Chapter 3 - Efficient AND Equitable Taxation PDF

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CHAPTER 3 - EFFICIENT

AND EQUITABLE TAXATION

I. Optimal Commodity Taxation At what rate should G&S should be taxed? This theory provides a framework for answering this question. We’ll obviously need to know the government’s goal, and we’ll assume it’s to finance the state’s expenditure and minimizing the EB, without lump-sum taxes. We’ll consider Stella who only consumes two goods X, Y and also leisure l with w, PX, PY and T´ . Therefore,

BC =

w∗( T´ .−l)

=

P X X + PY Y

wT =P X X + PY Y + wl Adding an ad valorem-tax to l, X and Y would then give,

1 wT =P X X + PY Y +wl 1+t Adding this tax is equivalent to reducing the available time by (1/(1+t) %. So, it would have the effect of a lump-sum tax as the individual doesn’t change his allocation as the relative prices are the same. But, putting a tax on leisure time is impossible. Therefore, an excess burden seems inevitable. The only possibility would be to tax as low as possible X and Y in order to get the fiscal revenue. It might seem as a solution to tax X and Y at the same rate (neutral taxation) but it’s inefficient. The Ramsey Rule How should we tax X and Y in order to get the FR but with the smallest EB? We’ll suppose X and Y, un-related commodities. Hence a price change in one doesn’t affect the other. Let’s suppose that a unit tax is levied on X which lowers the quantity, the excess burden of the tax is the area of triangle abc. Now suppose we raise the tax by 1, the quantity demanded falls by Δx to X2; and the associated excess burden is triangle fec.

The marginal excess burden is the difference between the two triangles, trapezoid fbae and equal to ΔX.

In order to minimize the overall excess burden, we’ll need that the marginal excess burden for the two goods are equal. Now, we must verify that

∆ X ∆Y = . Y X

This implies that there should be proportional changes in quantity, not prices! Why? Because EB is the result of distortions in quantities.

Definition:

ε X∗t X =ε Y ∗t Y εX tX = εY t Y

εi

: The compensated elasticity of demand for i

tX

: The tax rate on i

ε i t i : The proportional reduction in i

The inverse elasticity The Corlett-Hague Rule When there are two commodities, efficient taxation requires taxing the commodity that is complementary to leisure at a relatively high rate. This would increase the price of leisure therefore reducing the demand for leisure. Equity considerations It is fairly recognized that we should have a vertical equity: distribute burdens fairly across people with different ability to pay. The departure from Ramsey rule depend on two consideration: (1). How much society cares about equality (1$ of a rich = 1$ of a poor?) (2). How rich and poor consume both goods in the same proportion, applying a different tax rate can’t affect the income distribution.

II. Optimal User Fees So far, we’ve assumed that the production was only private and that the government’s only problem was so set taxes that determine the consumer prices. But the government can also produce goods and the government must directly choose a user fee (price paid by the consumers provided by G). Analytically the user fee and optimal tax are closely related the only difference is that the government decides indirectly on the price paid by the consumer but with public goods they decide directly. The government usually produces G&S in case of Natural Monopoly. If the monopoly is unregulated, this would occur:

The output Zm isn’t efficient as p ≠ MC. This is the justification for the government’s intervention. The obvious solution to this efficiency problem would be that the government would produce until p = MC with Z*. But at Z* the price doesn’t even cover the cost.

So, how should the government confront this dilemma? 

The Average-Cost Pricing

Just set produce until the point where p = AC, such that the profits are equal to 0. We therefore increase the output up to ZA. Still, this output isn’t efficient. 

Marginal Cost Pricing with lump sum taxes

Just set produce until the point where p = MC, and cover the deficit by levying lump sum taxes. Such that efficiency is assured. However, there’s 2 problems with this solution. (1) Lump sum taxes are generally not available, so this would require distorting taxes whose impact could outweigh the efficiency gain. (2) There’s a widespread belief that fairness requires consumers of public good to pay for its costs. The so-called benefits-received principle. 

A Ramsey solution

The government as a whole can’t lose money but some sectors could. So, by how much should the user fee for each service exceed its marginal cost? Set the user fees such that the demand for each commodity is reduced proportionally.

III. Optimal Income Taxation 

The Edgeworth’s Model

It’s an optimal income taxation model with 3 assumptions: (1) The goal is to maximize the social Welfare (s.t. W = U1 + U2 + … + Un) (2) All individuals have the same U function of only Y (3) Total Y is fixed

In order to max W, it requires that the MU of Y is the same. It states that taxes should be set such that the after-tax redistribution of income is as equal as possible. Rich (low loss of MU) → Poor (high gain of MU) 

Mirlees (1971) – Equity-Efficiency trade-off

Modern studies show that the 3rd assumption is impossible. Y is determined by the allocation ratio between work and leisure such that taxes on Y are distortive. High tax-rates engender less revenue to redistribute. He concludes to an approximately linear taxation of Y is the best way to

max W (U ) i=n

Y taxes are a much less powerful tool for income redistribution than believed. 

Stern (1987) – flat income tax

He reformulates the basic Edgeworth model considering the choice between l and w. YAT = tY – α The problem is to find a α and a t that minimizes EB. The conclusion is that higher Y should be taxed at lower marginal rate => such that they increase L and therefore the tax revenue.

IV. Politics and the time inconsistency problem Time inconsistency (Kydland and Prescott, 1977): a rational government that decides today an optimal policy to maximize citizens’ welfare, if it has the opportunity to re-optimize it and change policy tomorrow it will do so. Applied to taxation: if a tax on K is applied today with a promise that K will not be taxed in the future any more → a tax on K tomorrow is a lump sum tax → investment choices had already been done under the promise of no taxation tomorrow → this creates the incentive for the government to renege the promise. But rational individuals would understand that and therefore change their saving habits and some inefficiencies appear.

V. Other criteria for tax design a) Politics and Leviathan The optimal theory of taxation is purely normative. In the real-world tax systems are quite different from the optimal ones. Brennan and Buchanan (1980), developed a leviathan model where an unresponsive, undemocratic government maximizes tax revenues rather than SWF.

Constitutional constraints to taxation can be rationalized as an ex-ante precaution against a Leviathan government. Citizens may prefer an inefficient tax system to prevent government from taxing too much or to behave in time inconsistent ways.

b) Horizontal Equity This criterion for evaluating a tax system is embodied in the notion of horizontal equity. It states that people in the same position should be treated equally. We therefore need to define equal position, we could use Wealth, Income or even Consumption as an index of ability to pay. Unfortunately, those measures represent the outcomes of people’s decision, and are not really measure of equal position. If A works 150h and earns 100, while B works 2200h and also earns 10$ an hour. A’s income is 15 000$, while B’s is 22 000$, so they’re equal in terms of income, however they have the same earning capacities. A just works more than B, and this is decision so we could assume that two individuals with not the same income are equal. [Same thing for Wealth or C]. So, we could assume that the wage rate could be a better indicator but we could apply the same criticism as depends of Human K (on-the-job-training, education...). Feldstein suggests therefore to measure equal position with a utilitarian approach. Hence, the utility horizontal equity but this would require that individual have the same preferences and calculating U’s are complicated. The solution is to keep the tax system constant and let people optimize. Rule definition of horizontal equity: The rules that govern the selection of taxes are more important for judging fairness than the outcomes themselves. Nozick’s view is to say that redistribution is unacceptable only if it’s the result of improper rule (e.g. theft) But we could also consider that redistribution is not so important as individuals are mobile (social elevator) they change social classes.

c) Cost of Running the Tax System An implicit assumption we’ve made is that administering the tax system has no cost although, in the U.S. for every 100$ raised there’s 0.44$ in costs. However, we could also consider the compliance cost of taxes (time spent to prepare tax declaration, professional advices, ect…) this is quite substantial around 10% of tax revenues. Obviously, no tax system is cost-less, but we need to compare the gains in excess burden (for example) to the incremental administrative costs.

d) Tax Evasion This is one of the most important problems facing any tax administration. First off, we need do differentiate Tax Evasion and Tax avoidance. Tax avoidance: Changing its behavior in order to pay less tax [Legal] Tax Evasion: Failing to pay legally due taxes [Illegal] Positive Analysis of Tax Evasion If we consider R the amount, he hides from the tax system; p the probability to get caught and the MP the marginal penalty. We can therefore compute and see what decision the player will make.

The optimal cheating will therefore be,

MB = MC The model predicts that when marginal tax rates go down so does cheating. The more progressive the tax system, the more convenient evading.

e) Measuring and Remedying Tax Evasion (1) Correlating Income to expenditures [Living Standards] => Pretty unfair and rigid to assume that everybody with the same income has the same lifestyle. (2) Surveys => People can lie (3) Measuring the preference for cash payments in the economy. => Increase the psychic cost of being caught (dishonour) => Lowering the tax progressivity => Changing the probability of being audited => Improving tax morale, people evade because the government doesn’t provide enough good quality for the taxes collected.

However, eliminating the underground economy could be not optimal as some activities would disappear as t>0....