4. A monopolist is faced with the inverse demand function P(Q) denoting the price when output is Q. The monopolist has a constant average cost k per unit produced. (a) Find the profit function (Q), and prove that the FOC for maximal profit at Q* > 0 is P(Q*) + Q*P' (Q*) = k (b) By implicit differentiation of the equation from part (a) find how the monopolist's choice of optimal production is affected by changes in k. (c) How does the optimal profit react to a change in k. 5. A firm has a monopoly in the sale of a certain commodity. Assume that the price P(Q) per unit varies with Q according to the formula P(Q) = 100-Q, QE [0, 300]. Suppose the cost function is C(Q) = 610Q3 Q+500 + 1000 1 (a) What is the profit function? 3 " then (b) Find the production level that maximizes profit, and compute the maximum profit.