Consider the monopolistic competition model of increasing returns to scale studied in class. Consider a single country in isolation. The demand for each variety is the following: q(p)=S*[(1/n) ‐ b*(p–Pm)] The price set for a variety is p. The average industry price is Pm. The market size is S = 100. The responsiveness of consumers' demand for this variety to price deviations from the average market price is given by a constant, b = 1. Each firm's average total cost is given by ATC(q) = F/q + c where marginal cost is constant at c = 10 and fixed cost is F = 20.a. In a symmetric equilibrium, find an expression for each firm's average cost as a function of the number of firms, n. Graph this with cost on the vertical axis and the number of firms on the horizontal axis. b. Again assuming a symmetric equilibrium, write the expression for a firm’s price as a function of the number of firms. Graph this the price on the vertical axis and the number of firms on the horizontal axis. c. Solve for the equilibrium number of firms, n. d. True or false? If the market size quadruples to S = 400, for instance, due to trade, the number of firms will also quadruple. (Explain your answer.)