Question 3. Suppose that two rms engage in price competition with the demand of each firm a function of both prices: 191091.192) = a - 5P1+CP2 926011102) = a - bpz + Cpl Here, a, b and c are positive parameters dening the demand functions. Assume that b > c. You see that the demand for rm i is decreasing in its own price bp,- and increasing in the price of its competitor +cpj. So, for example, an increase in p1 reduces 01 while an increase in p2 increases D1. The cost of production is 0, there is no cost in this model. Prot is given for each rm as the price it sets multiplied by its demand. For example, the prot of rm 1, n1, is 111 = p101 (391,332). 1. Suppose that rms set price simultaneously. Find the equilibrium price pair, (p'f,p). (Hint: The payoffs are symmetric so look for the symmetric equilibrium where prices are equal.) 2. Find the prot for each rm. 3. Suppose that b = we, 1/ > 1. How does prot vary as c varies. 4. Finally, suppose that the rms behave in Stackelberg fashion. Firm 1 sets a price, p1, rm 2 observes that price and then sets its price, p2. Find the equilibrium prices (361, p2). So, rm 1 acts as a price leader