TAXATION AND EFFICIENCY Chapter 15

Government levies tax on barley Excess Burden Defined Government levies tax on barley A Pounds of corn per year Ca Cb E1 C1 i F D B0 B1 Pounds of barley per year

Effect of Tax on Consumption Bundle Pounds of corn per year G Ca E2 Cb E1 C1 i ii F D B0 B1 Pounds of barley per year

Excess Burden of the Barley Tax Pounds of corn per year G Ca Tax Revenues H M Equivalent variation E2 Cb E1 C1 i ii F I D B0 B3 B1 Pounds of barley per year

Questions and Answers If lump sum taxes are so efficient, why aren’t they widely used? Are there any results from welfare economics that would help us understand why excess burdens arise? 15-5

Questions and Answers Does an income tax entail an excess burden? 15-6

Questions and Answers If the demand for a commodity does not change when it is taxed, does this mean that there is no excess burden? A Uncompensated response Income effect Substitution effect-compensated effect Compensated demand curve Pounds of corn per year E1 Ca i J R E2 Cb S C1 ii F K D B1 = B2 B3 Pounds of barley per year

Excess Burden Measurement with Demand Curves Excess burden = ½ ηPbq1tb2 Price per pound of barley Tax revenues Excess burden of tax (1 + tb)Pb S’b g f h d i Pb Sb Db q2 q1 Pounds of barley per year

Preexisting Distortions Theory of the Second Best Double-dividend hypothesis

Excess Burden of a Subsidy m Price per unit of housing services Excess burden n o v Ph Sh q r u (1 – s)Ph Sh’ Dh h1 h2 Housing services per year

Excess Burden of Income Taxation Excess burden = ½ εωL1t2 Excess burden SL Wage rate per hour f i d w (1 – t)w g h a L2 L1 Hours per year

The Allocation of Time Between Housework and Market Work Excess burden = ½ (ΔH)tw2 $ $ (1 – t)VMPmkt b w2 a w1 w1 (1 – t)w2 e VMPmkt VMPhome d c Hours worked in home per year H* H1 Hours worked in market per year 0’

Does Efficient Taxation Matter? Why no excess burden budget? Is efficiency the primary objective of government policy? Does excess burden mean a tax is bad?

Chapter 15 Summary Taxes and subsidies generally impose excess burdens, caused by tax- or subsidy-induced distortions in behavior Differential taxation of inputs also create excess burdens Lump sum taxes have no excess burden, although are unattractive for other reasons

Appendix A – Formula for Excess Burden A = ½ * base * height = ½ * (di) * (fd) fd = ∆Pb = (1 + tb) * Pb – Pb = tb * Pb di = ∆q η = (∆q/∆Pb)(Pb/q) ∆q = η(q/Pb)∆Pb since ∆Pb = tb * Pb ∆q = η(q/Pb)*(tbPb) = η * q * tb since di = ∆q A = ½(di)(fd) = ½(ηqtb)*(tbPb) = ½ * η * Pb * q * (tb)2

Appendix B – Multiple Taxes and the Theory of the Second Best Price per gallon of gin Price per gallon of rum f c (1 + tg)Pg (1 + tr)Pr g b h Pr a d Pg e Dr’ Dg Dr g2 g1 r3 r2 r1 Gallons of gin per year Gallons of rum per year