Assume a “Hotelling” line of a distance l = 1. There are two companies A and B, both of them being located at a longer distance. Company A is placed closer to the end of the line, while company B is placed further away. The distance from the beginning of the line to company A is a (a > l) and to B is b (b > a > l). Assume also that an indifferent consumer is located close to the beginning and the distances to A and B are, x and y respectively, where y = x + b – a. Assume quadratic transportation costs, i.e. cx2 and cy2, and prices PAand PB. Find the equilibrium prices and the condition under which both firms will have positive sales. (Hint: Assume that the quantity demanded of firm A is qA = a – x).

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SOLUTION This is a classic problem in spatial economics known as the Hotellings linear city model To solve this problem we will use the following assu... View the full answer