In a market characterized by monopolistic competition each firm faces the following demand and cost functions: S[1 - bN (p − p)] 9 = TC = F + cq All variables are defined as in the class notes. a. Derive the inverse demand function and compare it to the one we used in class. What is the main difference? 1 b. Derive the profit-maximization condition for a firm in this model and solve for the firm's optimal price and quantity supplied (when firms take N and p as given) c. Is price equal to marginal costs? Under what conditions price will be equal to marginal cost, as in a perfectly competitive market? d. What is the equilibrium number of firms, prices, and average costs? e. Now suppose that the country we consider can trade with another identical country. Analyze the effect of free trade on the number of firms and prices. Provide a short and intuitive explanation for your result