3. Consider a monopolistic competition model similar to the one developed in class and in the textbook, but let the demand inction faced by a producer of differentiated 1rarieties be given by: or, = (35'an (Pray-1 Where 13 is the average price in the industry. Each firm as a fixed cost of production equal to F and a constant marginal cost c. a} h} E} 11} IWhat is the market share of each rm in a symmetric equilibrium in which all firms charge the same price? Without imposing symmetry. use the demand equation to express P as a function of Q, S, n' and P. Derive marginal revenue using the answer from {b} to express MR as a function of P. Use the optimality condition MR = ME, to express the optimal price as function of :3 only. By how much do prices go up when marginal costs doubles? Compare your result to those obtained in class. What explains the difference? Assume now a symmetric equilibrium in which P=f'. Use the original demand equation to express average costs in a symmetric equilibrium as function of F, c, S, and n. Draw the MR=MC curve and the AC curve (with the number of firms on the x-axis). f) Use your answers from d) and e) to derive the equilibrium values of n and P in a long-run symmetric equilibrium in which free entry drives each firm's price down to the value of average cost. g) Solve for the implied sales QD by each firm as a function of F and c. h) Discuss the effects of trade integration (an increase in S) on the equilibrium value of n, P and Q. How are these effects different from the ones derived in class? What explains the difference? i) Discuss the welfare effects of trade integration assuming that consumers value being able to consume a large number of varieties