) Grand avenue in the city of Pullman is best described as the interval [0,1]. Two Mexican restaurants serving identical food are located at the edges of the street, so that restaurant 1 (Rancho Viejo) is located on the most lefthand side, and restaurant 2 (Nuevo Vallarta) is located on the most right-hand side of Grand avenue. Consumers are uniformly distributed on the interval [0,1], where at each point on the interval lives one consumer. Each consumer buys one meal from the restaurant in which the price plus the transportation cost is the lowest. In Grand avenue, the road conditions are worse in the right than in the left part, hence the transportation cost for a consumer who travels to the right is $T per unit of distance, and only $2 per unit of distance for a consumer who travels to the left. Answer the following questions: Let pi denote price of meal at restaurant i, i=1,2. Assume that p1 and p2 are given and satisfy a) Denote by the location of the consumer who is indifferent to whether he or she eats at restaurant 1 or restaurant 2 and calculate as a function of p1, p2, and T. b) Solve Rancho Viejo’s and Nuevo Vallarta’s maximization problem with respect to price, and identify their profits. Part (a) In order to find we need to guarantee that consumers obtain the same payoff when buying from either firm. That is, Hence, Therefore, restaurant 1 faces a demand , and restaurant 2 faces a demand , that is Part (b) Rancho Viejo’s maximization problem is Solving for p1 we obtain that . Nuevo Vallarta’s maximization problem is EconS 425, Ana Espinola Solving for p2 we obtain that Hence, . Finally, substituting (B) into (A): and substituting p1 into (B) we have that or . In addition, we can obtain restaurant 1’s and 2’s profits: EconS 425, Ana Espinola