# Suppose that two firms produce differentiated products and compete in prices. As in class, the two firms are located at two ends of a line one mile…

Suppose that two firms produce differentiated products and compete in prices. As in class, the two firms are located at two ends of a line one mile apart.

Consumers are evenly distributed along the line.

The firms have identical marginal cost, \$60. Firm B produces a product with value \$110 to consumers.

Firm A (located at 0 on the unit line) produces a higher quality product with value \$120 to consumers.

The cost of travel are directly related to the distance a consumer travels to purchase a good.

If a consumer has to travel a mile to purchase a good, they incur a cost of \$20. If they have to travel x fraction of a mile, they incur a cost of \$20x.

(a) Write down the expressions for how much a consumer at location d would value the products sold by firms A and B, if they set prices Pa and Pb?

(b) Based on your expressions in (a), how much will be demanded from each firm if prices Pa and Pb are set?

(c) What are the Nash equilibrium prices?