A Spatial model of product differentiation , see the figure attached

Consider a spatial (Hotellingl model of product differentiation. There is a customer at each point of the segment on the interval [0,20]. Their location on this interval is their taste as. A customer with taste 7: who pays p for the product from the firm located at y gets a utility of 4-0 2|x yl p, and there is always an option of not buying a product at all, which gives a utility of 0. Suppose that there are two firms that produce two kinds of a product. Firm A produces the good that corresponds to taste of 0, and firm 3 produces the good that corresponds to the taste of W20 U=40-2|x-y|-p Note: for all problems below, we assume Total Cost = Marginal Cost = 0 (3} Assume that firms A and B both set a price equal to 6. Which consumer is indifferent between buying from firm A and not buying anything? Which consumers don't buy anything? What is the prot of each rm? (b) Now suppose that the prices are pd and 115, respectively. Which customer (defined by taste 1:} is indifferent between buying from Firm A and B? Find at as a function ofthe two firms' prices. Are all customers buying the product? [c] What is Firm A's optimal price (as a function of Firm B's price)? What are the equilibrium prices that rms A and B will charge? (d) Suppose that firm A gets an option to adjust its brand "location\" to y = 5. Assume that firms charge the same prices as the optimal prices from part (c). What would the profits of firms A and B be now? How much is rm A willing to pay for the possibility to make this move? Which consumers are made worse off by this change