14.7 Taxation of a monopoly good The taxation of monopoly can sometimes produce results different from those that arise in the competitive case. This problem looks at some of those cases. Most of these can be analysed by using the inverse elasticity rule (Equation 14.1).

a.

Consider irst an ad valorem tax on the price of a monopoly’s good. This tax reduces the net price received by the monopoly from P to P(1 − t) −

where t is the proportional tax rate. Show that, with a linear demand curve and constant marginal cost, the imposition of such a tax causes price to increase by less than the full extent of the tax.

b.

c.

d.

Suppose that the demand curve in part

(a) were a constant elasticity curve. Show that the price would now increase by precisely the full extent of the tax. Explain the difference between these two cases.

Describe a case where the imposition of an ad valorem tax on a monopoly would cause the price to increase by more than the tax.

A speciic tax is a ixed amount per unit of output.

If the tax rate is τ per unit, total tax collections are τQ. Show that the imposition of a speciic tax on a monopoly will reduce output more (and increase price more) than will the imposition of an ad valorem tax that collects the same tax revenue.