Again we have two prot-maximizing rms, A and B, that engage in price competition with differentiated products. Again each rm has to decide on a price for its own product; and if rm A charges price hand rm B charges price PB, the demand for firm A's product is QA = 50 PA + PR and the demand for rm B's product is Q; = 40 + PA 3P3. Again, both rms have a constantmarginal cost of 55 per unit and no xed cost. But in this industry rm A rst sets its price PA. (and commits to it no matter what rm B does subsequently). Then rm B decides on P3 aer it learns the price ofnn A. We can thus regard this situation as a game in extensive form with perfect information. Solve this game by Backward Induction, and nd the prices (PA, Pa) charged by the two rms in the Backward Induction solution. Show your reasoning and mathematical derivation