Reference no: EM131104314
Consider a circular city of length L in which the consumers are uniformly distributed and firms decide sequentially whether to enter the market in the first stage, and then decide simultaneously its price in the second stage. Every consumer buys one unit to the firm with the lower integrated price: price per unit plus transportation cost. Transportation costs are quadratic (t*d 2, where d is distance). The profit function of every firm (i=1,2,3…n) is: Profit i(p) = pi D(p) – F if the firm enters the market, and (Profit)i = 0 if it decides not to enter, where pi is the price of firm i, p is a vector of the prices of all the firms, Di is the demand faced by firm i, and F is the entry cost.
1. Find the demand faced by every firm
2. Find the best response function of every firm in the second stage of the game. This is a function that relates the maximum profit price with the number of firms (n).
3. Find the Nash equilibrium of the second stage
4. Find the number of firms and the price level of every firm that result from the perfect Nash equilibrium
5. Relate barriers to entry (as represented by the entry cost F) with market structure (n).
6. Relate the size of the market (as represented by L) with market structure (n).
7. Relate the degree of differentiation (as represented by t) with the market structure (n).
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