Chapter 20 Tax Inefficiencies and Their Implications for Optimal Taxation

1. Chapter 20Tax Inefficiencies and Their Implications for Optimal Taxation • Social efficiency is maximized at the competitive equilibrium (in the absence of market failures). • Taxes entail a deviation from competitive, frictionless markets. Consequently, taxing market participants creates deadweight loss. • So, we will look at • Taxation and economic efficiency • Optimal commodity taxes • Optimal income taxes, and • Tax-benefit linkages in financing social insurance programs.

2. Figure 1 Imposing a Tax on Producers Price per gallon (P) S2 S1 The tax creates deadweight loss. The tax on gasoline shifts the supply curve. B DWL P2 = $1.80 P1 =$1.50 A C $0.50 D1 Q2 = 90 Q1 = 100 Quantity in billions of gallons (Q)

3. DWL When Supply is Infinitely Elastic • DWL=.5*b*h • .5*t*dx • So in this simple example, DWL is proportional to the square of the tax rate and the demand elasticity. DWL q=p+t p x0

4. Taxation and economic efficiencyElasticities determine tax inefficiency • The efficiency consequences are identical, regardless of which side of the market the tax is imposed on. • Just as price elasticities of supply and demand determine the distribution of the tax burden, they also determine the inefficiency of taxation. • As shown in the following figure, higher elasticities imply bigger changes in quantities, and larger deadweight loss.

5. Figure 2 Deadweight Loss Increases with Elasticities Demand is fairly inelastic, and DWL is small. (a) Inelastic Demand (b) Elastic demand P P Demand is more elastic, and DWL is larger. S2 S2 S1 S1 B P2 B DWL DWL P2 A P1 P1 A C 50¢ Tax 50¢ Tax C D1 D1 Q Q Q2 Q1 Q2 Q1

6. Taxation and economic efficiencyDeterminants of deadweight loss • This formula for deadweight loss: • Deadweight loss rises with the elasticity of demand. • The appropriate elasticity is the Hicksian compensated elasticity, not the Marshallian uncompensated elasticity. • Deadweight loss also rises with the square of the tax rate. • That is, larger taxes have much more DWL than smaller ones.

7. Figure 3 The “marginal” DWL increases as taxes increase. S3 P S2 S1 The next $0.10 tax creates a larger marginal DWL, BCDE. D P3 The first $0.10 tax creates little DWL, ABC. B P2 P1 A C $0.10 E $0.10 D1 Q Q3 Q2 Q1

8. Taxation and economic efficiencyDeadweight loss and the design of efficient tax systems • The more one loads taxes onto one source (and consequently, the higher the rate), the faster DWL rises. • Efficient tax systems spread the burden broadly. Thus, efficient tax systems have a broad base and low rates. • The fact that DWL rises with the square of the tax rate also implies that government should not raise and lower taxes, but rather set a long-run tax rate that will meet its budget needs on average. • For example, to finance a war, it is more efficient to raise the rate by a small amount for many years, rather than a large amount for one year (and run deficits in the short-run). • This notion can be thought of as “tax smoothing,” similar to the notion of individual consumption smoothing.

9. Optimal commodity taxationRamsey rule • Optimal commodity taxation is choosing tax rates across goods to minimize the deadweight loss for a given government revenue requirement. • The Ramsey Rule is: • It sets taxes across commodities so that the ratio of the marginal deadweight loss to marginal revenue raised is equal across commodities. • The goal of the Ramsey Rule is to minimize deadweight loss of a tax system while raising a fixed amount of revenue. • 8 measures the value of having another dollar in the government’s hands relative to the next best use in the private sector. • Smaller values of 8 mean additional government revenues have little value relative to the value in the private market.

10. Optimal commodity taxationInverse elasticity rule • The inverse elasticity rule, based on the Ramsey result, allows us to relate tax policy to the elasticity of demand. • The government should set taxes on each commodity inversely to the demand elasticity. • Therefore, ignoring equity, less elastic items should be taxed at a higher rate. • Two factors must be balanced when setting optimal (efficient) commodity tax rates (again, ignoring equity): • The elasticity rule: Tax commodities with low elasticities. • The broad base rule: It is better to tax many goods at lower rates, because deadweight loss increases with the square of the tax rate. • Thus, the government should tax all of the commodities that it is able to, but at different rates.

11. OPTIMAL INCOME TAXES • Optimal income taxation is choosing the tax rates across income groups to maximize social welfare subject to a government revenue requirement. • Raising tax rates will likely affect the size of the tax base. Thus, increasing the tax rate on labor income has two effects: • Tax revenues rise for a given level of labor income. • Workers reduce their earnings, shrinking the tax base. • At high tax rates, this second effect becomes important. • Thus, there are equity-efficiency tradeoffs in designing income tax rates.

12. The Laffer curve motivated the supply-side economic policies of the Reagan presidency Figure 7 The Laffer curve demonstrates that at some point, tax revenue falls. Tax revenues right side wrong side τ*% Tax rate 0 100%

13. Optimal income taxesGeneral model with behavioral effects • The goal of optimal income tax analysis is to identify a tax schedule that maximizes social welfare, while recognizing that raising taxes has conflicting effects on revenue. • The optimal tax system meet the condition that tax rates are set across groups such that: • Where MUi is the marginal utility of individual i, and MR is the marginal revenue from that individual. • As with optimal commodity taxation, this outcome represents a compromise between two considerations: • Vertical equity • Behavior responses

14. Figure 8 MU/MR Mrs. Poor Mr. Rich Optimal income taxation equates the ratio of (MU/MR) across individuals. Tax rate 10% 20% Low income may have higher MUc. A given tax will raise more for a high income household (up to a point), so MR is higher.

15. TAX-BENEFITS LINKAGES AND THE FINANCING OF SOCIAL INSURANCE PROGRAMS • Tax-benefit linkages are direct ties between taxes paid and benefits received. • Summers (1989) shows that such linkages can affect the equity and efficiency of a tax. The link between payroll taxes and social insurance benefits can lead the incidence to fall more fully on workers than might be presumed. • The key point of Summers’ analysis is that with taxes alone, only the labor demand curve shifts, but with tax-benefit linkages, the labor supply curve shifts as well. • That is, workers are willing to work the same amount of hours at a lower wage, because they get some other benefit as well, such as workers’ compensation or health insurance.

16. Figure 10 Tax-Benefit Linkages Wage (W) Wage (W) C Creating smaller DWL. S1 S1 Mandated benefits also shift the supply curve. E S2 W1 W1 A A F B W2 W2 B W3 D D1 D1 D2 D2 Labor (L) Labor (L) L2 L1 L2 L3 L1 Wages adjust by more with the tax-benefit linkage, employment falls by less, and deadweight loss is smaller than with a pure tax.

17. Tax-benefits linkages and the financing of social insurance programs: The model • With full valuation, the cost of the program is fully shifted onto workers in the form of lower wages, and there is no deadweight loss or employment reduction. • This raises some issues with tax-benefit linkages, especially with respect to employer mandates. • If there is no inefficiency, why doesn’t the employer simply provide the benefit without government intervention? • Market failures, such as adverse selection, may be present. The employer that provides a benefit such as workers’ compensation or health insurance may end up with high risks. • When are there tax-benefit linkages? • They are strongest when the taxes paid are linked directly to a specific benefit that workers can receive.