Consider a broking firm that supplies consulting services. The corresponding demand relation and cost functions are and , respectively.
(a) Derive the first-order condition for the firms profit maximization. Determine the profit maximizing level of Q.
(b) Verify that, at the point of maximum profit that the second-order sufficient condition holds.
(c) Check that marginal revenue is equal to marginal cost at the profit-maximizing level of output determined in (b).