A price-making firm sells its product in two separated markets. Total revenues of the firm are given as TR(y) = P()> + P2(12)>2. where p, is the price in submarket i(/ =1,2), and y= y + 2. The total cost function of the firm is given as C(y) = C(Vi + 12). Set up a profit maximization model for the firm and answer the following: a) Find the first-order conditions and show that the monopolist will equate the marginal cost of production to the marginal revenues in each market. b) Find the second-order conditions for profit maximization. Assuming that an interior maximum position exists, what conditions on the slopes of the marginal-revenue and marginal-cost curves are implied by profit-maximization? c) Show that a price-discriminating monopolist will charge a higher price in the market whose demand is less elastic. (Hint: Express marginal revenue in terms of demand elasticity.)