1. Public Finance
Chapter15 Taxation and Efficiency
CHENG Beinan PH.D

2. Contents in this chapter
Excess Burden Defined
Excess Burden Measurement with Demand
Differential Taxation of Inputs
Does Efficient Taxation Matter

3. §1. Excess Burden Defined
Mini Case 1
Consider Breyer Dazs, a citizen who typically consumes 10 ice cream cones each week, at a price of $1 per cone. The government levies a 25 percent tax on his consumption of ice cream cones, so now Dazs faces a price of $1.25. In response to the price hike, Dazs reduces his ice cream cone consumption to zero, and he spends the $10 per week on other goods and services. Is Dazs unaffected by the tax?

4. Excess Burden: A loss of welfare above and beyond taxes collected
Excess Burden: A loss of welfare above and beyond taxes collected. Also called welfare cost or deadweight loss.

5. Mini Case 2
Ruth has a fixed income of I dollars, and consumes barley and corn. The price of barley is Pb and that of com is Pc. There are no taxes or "distortions" such as externalities or monopoly in the economy, so the prices of the goods reflect their social marginal costs. For convenience, these social marginal costs are assumed to be constant with respect to output. Now suppose the government levies a tax at a percentage rate of tb on barley. Analyze the tax's effect on budget constraint, consumption bundle, and consumers' welfare.

7. Mini Case 3
Ruth has a fixed income of I dollars, and consumes barley and corn. The price of barley is Pb and that of com is Pc. There are no taxes or "distortions" such as externalities or monopoly in the economy, so the prices of the goods reflect their social marginal costs. For convenience, these social marginal costs are assumed to be constant with respect to output. Now suppose the government levies a tax at a percentage rate of tb on barley. Is there any excess burden in this condition?

9. Equivalent Variation: A change in income that has the same effect on utility as a change in the price of a commodity.

10. 1.1 Questions and Answers Does every tax entail an excess burden?
Basic Conclusion: A lump sum tax has no excess burden. It is more efficient than the taxes which change the relative price. A tax that changes relative prices is inefficient in the sense that it lowers individual utility more than is necessary to raise a given amount of revenue.

11. Taxes that change the relative price
Lump Sum Tax
Taxes that change the relative price
Leaves the taxpayer on the same indifference curve.
Generates more revenue.
Raise the same revenue.
Leaves the taxpayer on higher indifference curve.
Leaves the taxpayer on lower indifference curve.
Conclusion
More efficient
Less efficient

12. The problem of Lump Sum Tax
Lump Sum Tax: A tax whose value is independent of the individual's behavior.
The problem of Lump Sum Tax
It is technically impossible to make Lump Sum Tax equitable.
The practical lump sum tax is unfair.
Any feasible way to modify the lump sum tax to produce more equitable results, actually is not a lump sum tax.

13. The Welfare Economics explanations on the Excess Burdens
The necessary condition of efficient allocation:
Tax effect:
The utility loss arises because the barley tax creates a wedge between what the consumer pays and what the producer receives.

14. The Welfare Economics explanations on the Excess Burdens on income tax
Basic Conclusion: Generally speaking, Income Tax entail an Excess Burden. ① If income were fixed, an income tax would be a lump sum tax. ②However, when people's choices affect their incomes, an income tax is not generally equivalent to a lump sum tax.

15. Mini Case 4
Ruth is consuming three commodities, barley, corn, and leisure time, l. Ruth gives up leisure (supplies labor) to earn income that she spends on barley and corn. The government levies an income tax on the wage at the rate of t. Will this policy introduce excess burden? Why?

16. Leisure is the substitution of barley and corn
Leisure is the substitution of barley and corn. Leisure is an input to produce of barley and corn.

17. If the demand for a commodity does not change when it is taxed, does this mean that there is no excess burden?
Mini Case 5
Naomi's initial budget constraint is AD, and after the barley tax, it is AF. She does not change her barley consumption after the barley tax; that is, B1 = B2. The barley tax revenues are E1E2. Is there an excess burden?

18. Basic Conclusion: Naomi purchases the same amount of barley after the tax as before the tax. Nonetheless, the tax still yields an excess burden of E2S.
(1) Analysis with the figure: Although B1 = B2, the barley tax E1E2 < equivalence variation RE3, the excess burden isE2S.

19. It is the substitution effect that breaks the Pareto efficiency condition.

20. Income Effect: The effect of a price change on the quantity demanded due exclusively to the fact that the consumer’s income has changed.
Substitution Effect: The tendency of an individual to consume more of one good and less of another because of a decrease in the price of the former relative to the latter.
Compensated Demand Curve: A demand curve that shows how quantity demanded varies with price, holding utility constant.

21. Contents in this chapter
Excess Burden Defined
Excess Burden Measurement with Demand
Differential Taxation of Inputs
Does Efficient Taxation Matter

22. §2. Excess Burden Measurement with Demand
△CS =gfih, among which tax revenue = gfdh, excess burden = fid .

23. The math expression of Excess Burden

24. Implications of equation :
① η (compensated price elasticity of demand)↑→ EB↑;
② ↑(the initial total commodity expenditure)→ EB↑;
③ A broader tax has less excess burden than a narrow tax.

25. Empirical evidence in U.S.
Oum(1992) shows that the airline ticket tax imposes an annual excess burden of $430 million, and collect $86 billion revenue annually. (Tax rate 10%, price elasticity of demand 1.0)

26. 2.1 Preexisting Distortions
Basic conclusion:
In the presence of existing distortions, policies that in isolation would increase efficiency can decrease it and vice versa.
Mini Case 6
Suppose that consumers regard gin and rum as substitutes. Suppose further that rum is currently being taxed, creating an excess burden "triangle". Now the government decides to impose a tax on gin. What is the excess burden of the gin tax?

27. Theory of The Second Best: In the presence of existing distortions, policies that in isolation would increase efficiency can decrease it and vice versa.
Double-Dividend Effect: Using the proceeds from a Pigouvian tax to reduce inefficient tax rates.
Tax-Interaction Effect: The increase in excess burden in the labor market stemming from the reduction in real wages caused by a Pigouvian tax.

28. Double-Dividend theory and policy
Basic conclusion: The environment tax increases efficiency both in the market with the polluter and in the markets that are distorted by the income tax. However, the consequences of Double-Dividend hypothesis for efficiency depend on the extent to which existing taxes already distort the labor market.

29. 2.2 The Excess Burden of a Subsidy

30. Basic conclusion: A subsidy is just a negative tax, and like a tax, it is associated with an excess burden.
Before tax：Demand curve: Dh; Supply curve: Sh = Ph; Equilibrium quantity: h1, CS = mno;
After tax：Demand curve: Dh; Supply curve: S’h= (1- s )Ph; Equilibrium quantity: h2, CS = mqu;
Subsidy effect: Benefit of subsidy is △CS =nouq; cost of subsidy is nvuq. Because Cost of subsidy > Benefit of subsidy, EB =ovu.

31. Deeper thoughts and implications on Excess Burden of a Subsidy
Whey subsidy is inefficient?
The tax wedge makes consumer price ≠ producer price, thus MRS ≠ MRT .
Policy implication: Commodity subsidy vs. Grant
Grant is better than Commodity subsidy.Less money could make them as well off if it were given to them as a direct grant.

32. 2.3 The Excess Burden of Income Taxation

33. Basic conclusion: The theory of excess burden applies just as well to factors of production as it does to commodities.
Before tax：Supply curve: SL; Wage: w; Working hour: L1; Labor Surplus(LS) = adf;
After tax：Supply curve: SL; After-tax Wage: (1-t)w; Working hour: L2; After-tax LS = agh;
Income Tax effect: △LS =fdhg; tax revenue is fihg, EB = idh.

34. The math expression of income tax Excess Burden

35. Excess Burden of Income tax in US
In the US, the excess burden of Income tax is approximately 4% of tax revenues. For American male, εL ≈ 0.2, w = $20/h, L = 2,000, t=40%, so the EB =640.
Jorgenson & Yun [2001] estimated the excess burden of labor income taxation in the United States is about 27 percent of the revenues raised.

36. Noteworthy aspects to estimate Excess Burden of Income tax
Wage rates, tax rates , elasticities, and tax rates on other factors should be considered.

37. Contents in this chapter
Excess Burden Defined
Excess Burden Measurement with Demand
Differential Taxation of Inputs
Does Efficient Taxation Matter

38. §3. Differential Taxation of Inputs

39. Model discription
OO': total labor available in society. Labor used at home and in the market.
VMPhome: the value of the marginal product of household work.
VMPmkt : the value of the marginal product of hours worked in the market sector.

40. Before tax
Equilibrium: H*; Labor used at home: OH*; Labor used in the market: O’H*.
After tax：
Procedure: Tax on market labor (t) → Real wage↓(tw)→VMPmkt becomes (1-t) VMPmkt
Equilibrium: Ht; Labor used at home: OHt; Labor used in the market: O’Ht.
Excess Burden: abe.

41. Result:
Too much labor is devoted to the housework; and too little labor is devoted to the market work.
Analysis:
At the new equilibrium, the value of Marginal Product is (1-t)w2. The tax wedge prevent efficiency improvement from Ht to H*.

42. Conclusion:
The tax leads to an inefficient allocation of resources, because it distorts incentives to employ inputs in their most productive uses.

43. Contents in this chapter
Excess Burden Defined
Excess Burden Measurement with Demand
Differential Taxation of Inputs
Does Efficient Taxation Matter

44. §4. Does Efficient Taxation Matter
Excess burden is conceptually a rather subtle notion and is not trivial to calculate.
Although the efficiency considerations alone are never enough to determine policy, ignoring efficiency is also incorrect.

45. It will be used to obtain something beneficial for society either in terms of enhanced efficiency or fairness.
Intelligent policy requires that excess burden be included in the calculation as a social cost.
Excess burden is extremely useful in comparing alternative tax systems.