Question

1- Consider Hotelling’s model (a street of length 1, consumers uniformly distributed along the street). Suppose that each consumer has a linear transportation cost equal to 3d, where d is the distance traveled. Suppose that there are two gas stations, one located in 0.4 and the other one in 1. Assume production costs are zero.

a) Find the indifferent consumer’ location.

b) Determine the demand functions for the two firms.

c) Determine the best response functions.

d) Assume production costs are zero. If the two firms compete in prices and settle at a Nash equilibrium, will they charge the same price for the gasoline?

Determine the corresponding total revenues. 

Answer 1

$$0.6-x=x$$

$$x=0.3$$

$$1-0.3=0.7$$

$$Q_{D1}=0.7\times3d=0.21d$$

$$Q_{D2}=0.3\times3d=0.9d$$

If prices are equal, then the gas station located in point 1 will lose. Consequently, the price at the station located in point 0.4 should be higher.