Fundamental tax theories Taxation and income distribution

Functions of tax revenues Financing the supply of public goods and services Redistributing income/resources Stabilizing macroeconomic fluctuations Incentivizing selected economic activities Correcting economic inefficiencies/distortions

Classification of public revenues - 1 There is a continuum of types of public revenues from prices (essentially private → voluntarily paid) and taxes (essentially public → coercive power) Price Price=argmax(profit) → MC=MR Fairly rare as a public revenue Quasi-private price MC=MR but with regulated supply (es. wood production) Public price (tariff) Paid by who demands the good/service, also the only beneficiary Price=average cost (but: X inefficiency) Goal of enlarging the consumption of the good/service Political price Price<average cost Costs not fully covered

Classification of public revenues - 2 Charge/fee Paid by the beneficiary Price=externality generated by the public supply Benefit often not divisible among members of the collectivity Sometimes not→ university education Sometimes yes→ stamp Special contributions Does not need the demand of the good/service by the citizen Benefits are not divisible, but there is a group which bears the burden of the tax Government autonously decides the tax burden → coercive power E.g. Street lightining Taxes Coercive levy without direct connection with the provision of a service Demand of the good/service by the citizen is not needed E.g. Personal income tax

Structure of a tax Features of a tax: Presupposition → fact/sitiuation to which the law associated the duty to pay the tax Tax base → quantitative evaluation of the presupposition In monetary terms → ad valorem tax In physical quantities → excise/unit tax Tax rate → how much one must pay per unit of tax base In % → ad valorem; In monetary units (e.g. gas) Legal/statutory → referred to the tax base Actual/economic → referred to overall income Tax revenue → tax rate * tax base

Statutory and economic tax incidence Statutory incidence of a tax → indicates who is legally responsible for paying the tax Economic incidence of a tax

Average and marginal tax rates Average tax rate (AVGTAX) → ratio between tax liability T(y) and tax base y Marginal tax rate (MTAX) → ratio of the variation of the tax liability and of the variation of the tax base Also defined as the change in taxes paid due to a change in income A tax system can be progressive with an increasing average tax and a constant marginal tax (see table) MTAX≤1 not to alter the before-tax ranking of income levels

Tax progressivity Measure of tax progressivity Proportional → tax liability increases directly with Y AVGTAX=T(y)=Ty=constant=MTAX Progressive → AVGTAX increases with Y AVGTAX<MTAX Regressive → AVGTAX decreases with Y AVGTAX>MTAX

Tax liability under a hypothetical tax system

How to implement tax progressivity-1 Continuous progressivity Average tax rate is an increasing continuous function of Y (not much used any more) E.g. Green line in diagram Progressivity by income brackets Average tax rate is an increasing discrete function of Y E.g. IRPEF in Italy (blue line in diagram)

How to implement tax progressivity-2 Progressivity can be implemented by defining the tax liability by means of: Tax deductions → reduction of taxable income before applying the tax Tax base =income - deductions Tax = tax base × tax rate Tax credit → subtraction from tax liability Tax liability=(tax base × tax rate) – tax credit

The « flat » tax Tax deductions and credits generate a highly progressive structure for lower incomes and a proportional one for higher incomes Flat tax → only in deductions and credits are constant → effective MTAX = statutory MTAX Flat tax possible in developed countries only with high tax rates (>50-60%) Deductions and credits are variable, usually decreasing Dynamics of effective MTAX is unpredictable Need to finance large welfare states

Classifications of taxes Direct taxes → affect direct manifestations of ability to pay E.g. Income and wealth Indirect taxes → affect direct manifestations of ability to pay E.g. consumption, trasferts of activities Real → affect the real presupposition of the tax (‘res’) E.g. Labor income, capital income Personal → affect individuals according to the characteristics of income earner and/or wealth owner Ordinary → levied regularly (e.g. every year) Extraordinary → levied irregularly (e.g. Special contribution to join the Euro)

Tax incidence - 1 Allows evaluating the tax system from an equity point of view Positive problem of how taxes affect the distribution of incomes Important! → all taxes produce their effects by changing relative prices Tax on income → affects relative prices of labor and leisure Tax on a commodity → affects the price of the taxed commodity relative to all others Tax incidence: Legal/statutory → points out who is legally responsible to pay the tax Economic or effective → points out who actually pays the tax (=bears the burden of the tax) → change in the distribution of private resources due to the tax Difference between statutory and economic incidence is tax shifting

Tax incidence - 2 Only individuals pay taxes Taxes on corporations paid by individual shareholders → classification of ind by Functional distribution of Y → defines ind according to role played in productive process (K, L) Quite outdated → workers are often shareholders Size distribution of Y → looks at how taxes affect how total Y is distributed among individuals Is it better to tax the uses or the sources of Y? → Looking at a tax on a commodity Use → P increases, Qd decreases→ Qd of inputs decreases Sources → P of input increases, Qd decreases→ Qs of good produced with input decreases Economists usually consider either one → assume their equivalence Often a reasonable hypothesis, but it should be verified

Tax incidence - 3 Tax produces economic effects by changing relative prices → tax incidence depends on how prices are determined Different between monopoly and perfect competition Changes in relative prices reflect changes in individual behavior (=behavioral esponses) Lump sum tax → a tax whose value is independent from individual behavior → no margin is affected Usually does not exist → capitation taxes of Middle Ages → but you could always commit suicide Community Charge (‘poll tax’) of Thatcher government in the UK has been the closest example of a lump sum tax Used especially for analyses of differential tax incidence

Tax incidence - 4 Especially appropriate for earmarked taxes Tax incidence depends on disposition of tax revenues Balanced-budget tax incidence → computes the combined effects of levying taxes and of expenditures financed by those taxes Especially appropriate for earmarked taxes Differential tax incidence → compares the incidence of a tax with that of another tax, usually lump sum, independently from the expenditures Absolute tax incidence → examines the effcts of a tax assuming no changes in other taxes and expenditures Used in macromodels

Partial vs. general equilibrium tax incidence Tax incidence in partial equilibrium framework Examines how a tax affects the distribution of income by changing the relative prices Focus on a single industry/sector OK if market is small wrt the economy Sensible to market type Ignores the effects on other sectors Tax incidence in a general equilibrium framework Considers feedback in other markets Considers effects on input markets (uses and sources) Considers functional distribution of income

Partial equilibrium: a unit tax Fixed amount levied per unit of commodity sold= excise tax First example with a statutory incidence on demand Before the tax in equilibrium QS=QD and sold at same P Seller (n) and buyer (g) face same P After tax Pg and Pn differ Demand curve measure the individual’s marginal willingness to pay, i.e., how much an individual is willing to pay for that quantity Q If a tax equal to u is intriduced → individual willingness to pay for that good does not change Producer/seller receives Pg =(Pn - u) Points a and m on the demand curve no longer perceived by the seller who instead perceives b and n Equivalent to generating a new demand curve perceived by seller

Prices and quantities before the unit tax - 1

Description of diagram Equilibrium Q is now at Q1<Q0 Equilibrium P at Pg>P0 for buyer Price perceived by seller Pn<P0 Tax revenues are knfh Tax rate is u=kn Consumers and buyers divide the burden of the tax since Pg>P0 and Pn<P0

Prices and quantities after unit tax

Unit tax on demand vs. supply Tax incidence of a unit tax does not change if it is levied on supply or demand If a unit tax u’ is levied on supply (statutory incidence) and firm had to receive at least Pi before the tax in order to Qi, after tax it must receive pi+u’ Equilibrium points are identical

Unit tax on supply

A numeric example - 1 Suppse that market for champagne wine is characterized by the following linear demand and supply functions: A unit tax of €8 per bottle opens a wedge between P paid by consumers and P recived by sellers. Before tax, the system of equations looks ike the following:

A numeric example - 2 After tax seller receive, per bottle sold, €8 less than the price paid by consumers Solvying the before tax system of equations Risolvendo il sistema iniziale one gets an equilibrium price P = 20 and an equilibrium quantity Q = 60. Solvying the after tax system of equations one obtains

A numeric example - 3 In this case, the statutory incidence falls 100% on consumers, but economic incidence is evenly split between consumers and producers: In other words, half of the tax burden is shifted from consumers to producers

Tax incidence and relative elasticities Incidence of a unit tax depends on the relative elasticity of supply and demand The more a curve is elastic, the easier is substituting that goo with another one → the easier is escaping the tax by shifting it onto the other side of the market If the supply is perfectly inelastic the tax due decrease of P is entirely borne by the seller If the supply is perfectly elastic the tax due rise of P is entirely borne by the consumer

The case of a perfectly inelastic supply Perfectly inelastic supply: the decrease of P is entirely borne by the seller

The case of a perfectly elastic supply Perfectly elastic supply: the increase of P is entirely borne by the consumer

Ad valorem tax A tax whose rate is a percentage of the P is defined an ad valorem tax e.g. VAT Tax incidence analysis of an ad valorem similar to that of a unit tax Examine how the ad valorem tax changes the effective demand and find the new equilibrium Difference from unit tax is that the demand curve shift downwards by the same percentage value for each unit, not by the same absolute value as in unit tax → slope of demand curve changes, not just the intercept Ad valorem taxes much more common than unit taxes

Diagram of an ad valorem tax

Diagram of an ad valorem tax - 2

Taxes on labour input The analysis of the PE incidence of a tax on input is analogous to that of a tax on a commodity Payroll tax → tax levied on wages to finance the U.S. Social Security System → similar in other tax systems Nominally divided between employee and employer (7.65% each, for a total of 15,3%) The statutory distinction between employer and employee is economically irrelevant If LS is inelastic, payroll tax is entirely paid by employees in the form of lower salaries Equivalent to ad valorem tax with inelastic supply Payroll tax shifts demand curve from DL to D’L → employers are not willing to pay workers more than w0 w0=equilibrium initial wage; wg=w0=wage paid by employer; wn=after tax net wage The burden of the payroll tax is entirely borne by employer

Diagram of a payroll tax with inelastic LS

Capital taxation in a global economy The analysis is the same as for commodity taxation and payroll taxes on labor If capital markets are closed to international trade → demand for capital is downward sloping (firms demand less capital when it becomes more expensive) while the supply of capital SK is upwardly sloped (individuals save more when the return to saving increases) → tax on K is partly borne by capital owners, depending on the relative elasticities → capital tax generates revenues In an open economy (perfectly mobile K) K supply is perfectly elastic If suppliers of K get less than the international rate of return, they will invest abroad Either the before tax rate of return increases to offset the tax, or capital will be invested elsewhere → tax on K generates no revenues

Commodity taxation under monopoly Simple unit tax → logic of the analysis the same as before Pg=P paid by consumers after tax P0= equilibrium P before tax Pn= perceived P by monopolist after tax Pg>P0>Pn X0= equilibrium Q before tax X1= equilibrium Q after tax X1<X0

Before tax equilibrium of a monopolist

After tax equilibrium of a monopolist

Tax incidence under monopoly After tax equilibrium price has gone up (Pg>P0) and quantities have gone down X1<X0 Consumers partly bear the burden of the tax, depending on the elasticity of demand Monopoly profits are lower: abcd>fghi Monopolist bear part of the tax burden notwithstanding his market power Result is the same under ad valorem tax Is taxing monopolies a way to transfer resources from monopolists to the state (and hence to reduce market failures associated with monopolies)? → One must not underestimate the lobbying abilities of a monopolist (→ public choice)

Profit taxes The tax does not affect either MC or MR Profits → rent to firm owners in excess of the opportunity costs of inputs used in the production process (including the firm owner) Entirely borne by firm owners The tax does not affect either MC or MR Equilibrium P e Q are not affected → only profits are reduced The reason is that, mathematically, what maximizes π maximizes also (1-t)π In the long run π=0 Profit tax generates no revenues Not used because the operational definition of π is fraught with difficulties

Tax incidence of property taxes and capitalization If a property/asset is durable and in fixed Q (e.g. A house) →reduction of P due to the tax on property is entirely capitalized in the PV of the property The P of property decreases by the PV of all the future tax payments → capitalization → the tax is fully paid by the owner of the property at the moment the tax is introduced (→ the price is reduced) Future owner will bear the future tax payments, but he/she has bought the property at a lower price

An example of tax capitalization