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4. Consider a Hotelling model of product differentiation in which there is a continuum of consumers...

4. Consider a Hotelling model of product differentiation in which there is a continuum of consumers uniformly distributed on the interval [0; 1] : Firms will also be located at two endpoints of the interval. Consumers have unit demands. A consumer who buys at price pA from firm A located a distance x away obtains utility v-pA-tx: If this consumer buys at price pB from firm B, his utility is v-pB- t(1-x): Assume all goods can be produced at zero marginal cost and that v is sufficiently large that all consumers will buy one good.

(a) Derive the demand curves for the two firms. Solve for the Nash equilibrium prices.

(b) Suppose that firm A chooses its price first, and firm B chooses its price later after observing the firm A's price. Solve for the subgame Perfect equilibrium prices.

(c) Compare the firms profits in (a) and (b). Do you find the first-mover advantage or the second mover advantage. Explain

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