QUESTION 7. Increasing Returns to Scale and Monopolistic Competition. 2|] POINTS. A country produces manufactured goods, whose industry is characterized by increasing returns to scale, monopolistic competition, and rms that differentiate their products. Firms are symmetric: all firms have identical cost functions and demand functions given below. 1 _ QS[;b(PP)] TC=F+aQ Where Q is the quantity demanded when the total industry demand is S , the number of lms in the industry is n , the average price in the industry is F and the price charged by the firm is P . T C is the total cost of producing Q units, where F is the xed cost of production and a is the marginal cost of production. Assume that S does not change with the price in the industry. EE a) Derive an equation that relates average cost (AC) to n, F , S , and a . That is, derive an equation with AC on the left-hand side and I? , F , S and a on the other. Hint: rm symmetry implies that each rm charges the same price. b) Derive an equation that relates marginal revenue (M) to P , n and b . Hint: use demand to get P in terms of Q then multiply by Q to get total revenue. c) To maximize prots, firms set marginal revenue equal to d) Given your answers to b) and c) derive an equation that relates P to a , b and n . e) Sketch the equations from a. and d. below. Label the equilibrium number of firms of and the equilibrium price pc . f) Suppose the country opens to trade, which leads to a larger market size, S . Show the effect of this on your gaph from e., labeling the new price p\" and the new number of rms no . Clearly label any curves that shift, and in which direction they shift