1. Taxation and Efficiency
Session 7
Taxation and Efficiency

2. Taxation and Efficiency
Taxes impose a cost on the taxpayer.
The amount paid to the tax collector is not the only cost.
A tax increases the price and diminish the quantity demanded, reduce the tax revenue and change consumer preferences.
A tax distorts economic decisions- it creates excess burden.

3. Excess burden
Excess burden is a loss of welfare above and beyond taxes collected. Also called welfare cost or deadweight loss.
Assume Ruth has a fixed income of I dollars, spent on barley and corn (only 2 commodities).
The prices per pond are Pb and Pc respectively.
Assume no taxes or distortions (externalities or monopoly).
Prices of goods reflect the social marginal costs which are constant w.r.t to output.

4. Effect of a tax on the budget constraint
Ruth’s budget constraint is AD.
At E1 she maximises her utility(B1,C1).
Suppose govt levies a tax at a % tb on barley.
New price of barley is (1+tb)Pb
Ruth’s budget constraint changes to AF.
Government levies tax on barley A Ca Cb E1 C1 i F D B0 B1

5. Excess Burden
The vertical distance between AD and AF at each barley consumption level shows Ruth’s payments measured in corn.
If Pc = 1, then distance CaCb measures tax receipts in corn or dollars.

6. Effect of Tax on Consumption Bundle
Pounds of corn per year G Ca E2 Cb E1 C1 i ii F D B0 B1
Pounds of barley per year

7. Excess burden
Ruth’s most preferred bundle on the new budget line is at E2, on indifference curve ii.
Her tax bill is GE2.
Ruth is worse off at E2 than at E1.
Has the barley tax inflicted a greater utility loss than is necessary to raise GE2?
If there is some other way of raising revenue GE2 that would cause a smaller utility loss to Ruth, then the barley tax has an excess burden

8. Excess Burden of the Barley Tax
Pounds of corn per year G
Tax Revenues Ca H M
Equivalent variation E2 Cb N E1 C1 E3 i ii F I D B0 B3 B1
Pounds of barley per year

9. Equivalent variation How do we investigate excess burden?
We need to find a dollar equivalent of the loss that Ruth suffers by having to move from indifference curve i to ii.
We use equivalent variation- the amount of income we would have to takeaway from Ruth to induce her to move from i to ii.
In other words it is a change in income that has the same effect on utility as a change in the price of a commodity.

10. Equivalent variation
Reduction in income leads to an inward parallel shift of the budget constraint.
The amount by which we shift the curve AD to be tangent with ii is the equivalent variation.
HI is parallel to AD and the vertical distance ME3 is the equivalent variation.
Ruth is indifferent between losing ME3 dollars and facing the barley tax.
The excess burden is E2N which is the distance between the equivalent variation and the barley tax revenue.
The barley tax makes Ruth worse off(loss in welfare) by an amount that actually exceeds the revenues it generates.

11. Does every tax entail an excess burden?
A lump sum tax is a tax whose value is independent of the individual’s behaviour.
The barley tax is not a lump sum tax becoz it depends on Ruth’s barley consumption behaviour.
Lets analyse a lump sum tax that leaves Ruth with the same utility as the barley tax.
The associated budget line is parallel to AD and tangent to indifference curve ii.
The revenue yield of a lump sum tax equals its equivalent variation.
A lump sum tax has no excess burden.

12. If lump sum taxes are so efficient, why aren’t they widely used?
A lump sum tax generates more revenue for the govt.
Or a lump sum tax leaves Ruth on a higher indifference curve(same revenue case).
Lump sum taxes are perceived as unfair becoz they ignore amount of income earned or property owned.
Individual lump sum taxes are best viewed as standards of efficiency, not as major policy options.

13. Are there any results from welfare economics that would help us understand why excess burdens arise?
A necessary condition for a Pareto efficient allocation of resources is that the marginal rate of substitution of barley for corn in consumption (MRSbc) equals the marginal rate of transformation of barley for corn in pdn (MRTbc).
Under the barley tax consumers face a price of (1+tb)Pb:
Profit maximising producers set:

14. Are there any results from welfare economics that would help us understand why excess burdens arise?
As long as tb is not zero, MRSbc exceeds MRTbc and the necessary condition for an efficient allocation of resources is violated.
When the MRSbc >MRTbc, the MU of substituting barley consumption for corn consumption exceeds the change in pdn costs necessary to do so.
The excess burden is just a measure of utility loss. The loss arises becoz the barley tax creates a wedge btwn what the consumer pays and what the producer receives.

15. Does an income tax entail an excess burden?
Yes.
An income reduction moves the intercepts of the budget line closer to the origin but leaves its slope unchanged
If income s were fixed then an income tax would be a lump sum tax.
When people’s choices affect their incomes, an income tax is not generally equivalent to a lump sum tax.

16. Does an income tax entail an excess burden?
Assume a three commodity case- barley, corn and leisure. In consumption- leisure is given up to earn income to spend on barley and corn. In pdn leisure is an important input. The rate at which leisure is transformed into barley(MRTlb) and corn(MRTlc). The necessary Pareto conditions are:

17. Does an income tax entail an excess burden?
A proportional income tax (equivalent to a tax at the rate on barley and corn, leaves the 3rd condition unchanged.
It introduces a tax wedge in the 1st 2 conditions.
Ruth’s decisiondepends onher after tax wage (1-t)w, therefore her allocation will be
MRTlb =(1-t)w/Pb
But the producer set her MRT=w/Pb
=> MRSlb #MRTlb and MRSlc # MRTlc.
Once any of the 3 equalities fails to hold, a loss of efficiency results and the sizes of the welfare losses cannot be compared by just counting wedges.

18. If the demand for a commodity does not change when it is taxed, does this mean that there is no excess burden?
Excess burden results from distorted decisions.
If dd does not change one may conclude that there is no excess burden.
Assume another consumer Naomi. She begins with the same dd curve as Ruth(AD) and maximises at E1.
After the barley tax the new budget line is AF. But she does not change her barley consumption(B1=B2).
Barley tax revenue is E1E2 but the equivalent variation is RE3.
The barley tax still creates an excess burden of E2S.
This paradox is explained by 2 things: the income and substitution effect

19. If the demand for a commodity does not change when it is taxed, does this mean that there is no excess burden? A
Uncompensated response
Income effect
Substitution effect -compensated effect
Compensated demand curve
Pounds of corn per year E1 Ca i J R E2 Cb S C1 ii F K D
B1 = B2 B3
Pounds of barley per year

20. If the demand for a commodity does not change when it is taxed, does this mean that there is no excess burden?
The barley tax changes barley’s relative price, MRS and the composition of the commodity bundle is distorted.
There are 2 types of responses to the barley tax.
The move from E1 toE2 is the uncompensated response- this incorporates the effects due to lose in income and the change in relative prices.
We can divide the mvt from E! toE2 in to 2 parts
E1 to E3 – income effect – due to the loss of income becoz relative prices are unaffected.
E3 to E2- is the compensated response or the substitution effect.- strictly due to change in relative prices.
It is the tendency of an individual to consume more of one good and less of another becoz of a decrease in the price of the former relative to the latter.

21. Substitution effect This is important in calculating excess burden.
The calculation of excess burden involves the comparison of of tax collections at E2 and E3on indifference curve ii.
As we move from E3 toE2 the MRS changes.
A compensated demand curve shows how the quantity demanded changes when price changes and simultaneously income is compensated so that the individual’s commodity bundle stays on the same indifference curve.
Excess burden depends on mvts along the compensated rather than the ordinary dd curve.

22. Excess Burden Measurement with Demand Curves
We can use the compensated dd curves to show excess burden. We use consumer’s surplus-the difference btwn what people would be willing to pay for a commodity and the actual amount they pay. Db is the compensated dd curve for barley.
Assume a constant social MC of barley at Pb (ss curve is horizontal).
Consumer's surplus (CS) is aih.
Tax tb is levied and the price increases to (1=t)Pb.
CS falls agf . Revenue is gfdh.
The sum of the posttax CS and the tax revenues (hafd) is less than the original CS (ahi).
The triangle fid is the excess burden,

23. Excess Burden Measurement with Demand Curves
Excess burden = ½ ηPbq1tb2
Price per pound of barley
Tax revenues
Excess burden of tax
(1 + tb)Pb
S’b g f h d i Pb Sb Db q2 q1
Pounds of barley per year

24. Excess Burden Measurement with Demand Curves
Excess burden = ½ ηPbq1tb2
η the absolute value of the compensated price elasticity of dd for barley.
High η indicates that the compensated quantity demanded is quite sensitive to changes in price. The more the tax distorts the consumption decision the higher the excess burden.
Pbq1 is the TR expended on barley. The greater the initial expenditure on the taxed commodity the greater the excess burden.
A broader tax has less excess burden than a narrow tax. As tb2 increases excess burden increases.