Consider a monopolist who faces a linear demand curve P = 24 – Q, where P is the price the monopolist charges and Q is the quantity consumers purchase. The monopolist’s marginal revenue is MR = 24 – 2Q (as the chapter explains, if demand is linear then demand and marginal revenue have the same intercept but marginal revenue has twice the slope). The monopolist produces this good at a constant average and marginal cost of $6.
a. Show that the monopolist’s profit-maximizing price is $15.
b. Suppose the government imposes a tax of T dollars per unit on the monopolist, and therefore the monopolist’s marginal cost is now 6 + T. Show that the monopolist will pass along half of the tax to its customers, i.e., show that the profit-maximizing price is now 15 + (T/2).