1. Consider a market characterized by competition around a unit circle, where consumers are uniformly distributed on the circle(their density is equal to 1). Consumers wish to buy one unit of the good and have a transport cost t of $16 per unit distance. Each consumer will purchase exactly one unit from the lowest-effective-price firm provided that their effective price, is less than their reservation price s of $50 and zero otherwise Also, assume marginal cost of production c is $8 and that there is a fixed cost f of $l for a firm to locate on the circle. In the first stage, potential entrants simultaneously choose whether or not to enter. Let n denote the number of entering firms. Firms are automatically located equidistant from one another on the circle a. Given n firms, so that the first stage of the game has already occurred, what is the equilibrium price p? b. What is the equilibrium number of firms in the market? What is the equilibrium price now? (You need to show the derivation of equilibrium prices and number of firms in order to See problem set 4 for the solutions 2. Consider the tourist trap model that we discussed in class. Under the assumption of search cost c, all firms selling identical products, all consumers being uninformed about the price charged by each firm and all consumers having identical demand functions, show how can you break the full information competitive equilibrium. Does reducing the search cost change your result. Also explain briefly without proving: does it make a difference if some consumers are informed. Do we need all the consumers to be informed? Suppose each firm is charging the full information price p then any firm can deviate to charge a higher price to the consumer by raising to the price such that it is higher by an amount less than c This result is independent of the magnitude of the search cost because reducing the search cost does not prevent the firm from raising the price in this manner and consequently the level of information in the economy remains unchanged as consumers search no more It does make a difference if some consumers are informed provided their numbers are reasonably large. In such a situation by deviating to a higher price the deviant firm gets to sell only to the1. Consider a market characterized by competition around a unit circle, where consumers are uniformly distributed on the circle (their density is equal to 1). Consumers wish to buy one unit of the good and have a transport cost t of $16 per unit distance. Each consumer will purchase exactly one unit from the lowest-effective-price firm provided that their effective price, is less than their reservation price s of $50, and zero otherwise. Also, assume marginal cost of production c is $8 and that there is a fixed cost f of $1 for a firm to locate on the circle. In the first stage, potential entrants simultaneously choose whether or not to enter. Let n denote the number of entering firms. Firms are automatically located equidistant from one another on the circle. a. Given n firms, so that the first stage of the game has already occurred, what is the equilibrium price p? b. What is the equilibrium number of firms in the market? What is the equilibrium price now? (You need to show the derivation of equilibrium prices and number of firms in order to get credit) See Problem set 4 for the solutions. 2. Consider the tourist trap model that we discussed in class. Under the assumption of search cost c, all firms selling identical products, all consumers being uninformed about the price charged by each firm and all consumers having identical demand functions, show how can you break the full information competitive equilibrium. Does reducing the search cost change your result. Also explain briefly without proving: does it make a difference if some consumers are informed. Do we need all the consumers to be informed? Suppose each firm is charging the full information price c p then any firm can deviate to charge a higher price to the consumer by raising to the price such that it is higher by an amount less than c. This result is independent of the magnitude of the search cost because reducing the search cost does not prevent the firm from raising the price in this manner and consequently the level of information in the economy remains unchanged as consumers search no more. It does make a difference if some consumers are informed provided their numbers are reasonably large. In such a situation by deviating to a higher price the deviant firm gets to sell only to the