Tax Inefficiencies and Their Implications for Optimal Taxation

Optimal Commodity Taxation:

Choosing the tax rates across goods to minimize deadweight loss for a given government revenue requirement

What is the empirical evidence on tax-benefit linkages?

Gruber and Krueger (1991) estimated labor market effects of changes in workers' compensation while Anderson and Meyer (2000) studied the impact of unemployment insurance payroll taxes. Both studies found that these programs lead to lower wages, with relatively little effect on employment. Gruber (1994) estimated labor market effects of state laws (and a follow-up federal law) in the mid-1970s that mandated the costs of pregnancy and childbirth be covered comprehensively. These laws increased the insurance cost of women of child bearing age which raised the cost of employing this group. The results show that the cost of this new mandate was fully passed on to the wages of the affected groups, with little effect on their labor supply. These findings have important implications for debates of group- specific mandates such as paid maternity leave. While these policies are good from an efficiency standpoint, they can be viewed negatively from an equity perspective as the burden is fully absorbed by women in the form of lower wages.

Inverse elasticity rule:

If we assume the supply side of commodity markets is perfectly competitive (elasticity of supply is infinite) then the Ramsey result implies that elastically demanded goods should be taxed less and goods with an inelastic demand should be taxed more. It is better to tax a wide variety of goods at a moderate rate than to tax very few goods at a high rate.

Set income tax rates across groups such that

MUi/MRi = λ where MU is the marginal utility and MR is the marginal revenue raised from taxing that individual. Remember in order to increase MU we need to decrease consumption (tax more).

What if workers fully valued the benefit of the workers' compensation?

No deadweight loss. The cost of the workers' compensation is fully shifted to the workers in the form of lower wages.

When are there tax-benefit linkages?

Taxes paid should be linked directly to a benefit for workers

The government of Washlovia wants to impose a tax on clothes dryers. In East Washlovia, the demand elasticity for clothes dryers is -2.4 while in West Waslovia, the demand elasticity is -1.7. Where will the tax inefficiency be greater? Explain.

The more elastic the demand, the more inefficient the tax; therefore, the tax will be less efficient in East Washlovia. Tax inefficiency is measured by the area of deadweight loss it generates. The height of the deadweight loss triangle will be the same in both areas, as it is the dollar amount of the tax. The base of the deadweight loss triangle, though, will differ, be- cause it is the quantity change, or the quantity response, to the tax. Elasticity is a measure of quantity response to a price change: the higher the elasticity, the greater the quantity change for a given price change. When demand is elastic, a price change will distort quantity de- manded by relatively more than when it is inelastic, and it is this quantity distortion that causes inefficiency.

If there is no inefficiency to providing a benefit, why doesn't the employer do so without government involvement?

There may be market failures that lead employers to not reflect workers' valuation of this program without a government mandate. Ex. Adverse selection

Luxury goods often have much higher elasticities of demand than do goods purchased by a broad base of people. Why, then, are governments more likely to tax luxuries than these "staple" goods?

While the Ramsey Rule would suggest taxing goods that are inelastically demanded, thus minimizing deadweight loss, there are other factors to consider; in particular, equity concerns are often inconsistent with this implication of optimal taxation. A tax on inelasti- cally demanded staples such as food would be regressive. Poorer people would spend a higher proportion of their income on necessities, so they would bear a disproportional share of a tax on those items. Wealthy people are much more likely to purchase luxury items, so the direct effects of a tax on these goods would be progressive. (Indirect effects, like em- ployment in the sectors that produce and service luxury goods, might not be as progressive.)

Now suppose the government creates a tax policy in which there is no tax on the first $10 of hourly earnings, but a 60% tax rate on the next $10 of hourly earnings. It may raise the same amount of revenue, but it has a very different efficiency consequence. Why?

You are levying a tax on a smaller tax base. A smaller tax base means higher tax rates which means higher marginal deadweight loss.

Optimal Income Taxes:

choosing the tax rates across income groups to maximize social welfare subject to a government revenue requirement. The tax rate on incomes will affect the size of the incomes that are subject to taxation. The government needs to consider the effect of raising tax rates on the size of the tax base

If there a negative externality, what's the DWL?

could have zero deadweight loss since those goods were overproduced to begin with

as taxes rise on any one group, individuals in that group may respond by

earning less income

Deadweight loss rises with

elasticities of demand and supply

elasticities determine

equity and inefficiency

What is the fundamental issue in designing tax policy?

equity efficiency trade off

Laffer curve:

for low tax rates, increasing the tax rate will increase revenues. At some point, an increase in tax rates decreases revenue because workers will reduce their labor supply. If we are on the "correct side" of the curve you can raise taxes and increase revenues. If you are on the "wrong side" of the curve raising taxes will lower revenue. If the early 1980s, Congress passed tax cuts on higher-income individuals with the belief we were on the "wrong side". However, analysis shows that we were on the "correct side" so cutting taxes decreased revenues.

the fact that the marginal deadweight loss rises with the tax rate implies that

government should not raise and lower tax rates as they need money, but should smooth it over the deficits and surpluses. Just as individual utility is maximized by consumption smoothing, government efficiency in taxation is maximized by tax smoothing.

As elasticity of demand and supply increase (become more elastic), the deadweight loss of taxation

grows. The tax inefficiency increases as people change their behavior more in order to avoid having to pay the tax. Graphs:

deadweight loss is larger for

higher-wage workers because they are more productive (and that's why the get paid more). Thus, the same reduction in hours worked means more lost productivity for the highly productive workers

the efficiency cost of imposing a tax on ___________ markets is greater than the cost of imposing the same size tax on a market that is initially in _________

imperfectly competitive, competitive equilibrium

If MDWL/MR for good A > MDWL/MR for good B, taxing good A causes

more inefficiency per dollar of revenue raised than does taxing good B. Reduce taxation on good A and raise the tax on good B until the equation holds with equality.

key determinants of the efficiency of a new tax

preexisting distortions in a market such as externalities, imperfect competition, or existing taxes because marginal deadweight loss rises with the tax rate graph

Ramsey Rule:

set commodity taxes such that 𝑀𝐷𝑊𝐿𝑖/𝑀𝑅𝑖 = λ where MDWL is the marginal deadweight loss, MR is the marginal revenue raised and λ is the value of additional government revenues. The value is the value of having another dollar in the government's hands relative to its next best use in the private sector.

The appropriate elasticities need to reflect

substitution effects and not income effects since we want to know how people substitute away from goods/services as taxes are added = compensated elasticities

Tax efficiency is about

the amount of social efficiency sacrificed when trades are impeded by the presence of taxation.

Tax-Benefit Linkages and the Financing of Social Insurance Programs. Direct ties between taxes paid and benefits received can affect

the equity and efficiency of a tax Ex. Worker's compensation plan that is financed by a payroll tax on employers. graph

Marginal deadweight loss:

the increases in deadweight loss per unit increase in tax Graph:

with workers' compensation, there does not need to be such a high compensating differential for higher risk jobs since

the insurance will cover lost income and medical expenditures. graph

Distortion from any tax increases as

the rate increases since it depends on 𝜏2

government should set taxes across commodities so that

the ratio of marginal deadweight loss to marginal revenue raised is equal across commodities.

social welfare is maximized when

those who have a high level of consumption, and thus a low marginal utility, are taxed more heavily, and those who have a low level of consumption, and thus a high marginal utility, are taxes less heavily. = vertical equity

Need to decide how to trade off

vertical equity and behavior response

What are the equity implications of the inverse elasticity rule?

while efficient this rule may not be fair. It would say tax the stuff that everyone needs (food, medicine, etc) at a higher rate than things only the wealthy buy (luxury cruises, sports cars, etc). You may want to deviate from this rule for a more equitable outcome.

Progressive tax systems can be less efficient. Why?

Because taxation of goods is similar to taxation of incomes. Moving to a more progressive system means narrowing the base for taxation because the part of the tax that applies to the rich is levied on only the narrow income base of the rich

Suppose the government of Michconsin imposes a tax on cheese curd production. When will the efficiency cost of the tax be greater - in the short run or in the long run? Why?

Both demand and supply elasticities are greater in the long run because consumers have more time to seek out or learn about substitutes and producers have more time to switch pro- duction to other goods to avoid the tax. Both of these long-run adjustments will result in a greater decrease in the quantity of cheese curds produced relative to the short-run decrease. Therefore, consistent with the rule that higher elasticity leads to greater inefficiency, the effi- ciency costs of this tax will be greater in the long run.

Consider a social insurance program that is financed by a payroll tax. How does the incidence of this tax differ if the benefits of the insurance program are restricted to workers, rather than if benefits are available to all citizens? Under which circumstances will these differences be particularly large?

A payroll tax is paid by firms that hire workers. Thus, a program in which the benefits are restricted to workers is one in which there is a strong tax-benefit linkage. In that case, the tax causes firms to demand fewer workers at every wage, but the effect is offset by workers' willingness to accept lower wages because they benefit from the program funded by the payroll tax. Both of these effects exert downward pressure on wages, so the incidence of the tax is shifted to the workers in the form of lower wages rather than a reduction in the level of employment. If the benefits funded by the tax were available to all citizens, there would be no corre- sponding shift in the supply of labor function (because there would be no additional benefit to being a worker), so deadweight loss would be greater but wages would not fall by as much. When a benefit is not tied to working status, workers do not bear as much of the inci- dence of the tax. The difference is driven by the labor supply response to the benefit provided. If labor does not respond to a new benefit by lowering its wage demands, firms will be less able to pass the entire cost of the tax to workers in the form of reduced wages. On the other hand, if workers value the benefit funded by the payroll tax, they will be more willing to accept lower wages in exchange for receipt of the benefit. Thus, the differences between these two programs will be particularly large when the benefit is highly valued by workers, or when workers believe there is a high probability they will be the recipients of the benefit.