Question 2 Surplus-increasing advertising in the Hotelling model Consider a horizontally differentiated product market in which rms are located at the extreme points of the unit interval. Firms produce at marginal costs equal to zero. A continuum of consumers of mass 1 are uniformly distributed on the unit interval. They have unit demand and have an outside utility of oc-. A consumer located at a: E [0,1] obtains indirect utility v1 = r1 t1. 1)] if she buys one unit from rm i and o; 2 1'2 till ac) p2 if she buys from firm 2. Firms have marginal costs equal to zero. {i} Suppose that rms have set prices at 331 and p2 respectively. Determine the demand function for each rm for each admissible price pair (pk-pg). {ii} Suppose that the social planner chooses rstbest optimal prices. Which price pairs would be socially optimal? (iii, Suppose that the two rms simultaneously set prices. Determine the market equilibrium for all possible combinations of (11,133). (iv; .From now on considerthe special case that t = 1. Suppose that each rm 2' can use adver tising 1U increase the willingness to pay from n = 1 to n = 2. Consider the twostage game in which rms choose whether to advertise at the rst stage and price at the second stage. Characterize the subgameperfect Nash equilibrium of the game depending on the advertising cost A. Consider the cases A = 2/9, A : 3/9, and A = 4/9. What is the welfare ranking? (v) " i What are the equilibria for A = 0/18 and A = 7/18? (vi) ' What are the welfare consequences of a reduction in advertising the advertising cost from A = 5/18 + e to A = 5/18 a for the limit where e > 0 (determine whethertotal surplus increases or decreases and by how much)? Comment on your result in one sentence. (vii) , What are the welfare consequences of a reduction in advertising the advertising cost from A = 7/18 + e to A = 7/18 a for the limit where e > 0 (determine whethertotal surplus increases or decreases and by how much)? Comment on your result in one sentence