labour income taxation

8/7/2019 Labour Income Taxation

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PUBLIC ECONOMICS


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LABOUR INCOME TAX

When discussing Labour Income Taxation, we are primarily concernedwith MARGINAL TAX RATES.

T

he marginal tax rate is the derivative of the tax function (which is afunction of income (z):

A PROGRESSIVE tax structure is one where the marginal tax rate isincreasing in income (with a positive derivative).

A FLATE RATE tax structure has a constant marginal tax (derivative is0).

A REGRESSIVE tax structure is one where the marginal tax rate isdecreasing in income (with a negative derivative).

We do not need to derive the optimal labour income tax, but the nextslides will focus on its ASSUMPTIONS and RESULTS.

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LABOUR INCOME TAX

Assumptions:

PERFECT COMPETITION

Labour L is only factor of production.One unit of effective labour provides oneunit of consumption good x (CRS):

L = x

Each household is characterised by theirSKILL LEVEL s. This is their marginalproduct of labour, and is constant.Itdetermines their labour supply.

Skills are distributed within a finitebounding: S =[S1, S2]. Has a densityfunction (s).

Income is therefore a function of the skilllevel, and can be termed the EFFECTIVELABOUR SUPPLY:

Z(s) = s.L(s)=s.x

Normalise the price of x to 1, and the

wage is s:

Z(s) = s

Individuals maximise a quasi-concaveutility function subject to a budgetconstraint:

Max: U(x, L(s))s.t: x(s) = s.L(s) T(s.L(s))

T(s.L(s)) = T(z(s))is the labour incometax.

Governments aim to maximise a

BERGENSON-SAMUELSON SOCIALWELFARE FUNCTION, which is a functionofindividuals utilities only, not nationalincome or income distribution (directly).

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LABOUR INCOME TAX

No externalities to take into account; the problem only considers the efficiency-equitytrade off.

The assumptions also imply:

Individuals only care about their own consumption; there are no envy effects that causethem to behave like higher income individuals.

All individuals exhibit the same preferences, utilities are increasing in consumption anddecreasing in labour supplied.

Skill is independent ofthe amount of labour supplied; there is no learning by doing.

The Government has a constant revenue requirement.

In addition, we need:

AGENT MONOTICITY: Labour income is increasing in skill level, the sufficient condition isthat the consumption good x is a normal good. Equivalent to saying that consumptionincreases as the wage increases.

INCENTIVE COMPATABILITY CONSTRAINT: Every individual has an optimal bundle of incomeand consumption (x(s), z(s)) for any worker ofskill s. Labour tax is chosen to realise theseoptimal quantities. However, there is information asymmetry adverse selection as theagent knows their true skill level whilst the planner (Gov.) only observes purchases and

labour income.

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herefore, the tax must constructed such thatTHE OPTIMAL BUNDLE GIVES

AT LEAST AS MUCH UTILITY AS ANY OTHER CHOICE.


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LABOUR INCOME TAX

Results from the optimal tax problem:

I. Mirrlees: Ifthere is an ability level Sx within [S1, S2]where L(Sx)=0, then L(S)=0 for all skill levels S


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LABOUR INCOME TAX

The optimal tax schedule therefore looks somethinglike below (note that there is an implicit level belowwhich net tax collection is negative due to the impliedsubsidy).

0

SkillS1 S2

T(z)

-ve tax

collection

+ve tax

collectionArea under curve =

Total tax revenue

Progressive Regressive


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LABOUR INCOME TAX

LxU ! 1lnln

Cobb-Douglas Utility Function:

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Parametric SWF(utilitarian when v=0):

Density function

for skill

distribution


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LABOUR INCOME TAX

The Mirrlees (1971) results are on the left; notethe low M.T rates, and the rise after increasingequity v.

Atkinson (1972 shows the same thing (above) inmore drastic a fashion Rawlsian SWFonly caresabout utility of worst-off individual, you can see arise in both the average and marginal rates.

Mirrlees (1971) and Kanbur + Tuolmala (1994)both show that an increased dispersion ofskillsleads to higher tax rates AND moves the maximumtax rate up the income scale (increases theprogressivity of the system).


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LABOUR INCOME TAX

Empirical data:

The UK Income tax follows the optimal taxtheory to an extent (see the schedule).

It has a 0 marginal tax rate at the bottom ,

none of the rates are above 100% or negative.The rates are also in line with those in thenumerical computations. Rates are notprogressive everywhere, some regressivity atthe latter end.

However, rates at the top contradict theory.They are progressive and greater than 0 thereis distortion at the top. Why? We need to alterthe assumptions of the model:

There could be externalities associatedwith activities that are popular with richpersons (fast cars), introducing acorrective element.

There could be capital income taxincluded with the income tax schedule.

Utilities could be interrelated, and there

are fashion/envy effects.

labour income taxation

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