Question

1. Pricing along the mile-long road (30 points) Two stores selling bottled water, Goodwater and Sweetwater are located at the two extreme ends of a mile-long road. 100 customers are uniformly distributed along this road. The problem faced by the two stores here has to do with the pricing of bottled water. Owners of the two stores are aware of the following: (Figure 1) • Sweetwater charges Ps per bottle and Goodwater charges PG per bottle. • Traveling to either store is costly, and the prices charged do affect where the customer buys water. • A customer located a distance D from Sweetwater and 1-D from Goodwater will buy from Sweetwater if and only if the price of a bottle of water plus the cost of traveling (which of course depends on the unit cost of travel (4) and the distance to be traveled (D or 17-D) to Sweetwater is less than the price plus traveling cost if he chooses to purchase from Goodwater. Or: Ps + 4D <Pc+41-D). • Customers bring their own bottles and the marginal cost of providing water is zero... these are the only locations along the mile-long road that have access to clean tap water. (a) If Sweetwater charges $1 and Goodwater charges $2 per bottle, what is the location of the customer who is exactly indifferent between buying at either store? (b) What is the quantity demand (market share) for Sweetwater? What is the quantity demand for Goodwater at these prices ($1 and $2)? (Hint: Since you know the consumer who is just indifferent, what is Sweetwater's market share? Likewise, what about Goodwater?)

Pricing is provided in the question.