A mass of consumers is uniformly distributed along the interval [0, 1]. Two firms, A and B, are located at points 0 and 1 respectively. We denote by p, the price of firm i E A, B. A consumer located at point x = [0, 1] obtains utility UA(z)=u-PA-ta² if he consumes from firm A, and UB(x)=u-PB-t(1-2)² if he consumes from firm B. In the following, we assume that the gross utility u is sufficiently high, so that the market will be covered and all consumers will get positive utility in equilibrium. Both firms have a cost function equal to Ti(q) = (1+X)qi, where you should substitute X for the last number of your student ID number. (a) Find the demand function for both firms. (b) Assume firms set their prices simultaneously. Solve for the Nash equilibrium prices, and compute the equilibrium profits.
