1. Fundamental tax theories Taxation and income distribution

2. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

9. Tax liability under a hypothetical tax system

10. 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)

11. 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

12. 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

13. 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)

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. Prices and quantities before the unit tax - 1

21. 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

22. Prices and quantities after unit tax

23. 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

24. Unit tax on supply

25. 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:

26. 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

27. 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

28. 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

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

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

31. 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

32. Diagram of an ad valorem tax

33. Diagram of an ad valorem tax - 2

34. 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

35. Diagram of a payroll tax with inelastic LS

36. 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

37. 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

38. Before tax equilibrium of a monopolist

39. After tax equilibrium of a monopolist

40. 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)

41. 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

42. 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

43. An example of tax capitalization