# MGEC31H3 : Taxation

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1. Terms and Concepts

2. Optimal Taxes on Consumption

3. Optimal Taxes on Labour

4. Optimal Taxes on Capital

5. Tax Evasion

LEARNING OBJECTIVES

1. What are the essential features

of optimal taxes

2. What factors influence tax evasion

ECMC31 – TOPIC 4

OPTIMAL TAXATION

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1. TERMS AND CONCEPTS

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Requirements

efficiency

o minimum excess burden

o minimum compliance costs

o minimum administrative costs

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Requirements, continued

optimal taxes balance efficiency with fairness

fairness principles are subjective and may include

o horizontal equity

o vertical equity

o benefit principle

o minimum tax evasion

o inter-generational equity

equity = fairness

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5

Defining optimal taxes

economics => prescribes efficient taxes

value judgments => prescribe fairness

specified values

+ => prescribe optimal taxes

economics

different values will lead to different versions of

“optimal” taxes

fairness principle illustrated in the remainder of

this topic is “utilitarianism”

o place equal value on everyone’s utility

o try to maximize the sum of everyone’s

utility = maximize average utility

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2. OPTIMAL TAXES

ON CONSUMPTION

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Efficient commodity taxes

if income I is fixed,

a uniform, general, ad-valorem commodity tax

looks like a lump-sum tax => no EB

I = wL + rK = what we earn

income from capital ownership

income from work

but if L or K also fall in response to commodity

tax, then tax base I also falls and EB > 0

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K = savings decision

your current income from capital came from a past

savings decision of yours

=> K = fixed in following short-run analysis

L = labour supply decision

Z = leisure decision

MAXT = total time available = L + Z

L changes when choice of leisure Z changes

thus I = wL + rK = w(MAXT - Z) + rK

= w·MAXT – wZ + rK

define potential income I* ≡ income from

working 24/7 plus your income from past

investment decisions = w·MAXT + rK, so I*= fixed

I is also what we spend on consumption,

i.e. I = PxX + PyY

so I* = PxX + PyY + wZ

fixed spending on spending on

income consumption leisure

A uniform ad-valorem tax on all consumption

plus leisure would act like a lump sum tax

with EB = 0. However, we can’t tax leisure.

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Ramsey Rule for efficient commodity taxation

tx, ty = ad valorem commodity taxes on X, Y

assume X and Y are consumed independently

=> EB = EBx + EBy

EBx = (1/2) εJx tx² (PxX)o for

MEBx = εJx tx small

EBy = (1/2) εJy ty² (PyX)o tax rates

MEBy = εJy ty

optimality criterion: set tax rates to make

marginal excess burdens equal: MEBx = MEBy

recall: εJ = εDεS /(εD+εS)

if supply is horizontal, i.e. production is constant

returns to scale (CRS), Ramsey Rule becomes

tx = εDy

ty εDx

Ramsey Rule = “inverse elasticity rule”

tx = εJy

ty εJx

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Implications of the Ramsey Rule

1. Necessities can be taxed more heavily

than most discretionary goods

2. Addictive goods can be taxed more heavily

than most ordinary goods

examples?

are such taxes fair?

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Corlett-Hague Rule

for efficient commodity taxation

tx, ty = ad valorem commodity taxes on X, Y

assume X ,Y are substitutes in consumption

w = wage-rate for labour = price of leisure

εXy = cross price elasticity of Py on X

= %∆X / %∆Py

εXw = cross price elasticity of wage-rate w on X

= %∆X / %∆w

note: tx = εyw + same

ty εxw + same

Corlett-Hague Rule for efficient tax rates

tx = εyw + εXy + εyx

ty εxw + εXy + εyx

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Implications of the Corlett-Hague Rule

Goods connected with leisure can be taxed more

heavily than most goods connected with work

examples?

are such taxes fair?

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## Document Summary

Learning objectives: what are the essential features of optimal taxes, what factors influence tax evasion. Requirements efficiency: minimum excess burden, minimum compliance costs, minimum administrative costs. 2 optimal taxes balance efficiency with fairness fairness principles are subjective and may include: horizontal equity, vertical equity, benefit principle, minimum tax evasion, inter-generational equity equity = fairness. Defining optimal taxes economics => prescribes efficient taxes value judgments => prescribe fairness specified values. + => prescribe optimal taxes economics different values will lead to different versions of. Optimal taxes fairness principle illustrated in the remainder of this topic is utilitarianism : place equal value on everyone"s utility, try to maximize the sum of everyone"s utility = maximize average utility. K = savings decision your current income from capital came from a past savings decision of yours. => k = fixed in following short-run analysis. Maxt = total time available = l + z.