Consider a version of the Hotelling model of duopoly with both firms initially located at 0 in the product space. Consumers are uniformly distributed between 0 and 1, with each Consumer's location giving his most preferred type of product. For simplicity, normalize the total measure of consumers to be 1. Each consumer places value on one unit of his most preferred product, but encounters a transportation cost 2 when purchasing a product which is located a distance away. Assume is sufficiently large that all consumers purchase one unit. Firms have no fixed costs but marginal costs of c per unit.

Firms compete by choosing prices simultaneously. However, before the firms compete in prices, firm 1 has an opportunity to move to location 1 (i.e., to invest in product differentiation). The cost of changing its product characteristics to make this move is . Under what conditions on will firm 1 choose to make this move? Explain the tradeoff faced by firm 1 when making this decision (i.e. what are the benefit and costs of this move?)