Answers to numerical questions Chapters 20-34

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Answers to Questions in Public Economics Chapters 20 to 34 Peter Abelson Chapter 20 Introduction to Public Finance 4 The tax paid on \$60,000 would be (\$20,000 × 0.20) + (\$40,000 × 0.35) = \$18,000. The average tax rate would be 30 per cent. 5 No, this is a progressive tax rate structure. The average tax rate rises with income. With an income of \$20,000, tax is \$3500 and the average tax rate is 17.5 per cent. With an income of \$30,000, tax is \$6000 and the average tax rate is 20.0 per cent. The marginal tax rate is always higher than the average tax rate. Chapter 21 Incidence of Taxation 6 (i) At equilibrium Q d = Q s . Before tax, equate demand and supply and obtain Q d = 50 – 4p = 30. The market clearing price is \$5. (ii) After a tax of \$4 per unit is imposed on suppliers, they still supply 30 units (supply is perfectly inelastic). Demand is unchanged. So consumers pay \$5 and purchase 30 units. But producers receive only \$1 after paying the tax. Producers bear all the costs because supply is completely inelastic. Suppose that the tax is levied on consumers: Q d = 50 – 4(P s +4) = 30. It follows that 4P s = 4, so P s = 1. P c = 5 (as before). (iii) The tax raises 30 × \$4 = \$120 revenue. 7 (i) In equilibrium, Q d = Q s , 80 – 3P d = 40 + P s . But P d = P s. Therefore, the 4P = 40. The pre-tax price is \$10 and 50 units are supplied. (ii) Post–tax, 80 – 3P d = 40 + 1(P-2), where the tax is placed on the producer. The post-tax demand price is \$10.5 and the price that producers receive after tax is \$8.5. Consumers purchase 48.5 units. (iii) ¾ of the tax is paid by the producer given by P s / T = \$1.50, while the consumer pays P d / T = \$0.50 The tax paid is \$97.00 Consumers pay \$24.25. Producers pay \$72.75. Peter Abelson 25/08/2010 1

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8 (i) With no taxation, the present value (PV) of income = \$40,000 + \$40,000 / 1.05 = \$78,095. The PV of consumption = \$30,000 + (10,000 × 1.05) / 1.05 + \$40,000 / 1.05 = \$78,095. With no tax on income, PV of Bruce’s consumption = PV of earnings (ii) (a) With tax of 20% on income PV of income with no saving (consumption) = (\$40,000 × 0.8) + (\$40,000 × 0.8) / 1.05 = \$62,476 PV of consumption with saving = (\$40,000 × 0.8) –\$10,000 + (\$40,000 × 0.8) / 1.05 + (\$10,000/1.05) + (\$10,000 × 0.05* 0.8)/1.05 = \$62,380 (b) With tax of 20% on consumption PV of consumption = (\$30,000 × 0.8) + (\$40,000 × 0.8) / 1.05 + (\$10,000 × 1.05 × 0.8) / 1.05 = \$62,476 (iii) (a) With low tax rates and a low rate of interest, a tax on income marginally discriminates against saving. (b) With a tax on consumption there is no discrimination against
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