Consider the market for wine in a small town where all the 1000 residents live at equal distances on a 1-mile long stretch of Pine St. There are two wine stores, Tipsy’s and Jack’s, that are located on opposite ends of town; assume that Tipsy’s is located on the west side and Jack’s on the east side. All residents need only 1 bottle of wine. The wine at Jack’s is of a better quality than Tipsy’s. As a result, each resident values wine from Tipsy’s at VT = $15,
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and from Jack’s at VJ = $22. Assume that each store has a marginal cost of $4 per bottle. Each consumer experiences a transportation disutility cost of $10 per round-trip mile. So, the total travel cost of purchasing wine from a store 𝑥 miles away is $10𝑥. Suppose the stores set prices sequentially, with Tipsy’s going first.
(a) If Tipsy’s were to set a price of $11, what price should Jack’s set? Show your work.
(b) Suppose, instead, that in addition to setting a price of $11, Tipsy’s announces that they will refund 50% of the travel costs of anyone who buys wine from them. What price should Jack’s set now? Show your work.