. First, we examine a monopolistic firm. The firm faces a market described by the (inverse) demand function p(y) = A B y, where p is the (maximum) price at which y units of output can be sold on the market. The firm's cost function is given by C(y) = y ^2/2.

3.1 Find the profit-maximizing price-quantity combination for the monopolist and the corresponding profit for this firm.

3.2 Formulate your first-order condition from part 3.1 in terms of the elasticity of demand. That is, compute the demand elasticity, and use the elasticity formula to find the profit-maximizing quantity of output.

3.3 The demand is inelastic for prices below some cutoff p. What is p? Equivalently, the demand is inelastic for quantities above A/B p/B. Show that the profit is decreasing whenever y > A/B p/B. You have just shown that a monopolist will never choose to operate where the demand curve is inelastic. What is the intuition