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Consider the following variant to the Hotelling's model. Two stores are located at points zero (store 0) and one (store 1) along a linear street of length one. Due to heavy winds, it costs more to travel towards store 1. Suppose the marginal travelling cost is 1 towards store 0, but is 3 towards store 1 per unit of distance. Let the consumer's valuation of the commodity be 10. Each consumer buys only 1 unit. Let P0 and P1 be the prices of the commodity at store 0 and store 1, respectively.
A. Derive the utility of consumer located at point 0 < x < 1 if she buys from firm 0. Derive the utility if she buys from firm 1.
B. Suppose there are 100 consumers who are uniformly located on the line. Derive the demand for store 0, which is the number of people who want to buy at store 0. Derive the demand for store 1 as well. Show your work:
C. Assume no production cost. Suppose the firms compete over prices. Solve for the Nash Bertrand equilibrium price and quantity for each firm.
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