Linear City Model with Horizontal and Vertical Product Differentiation and Privacy Effects. Two firms, labelled 1 and 2, are located at opposite ends of a line of length 1. Each firm produces a single product (products 1 and 2, corresponding to the firmlabels) at constant marginal and average cost, c. L consumers are uniformly distributed along the line. A consumer located distance d from firm 1 receives utility v1 - p1 - td if it purchases from firm 1 where p1 is firm 1's price and t is the consumer's disutility per unit distance from the firm from which it purchases. A consumer located distance d from firm 1 is located distance 1-d from firm 2 receives utility v2 - p2 - t(1-d) if it purchases from firm 2.

1. Assume that v1=v2=t>c>0.
2. (i)Find the Bertrand equilibrium prices.
3. (ii)The upward pricing pressure index for product 1 due to a merger that combines products 1 and 2 is the upward pricing pressure discussed in class divided by the pre-merger price of product 1. What is the upward pricing pressure index for product 1 due to a merger between firms 1 and 2?
4. Assume now that v1=v2=v and that v is large enough that every customer purchases the product.
5. (i) Find the Bertrand equilibrium prices.
6. (ii) What is the upward pricing pressure index for product 1 due to a merger between firms 1 and 2?