1. Taxation and income distribution
Session 6
Taxation and income distribution

2. Introduction Is the tax burden distributed fairly?
Is the tax burden distributed fairly?
Statutory Incidence : indicates who is legally responsible for a tax.
Normally the statutory incidence is on the seller.
But the situation differ with respect to who really bears the burden..
Prices may change in response to the tax.
Tax Analysis – use of economic theory to analyze impact of taxes
Equity and Efficiency – how do taxes affect the distribution of income, how do taxes affect economic efficiency
Statutory Incidence - who is legally responsible for tax (who writes the check)
Economic Incidence – whose purchasing power is reduced by the tax
Tax Shifting – extent that statutory and economic incidence differ
Partial Equilibrium Models- look at a single market, appropriate when market for commodity is small relative to economy

3. Economic Incidence
It is the change in distribution of real income induced by a tax.
The main focus in this session is on tax shifting.
Tax shifting is the difference between statutory incidence and economic incidence

4. Tax Incidence: General Remarks
Only people can bear taxes
Functional distribution of income: People’s role in production used to classify tax incidence. E.g. capitalists, labourers and landlords classification according to the inputs they supply to the production process (this is considered old-fashioned)
Size distribution of income: Looks at how taxes affect the way that total income is distributed across income classes.

5. Tax Incidence: General Remarks
Both sources and uses of income should be considered
For instance if a tax reduces the demand for cigarettes, the factors employed in cigarettes production may suffer income losses.
Incidence depends on how prices are determined: different models of price determination may give different answers to the question of who really bears the burden.
The SR and LR incidence of a tax may differ.

6. Tax Incidence: General Remarks
Incidence depends on the disposition of tax revenues:
Balanced-Budget tax incidence: computes the combined effects of levying taxes and govt spending financed by those taxes
The idea is to determine how incidence differs when one tax is replaced with another, holding the govt budget constant (differential tax incidence). A lump-sum tax is often used as the basis of comparison.
Lump sum tax: is a tax whose value is independent of the individual’s behaviour.
Absolute tax incidence: examines the effects of a tax when there is no change in either other taxes or govt expenditure

7. Tax Progressiveness Can Be Measured in Several Ways
Average tax rate: Ratio of taxes paid to income
Marginal tax rate: the proportion of the last dollar of income taxed by the govt.
Proportional tax system: A tax system under which an individual’s average tax rate is the same at each level of income.
Progressive tax system: an individual’s average tax rate increases with income.
Regressive tax system: an indiv’s avg tax rate decreases with income.

8. Tax Progressiveness Can Be Measured in Several Ways
Tax Liabilities under a hypothetical tax system
Income
Tax Liability
Average Tax Rate
Marginal Tax Rate
$2,000
-$200
-0.10
0.2
3,000
5,000
400
0.08
10,000
1,400
0.14
30,000
5,400
0.18
Tax scheme depicted – Tax = 0.20*(Income - $3,000)

9. Measuring How Progressive a Tax System Is

10. Tax Progressiveness Can Be Measured in Several Ways
The greater the increase in avg tax rates as income increases the more progressive is the system. v1 is the formula for measurement of progressiveness
T0 and T1 are the true tax liabilities at income I0 and I1 respectively. I1 >I0.
The tax system with the highest v1 is more progressive.
The second measure of progressiveness is to say that for a more progressive tax system, its elasticity of tax revenue with respect to income is higher. V2 is the elasticity formula.

11. Tax Progressiveness Can Be Measured in Several Ways

12. Tax Progressiveness Can Be Measured in Several Ways
Assume that T0 = 200 and T1 = 300 and also assume that I0 = 800 and I1= 1000 respectively.
Now consider the following proposal: Everyone’s tax liability is to be increased by 20% of the amount of tax he or she currently pays. The new tax liabilities are T0 = 240 and T1 = 360 and also assume that I0 = 800 and I1= 1000 respectively.

13. Measuring How Progressive a Tax System is – A Numerical Example

14. Tax Progressiveness Can Be Measured in Several Ways
V1 increases by 20% meaning the proposal increases progressiveness.
V2 is unchanged.
This implies that measures of progressiveness can give different answers

15. Partial Equilibrium Models
Models that study only one market and ignore possible spill over effects in other markets.
The main question is how taxes affect income distribution.
The main tool of analysis is the ss and dd model.

16. Unit taxes on commodities
Unit tax: is a tax levied as a fixed amount per unit of the commodity purchased.
E.g. if govt imposes a tax of 10 cents per litre of petrol.
A unit tax changes the dd curve as perceived by suppliers. The new dd curve is located below the old one by the magnitude of the unit tax.
The equilib is where the ss equals dd as perceived by the suppliers
The tax lowers the quantity sold from 4 to 3.
There are two prices to consider: the price perceived by producers and the price paid by consumers.

17. Partial Equilibrium Models$
Partial Equilibrium Models
Before Tax
After Tax
Consumers Pay
Suppliers Receive
$1.20
$1.40
$1.20
$1.00 S1 S0
Unit Tax on Commodities
Consumer Pays $1.20
Producer receives $1.20
Tax on Consumers of $.40 per gallon
D curve shifts down – D curve perceived by supplier-amount of money the supplier will receive
Tax wedge – tax induced spread between price paid by consumer and price received by producer
Tax on Producers of $.40/gal
Draw new supply curve
Consumer Pays $1.40
Producer receives $1.40
Economic incidence independent of statutory incidence D0
Quantity
14-17 D1

18. Unit taxes on commodities
The price received by producers is at the intersection of their effective dd and ss curves (P = $1.00).
The consumers pay $1.00 plus the unit tax.
This is = $1.40. This is called the price gross of tax. $1.00 is the price net of tax.
The tax makes consumers worse off but the consumer’s price does not increase by the full amount of the tax.
Producers also pay part of the tax ( in our case it’s a situation). They are also worse off.

19. Unit taxes on commodities
The incidence of a Unit tax is independent of whether it is levied on consumers or producers.
Suppose the same unit tax is levied on suppliers of champagne.
The supply curve as it is perceived by consumers must shift up by the amount of the unit tax to S1.
The posttax equilibrium is at 3 and the price at the intersection($1.20) is paid by consumers.
The price received by producers is $1.00.

20. Unit taxes on commodities
What matters is the size of the disparity the tax introduces between the price paid by consumers and the price received by suppliers and not on which side of the market the disparity is introduced.
The tax induced difference between the price paid by the consumers and the price received by producers is called the Tax Wedge

21. Unit taxes on commodities
The incidence of a unit tax depends on the elasticities of ss and dd
A unit tax on a good that has perfectly inelastic ss causes the price received by the producers to fall by exactly the amount of the tax.
Producers bear the entire burden of the tax
A unit tax on a good that has perfectly elastic ss causes the price paid by the consumers to increase by exactly the amount of the tax.
The consumers bear the tax burden.

22. Perfectly Inelastic Supply$ SX
tax DX
Perfectly Inelastic Supply
DX’
DX1
Quantity
14-22

23. Perfectly Elastic Supply$
Perfectly Elastic Supply
tax SX DX
DX’
DX1
Quantity
14-23

24. Ad Valorem Taxes A tax computed as a % of the purchase value.
For example 10% tax (VAT) on the purchase of food in SA.
Ad valorem taxes are often levied on luxuries.
The analysis of an ad valorem tax is similar to that of a unit tax.
The basic plan is to find out how the tax changes the effective dd curve and compute the equilibrium.
The ad valorem tax however lowers the curve down by the same proportion(%) which is a swivel rather than a parallel shift.

25. Ad Valorem Taxes Sf Price per Pound of food Pr Pc P0 Ps Pm Df Df’ QrQn Q0 Qm
Pounds of food per year

26. Ad Valorem Taxes
An ad valorem tax on consumers shifts the dd curve down by the same proportion at each level of output.
Df’ is the effective dd curve faced by suppliers.
Df is the original dd curve.
The equilibrium is where Sf and Df’ intersect.
The incidence will be determined by the elasticities of supply and demand.
Pc is the price paid by consumers and Ps is the price received by suppliers.

27. Taxes on Factors: The Payroll Tax
A similar analysis can be applied to factors of production.
The Payroll Tax:is paid from the employer's own funds and that is directly related to employing a worker, which can consist of a fixed charge or be proportionally linked to an employee's pay.
If the labour ss is perfectly inelastic, a payroll tax causes the wage received by workers to fall by the exact amount of the tax. Workers bear the entire burden

28. The Payroll Tax SL Wage rate per hour Pr wg = w0 wn DL DL’ L0 = L1
Hours per year

29. Taxes on Factors : Capital Taxation in a Global Economy
In a closed economy the dd is downward sloping and the ss is upward sloping.
Therefore the owners of capital bear some burden of a tax on K. This depends on elasticities of dd and ss.
In an open economy where capital is perfectly mobile the ss of K to a country is perfectly elastic.
The before-tax price paid by the users of K rises by exactly the amount of the tax.
Suppliers of K bear no burden.
K moves abroad if it has to bear any of the tax.

30. Commodity Taxation without Competition: Monopoly
If a unit tax is levied on a product, the effective dd curve and MR curve facing the monopolist shift down by a vertical distance equal to the tax.
The profit-maximising output is found at the intersection of the new MR curve and the MC curve.
The tax reduces the equilib quantity from X0 to X1 and increases the price paid by consumers from Po to Pg.
The price received by the producer decreases from Po to Pn and decreases the monopoly profits.

31. Monopoly $ Economic Profits Economic Profits after unit tax MXX Pg c a
ATCX Pn i f d h g b
ATC0 DX
MRX
DX’
X per year X1 X0
MRX’

32. Oligopoly
If the oligopoly industry output is subject to a tax, the firms will reduce their output.
But the firms normally over-produce (exceed the cartel share) so the tax will move them closer to the cartel solution.
Their before –tax profits actually increase.
However, it is possible for the firms to become worse –off.

33. Profits Taxes
Economic profit: the return to the owners above the opportunity costs of all the factors used in pdn.
A tax on economic profits is born by the owners of the firm.
Under perfect compn a proportional tax on economic profits changes neither MC nor MR.
No firm has the incentive to change its output decision.

34. Tax Incidence and Capitalization
Capitalisation: is the process by which a stream of tax liabilities becomes incorporated into the price of an asset.
Suppose the annual rate of return of land is $R0 this yr. The rental will be R1 next yr and R2 after 2 yrs and so on. Under perfect compn the price of the land is the present discounted value of the future streams of returns. If the interest rate is r, then the price of land PR is
PR = $R0 + $R1/(1 + r) + $R2/(1 + r)2 + … + $RT/(1 + r)T

35. Tax Incidence and Capitalization
If a tax $ui is imposed for i=0,1,2,…,T. Since land is fixed in ss the ss curve is vertical, the owner of the land bears the whole tax.
The landlord’s return falls by the full amount of the tax. The after tax value of the land will be:
PR’ = $(R0 – u0) + $(R1 – u1)/(1 + r) + $(R2 – u2)/(1 + r)2 + … + $(RT – uT)/(1 + r)T

36. Tax Incidence and Capitalization
The two expressions above show that the value of the land will fall by:
u0 + u1/(1 + r) + u2/(1 + r)2 + … + uT/(1 + r)T
At the time of the tax the price of the land falls by the present value of all future tax payments.
Capitalization complicates attempts to assess the incidence of a tax on a durable item that is fixed in ss.

37. General Equilibrium Models
Partial equilibrium:
Are simple and uncomplicated.
They give an incomplete picture
E.g. a tax on cigarettes affects consumers, farmers and the farm pdn pattern and prices of other crops.
General equilibrium analysis takes into account the way in which various mkts are interrelated.

38. Tax Equivalence Relations
Thousands of different commodities and inputs are traded, so how can we keep track of their complicated interrelations?
Useful results can be obtained from GE models with 2 commodities [food, F and manufactures,M],2 fops(K and L) and no savings.

39. Tax Equivalence Relations
tKF = a tax on capital used in the production of food
tKM = a tax on capital used in the production of manufactures
tLF = a tax on labor used in the production of food
tLM = a tax on labor used in the production of manufactures
tF = a tax on the consumption of food
tM = a tax on consumption of manufactures
tK = a tax on capital in both sectors
tL = a tax on labor in both sectors
t = a general income tax

40. Tax Equivalence Relations
The 1st 4 taxes are levied on a factor in only part of its uses – partial factor taxes.
Certain combinations of these taxes are equivalent to other ad valorem taxes outlined above. E.g. a similar tax rate is applied on food (tF ) and manufactures (tM) , these are equivalent to an income tax (t), becoz they both create a parallel inward shift of a consumer’s budget constraint.
A proportional tax on both capital and labour is equivalent to an income tax.

41. Tax Equivalence Relations
Partial factor taxes
tKF
and
tLF
are equivalent to tF
tKM
tLM tM
are
equivalent to tK tL t
Source: McLure [1971].

42. The Harberger Model: Assumptions
Technology:
Assume 2 factors (K and L)
The model assumes constant returns to scale , although production techniques may differ across sectors.
They differ w.r.t
Elasticity of substitution (the ease with which one factor can be substituted for another)
Capital intensive (capital –labour ratio is high)
Labor intensive (capital –labour ratio is low)

43. Assumptions Behavior of factor suppliers:
Suppliers of K and L maximize returns.
K and L are perfectly mobile across sectors
Net marginal return for all factors in each sector is the same.
Market structure:
Firms are competitive, profit maximisers, and all prices are perfectly flexible.
There is full employment of factors
Each fop is paid the value of its MP.

44. Assumptions Total factor supplies: Amounts of K and L are fixed.
Consumer preferences:
Consumers have identical preferences
Focus is on taxes effect on the sources of income.
Tax incidence framework:
The model uses differential tax incidence analysis. The model considers the substitution of one tax by another.

45. Analysis of Various Taxes
Commodity tax (tF)
A tax on food causes the relative price to increase.
Consumers substitute manufactures for food.
Food pdn falls=> K and L moves to manufacturing=> relative prices of K and L changes.
If food is a K-intensive sector, more K should be employed in manufacturing, if the relative price of K falls.
In the new position all K is relatively worse off.

46. Commodity tax (tF)
A tax on the output of a certain sector induces a decline in the relative price of the input used intensively in that sector.
This result will depend on the elasticity of dd for food, difference in factor proportions and the difficulty in factor substitution.
On the sources side, a food tax will hurt those who receive proportionately more income from capital.
On the uses side those who consume proportionately more food would bear larger burdens
Total incidence- a capitalist who eats a lot of food is worse off on both counts.

47. General tax on labor (tL) Partial factor tax (tKM)
Income tax (t)
Since factor supplies are already fixed , this tax cannot be shifted. It is borne in proportion to people’s initial incomes.
Factors bear the full burden.
General tax on labor (tL)
It is a tax on labour in all its uses.
There are no incentives to switch labour use between sectors.
Labour bear the entire burden.
Partial factor tax (tKM)
Output effect: the price of manufactures tend to rise and the quantity demanded decreases.
Factor substitution effect: Producers use less K and more labour.

48. Partial factor tax (tKM)
If the manufacturing sector is capital intensive, the relative price of capital falls.
If it is labour-intensive, the relative price of capital rises.
The factor substitution effect leads producers to use less capital and more labour, leading to a drop in the relative price of capital.
If the manufacturing sector is K intensive both effects work in the same direction, and relative price of K falls.
If the manufacturing sector is labour intensive, the final outcome is ambiguous.
More generally, as long as there is factor mobility between uses, a tax on a given factor in one sector is ultimately affects the return to both factors in both sectors.

49. Some Qualifications Differences in individuals’ tastes:
When consumers have different preferences for the 2 goods, tax-induced changes in the distribution of income change aggregate spending decisions, relative prices and incomes
Immobile factors:
For technical or institutional reasons some factors maybe immobile. If the taxed factor is immobile the factor bears the whole burden.

50. Variable factor supplies
In the LR the supplies of both factors are variable.
If there is a tax on K, in the SR the tax is borne by capital owners. In the LR less K will be supplied due to the tax.
The K/L ratio decreases and the return to labour falls becoz it becomes less productive.

51. An Applied Incidence Study