Imposing a sales tax t can cause a profit-maximizing monopolist in a uniform-price monopolistic market to increase the price she charges by more than the tax.

a. Consider a monopolist who has no costs and faces two consumers, 1 and 2. Consumer i purchases one unit if the price she pays does not exceed Vi . Assume Vi v square = v > 0. Show that for some value of v and t, the imposition of a sale tax t causes the price charged by the monopolist to rise by more than t.

b. Show that if the monopolist faces a linear inverse demand function P(q) = A Bq and constant marginal cost c, then the price increase due to a tax of t is less than t.