Consider a market in which firms 1,……,N are equidistantly distributed on a circle with circumference 1. Firms have constant marginal costs of production c, which are the same for all firms. Consumers are uniformly distributed on the circle (and have mass 1). A consumer x incurs a transportation τ |x - l_i| when buying from firm i. Here the distance between consumer and firm is the arc distance on the circle (that is consumers move on the circle). Suppose that all consumers are active in the market.

1. Determine the demand function of firm i as a function of all prices. [Be careful!]

2. Determine equilibrium prices in the game in which all firms set prices simultaneously.

3. How do transport costs affect profits?

4. Argue informally whether or not you think that an equilibrium exists for all location configurations.