Consider sequential entry of restaurants to the linear city which is the interval [0, 1]. Consumers are uniformly distributed on the linear street with one consumer at every point x where (0?x?1). All restaurants charge the same price, so consumers go the restaurant closest to their location. Restaurants choose their location to maximize the number of customers. Suppose restaurant 1 is already located at x₁= 1 / 3. Then, after observing x₁, restaurant 2

chooses its location x₂, and only then restaurant 3 chooses x₃ after observing x₁ and x₂. Solve for the subgameperfect equilibrium locations of restaurants 2 and 3, x₂ and x₃(x₂) and the restaurants' profit levels (number of customers). Make sure clearly specify the best-response function of restaurant 3.

Question 1: Hotelling Consider sequential entry of restaurants to the linear city which is the interval [0, 1]. Consumers are uniformly distributed on the linear street with one consumer at every point x where (0 5 m g 1). All restaurants charge the same price, so consumers go the restaurant closest to their location. Restaurants choose their location to maximize the number of customers. Suppose restaurant 1 is already located at 3:1 = 1/3. Then, after observing 11:1, restaurant 2 chooses its location 3:2, and only then restaurant 3 chooses 3:3 after observing :31 and x2. Solve for the subgameperfect equilibrium locations of restaurants 2 and 3, 9:2 and :33 (x2) and the restau- rants' prot levels (number of customers). Make sure clearly specify the bestresponse function of restaurant 3