Suppose that Barnes and Nobles (B&N) and Borders are located at opposite endpoints of a street, modeled as a line of unit length with B&N at x = 0 and Borders at x = 1, that is, the two stores are located at the extremes of the street. These two stores compete in a simple hotelling model withhomogenousphysical products (think of books). Suppose there is a continuum of consumers uniformly distributed across the street with unit mass (so N=1 in this exercise). Consumers have utility of U= vi- t*x - pi, with i representing a store, if they purchase one unit of a product from "store i" located a distance x away from them and t is the unit transportation cost per unit of distance, piis the price of store i and viis the maximum willingness to pay for the product in store i. Thus, if vi> t*x - pithe consumer utility is positive, U>0, and the consumer acquires 1 unit of the product (e.g. 1 copy of Economics of Strategy textbook). They receive zero utility (U=0) however if they don't purchase a product. Consumer will buy a product from at most one store. Assume that vi for i= B&N and Borders are both large enough so that consumers prefer to purchase the good in equilibrium. Both firms have the same marginal cost c.

Write down the equations that determine the demand for B&N product as a function of the two stores' prices. Use this to determine B&N profit function and to find the price of B&N that maximized B&N profits holding the price of Borders fixed. Solve B&N and Borders profit maximization equations simultaneously to find the equilibrium prices.Based on the equilibrium found in, what are the economic implications from your analysis?