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Show transcribed image text 14.10 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 analyzed by using the inverse elasticity rule (Equation l4.1). a. Consider first an ad valorem tax on the price of a monopoly's good. This tax reduces the net by the monopoly P to PO1 t)- where t is the tax Show that, with a linear demand curve and constant marginal cost, the imposition of such a tax causes price to rise by less than the full extent of the tax. b. 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. c. Describe a case where the imposition ofan ad valorem tax on a monopoly would cause the price to rise by more than the tax. d. A specific tax is a fixed amount per unit of output. Ifthe tax rate is T per unit, total tax collections are TQ. Show that the imposition of a specific 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.

14.10 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 analyzed by using the inverse elasticity rule (Equation l4.1). a. Consider first an ad valorem tax on the price of a monopoly's good. This tax reduces the net by the monopoly P to PO1 t)- where t is the tax Show that, with a linear demand curve and constant marginal cost, the imposition of such a tax causes price to rise by less than the full extent of the tax. b. 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. c. Describe a case where the imposition ofan ad valorem tax on a monopoly would cause the price to rise by more than the tax. d. A specific tax is a fixed amount per unit of output. Ifthe tax rate is T per unit, total tax collections are TQ. Show that the imposition of a specific 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.