In questions 5-10, consider a spatial price competition model of differentiated products where the set of possible products is the line segment [0,1] and consumers are uniformly distributed along the line segment.For each consumer, the utility from buying at a pricep, from a firm that is at a distancedfrom the consumer is:

u = 8.5 - p - d.There are two firms that are located at the end points, 0 and 1. Their marginal costs of production arec₁= c₂=3. Assume that in equilibrium, all the consumers are served and both firms sell a positive quantity.

[The information provided above is relevant for questions 5-10]

Question 5. Derive the demand of firm 1 for any pair of pricesp₁, p₂. [Show/ explain the derivation, it is not enough to provide a formula.]

6. Using the information in question 5, find the equilibrium pricesp₁, p₂.

7. Using the information in question 5, and your answer to question 6, in equilibrium, what is the market's Lerner Index of market power?

8. Using the infomation in question 5, and your answer to question 6, find the equilibrium prices. You may assume in equilibrium,p₁=p₂.

9. In equilibrium, what is the Herfindahl HirschmanIndex of market concerntation? [Your answer should be a number between 0 and 1, write it as a decimal].

Given the information in question 5, and the equilibirum prices you found, what is the utility of a consumer located at x=0.6.