Commodity Taxation

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Chapter 14 Commodity Taxation

• Essential reading
– Hindriks, J and G.D. Myles Intermediate Public Economics. (Cambridge: MIT Press, 2005) Chapter 14.

• Further reading
– Diamond, P.A. and J.A. Mirrlees (1971) ‘Optimal taxation and public production 1: Production efficiency and 2: Tax rules’, American Economic Review, 61, 8—27 and 261—278. – Madden, D., (1995) ‘An analysis of indirect tax reform in Ireland in the 1980s’, Fiscal Studies, 16, 18—37. – Murty, M.N. and R. Ray (1987) ‘Sensitivity of optimal commodity taxes to relaxing leisure/goods separability and to the wage rate’, Economics Letters, 24, 273—277. – Myles, G.D. (1987) ‘Tax design in the presence of imperfect competition: an example’, Journal of Public Economics, 34, 367—378.

– Ray, R. (1986a) ‘Sensitivity of ‘optimal’ commodity tax rates to alternative demand functional forms’, Journal of Public Economics, 31, 253—268.

• Challenging reading
– Diamond, P.A. (1975) ‘A many-person Ramsey tax rule’, Journal of Public Economics, 4, 227—244. – Deaton, A.S. and N.H. Stern (1986) ‘Optimally uniform commodity taxes, taste difference and lump-sum grants’, Economics Letters, 20, 263—266. – Dreze, J.H. (1964) ‘Some postwar contributions of French economists to theory and public policy with special emphasis on problems of resource allocation’, American Economic Review, 54, 1—64. – Ray, R. (1986b) ‘Redistribution through commodity taxes: the non-linear Engel curve case’, Public Finance, 41, 277—284.

• Commodity taxes are imposed upon purchases of goods • Transactions are generally public information • The taxes drive a wedge between producer and consumer prices – This causes a distortion in choices

• The level of welfare is reduced compared to using lump-sum taxes • This is the price of incentive-compatible taxation

• On the demand side of the market income and substitution effects predicts the consequences of a price rise • On the supply side the tax is a cost increase and firms respond accordingly • The central question is the choice of the best set of taxes – Usually interpreted as the taxes that raise at given level of revenue with least efficiency cost

• This introduces the analysis of optimal taxation

Deadweight Loss
• Lump-sum taxation does not cause any distortions • Commodity taxation does cause distortions – Demand shifts from goods with high taxes to goods with low taxes

• These substitution effects are the tax-induced distortions • A commodity tax raises revenue but reduces welfare • The deadweight loss is the amount the welfare reduction exceeds revenue raised

Deadweight Loss
• Fig. 14.1 illustrates deadweight loss • Without taxation the price is p, consumption X0, and consumer surplus abc • With a tax of t the price is q = p + t, consumption X1, and consumer surplus aef • The tax raises revenue tX1 which is area cdef • The deadweight loss (DWL) is the triangle bde Price a

f q  pt p c

e b






Figure 14.1: Deadweight loss

Deadweight Loss
• • • • Triangle bde is equal to [1/2]t[X0 – X1] The elasticity of demand is d = pdX/Xdp Let dX = X0 – X1 and dp = t Using these definitions the deadweight loss is approximately DWL = [1/2]|d|[X0/p]t2 • DWL is proportional to the square of the tax rate – It rises rapidly with increases in taxation

• DWL is proportional to the elasticity of demand
– For a given tax less deadweight loss is produced when demand is inelastic

Deadweight Loss
• In Fig. 14.2 a is the initial choice with no taxation • Point b is the choice with a lump-sum tax • A commodity tax on good 1 raising the same revenue as the lump-sum tax leads to c • U1 – U2 is the deadweight loss in utility terms • The shift in budget from b to d is a monetary measure of loss Good 2

c b d

a U0 U1 U2 Good 1

Figure 14.2: Income and substitution effects

Deadweight Loss
• Deadweight loss is a consequence of substitution...
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