2. Consider a profit-maximizing firm producing a single commodity. If the firm gets a fixed price P per unit sold, its profit from selling @ units is n (Q) = PQ - C(Q), where C(Q) is the cost func- tion. Assume that C'(Q) > 0 and C"(Q) > 0. In Example 8.5.1, it will be shown that ( = (* > 0 maximizes profits w.r.t. @ provided that P = C(Q*) (* ) Thus, at the optimum, marginal cost must equal the price per unit. (a) By implicitly differentiating (*) w.n.t. P, find an expression for dQ*/dP. (b) Comment on the sign of do*/dP