Econ 132 Public Finance
Holcombe, 10, positive principles of taxation
Tax Shifting
The concept here is that a tax placed on one side of the market can be shifted to the other.
A unit tax: sales or excise tax charged per quantity unit, such as a gallon of gasoline.
Supply curve shifts up by the amount of the tax.
P. 202, fig. 10.1
The price increases by less than the amount of tax.
Part of the tax is paid by demanders as a higher price, and part by suppliers as a lower price,
and both are worse off from the reduced quantity.
Statutory incidence: the agent legally responsible for paying.
Economic incidence: the change in the distribution of income.
Difference between them is the amount of tax shifting.
Tax incidence is independent of statutory incidence.
A payroll tax is a tax on wages. Social security a payroll tax.
The statutory distinction between employer and employee, with the tax split, is
economically irrelevant.
Legislation cannot change the economic incidence of a tax.
It makes no difference whether taxes are placed initially on suppliers or demanders in a particular market, suppliers pay the same amount in either case and demanders pay the same amount in either case.
Which side of the market bears how much of the burden depends upon the elasticities of supply and demand.
The general principle is that the more elastic a schedule (supply or demand), the more the tax is shifted to the other side of the market.
The relative burden of the tax borne by demanders to suppliers is equal to the ratio of the slope of the absolute value of the demand curve to the absolute value of the supply curve.
The unresponsive agent bears most of the burden.
If demand is elastic, the tax is shifted to sellers
If demand is inelastic, the tax is shifted to buyers.
If supply is elastic, the tax is shifted to buyers.
If supply is inelastic, the tax is shifted to sellers.
If supply is totally inelastic, vertical, the total incidence is with the seller or agent renting
out the property.
p. 206, Fig. 10.5, inelastic supply, supplier bears the whole burden.
p. 207, Fig 10.6, elastic supply, demanders bear the whole burden.
The Welfare Cost of Taxation
The welfare cost, or excess burden, or deadweight loss.
The ways that people can change their behavior:
labor versus leisure, savings versus consumption, risk level, and tax avoidance and evasion.
The excess burden, i.e. in excess of the tax
paid, for US federal taxation has been estimated to be about $1.5 trillion per year.
Tideman, Nicolaus, and Florenz Plassman. 1998. "Taxed Out of Work and Wealth: The Costs of
Taxing Labor and Capital." In The Losses of Nations: Deadweight Politics versus Public Rent
Dividends. London: Othila Press, pp. 146-74.
The tax alters the taxpayers' behavior from their otherwise utility-maximizing behavior,
which lowers their well being further than if the money had been collected on rent.
The excess burden comes from reducing the production and consumption of the good.
p. 209, fig. 10.7
The triangle is called the Harberger triangle, after Arnold H. who first sought to measure it.
The triangle can be calculated graphically as the dollar value of the excess burden.
Consumers who substitute out of the taxed good and into something else lose utility from consuming less of the taxed good, and gain less utility from consuming the substitute.
The substitution effect causes the welfare loss.
The excess burden can be minimized by taxing the most inelastic demands or supplies.
But taxing inelastic demands such as medical services is regarded as immoral.
That leaves inelastic supplies, mainly as land.
p. 210 a lump sum tax
The tax amount is fixed.
But it can affect human action, such as inducing more labor.
Lump-sum taxes are not necessarily neutral.
A tax on land rent, with an inelastic supply, is better than a lump-sum tax,
because it is independent of the owner’s labor or produced wealth,
and it does not force him to work; it forces the land to work.
P. 211: no such fixed supply or demand exits.
Why not.
Holcome says that the supply of land offered for sale can change.
There are two types of supply.
1. The total amount in existence. Similar to the total amount of shares of stock.
2. The lots offered for sale at a moment in time, like shares of stock.
#1 is fixed, #2 is not.
The price of land depends fundamentally on #1, and only temporarily on #2.
The welfare cost of an income tax
There could be a completely inelastic supply of labor and a deadweight loss.
The can happen if the substitution effect offsets the income effect.
The substitution effect is a deadweight loss.
With land, there is no substitution effect, because land does not have leisure.
The Ramsey Rule
Named for Frank Ramsey.
Taxes should be placed in inverse proportion to elasticity.
Tx/Ty (tax rates) = Ey/Ex elasticities.
To minimize excess burden: the marginal excess burden of the last dollar of revenue
from each item must be the same.
Hence, tax each item so that the percentage reduction in the quantity supplied or
demanded of each commodity is the same.
If we rule out inelastic demands for medical services,
the two major inelastic supplies are land and time.
Commodity taxes should be inversely proportional to the compensated elasticities of
demand for the goods.
The inverse elasticity rule: tax rates should be inversely proportional to elasticity.
Hence, efficient taxation requires the taxation first of goods the most inelastic in supply
and demand.
The demands for all goods should be reduced by the same proportion.
Since excess burden of land is zero, to made the percentage reduction the same, taxes
on all other commodities must be zero so long as there is rent or land value left.
The size of the excess burden depends on both the elasticities and the size of the tax.
For linear supply and demand, the excess burden increases by the square of the tax size.
Partial equilibrium models only look at the market in which a tax is imposed.
General equilibrium examines all markets
Labor versus leisure
Let T be the time endowment, hours per week.
The two alternatives are L hours or leisure, or labor (T-L)
One buys an hour of leisure by working one less hour, the price is the foregone wage.
The hourly wage is w.
y = (T-L)w
Maximum income is Tw
The utility function is U = u(y,L)
MRS = mu(L)/mu(y)
The optimal choice is the point of tangency (p. 301)
The MRS = slope of the budget line (-w).
A lower wage flattens the budget line.
A change in the wage rate has two effects: an income and a substitution effect.
A tax that reduces the net wage reduces the price of leisure.
That creates a substitution effect in favor of more untaxed leisure.
But the income effect of less income, so one will consume less of all normal goods,
including leisure. Less leisure implies more labor.
So we have opposite effects.
To minimize excess burden: the marginal excess burden of the last dollar of revenue
from each item must be the same.
Hence, tax each item so that the percentage reduction in the quantity supplies or
demanded of each commodity is the same.
The responsiveness of labor supply to a change in the after-tax wage is called the
elasticity of labor supply.
It includes many dimensions:
working extra hours, taking a second job, whether a spouse is employed, when to retire, and how much to invest in human capital.
The elasticity of labor should be applied to the most elastic margin, just as the marginal utility of water is for its least important use.
If the labor supply curve slopes up, the elasticity is positive: higher wages get more labor.
The substitution effect dominates.
People work less if wages are taxed more.
Married women have a greater elasticity than average.
What is the effect of a tax on wages?
Let the tax rate be t
y = (T-L)w
With the tax,
y = (T-L)w(1-t)
If the substitution effect dominates, then higher taxes cause less labor and less investment and less investment income, and less income implies less tax revenue.
At very high tax rates, higher taxes reduce revenues.
This concept was popularized during the 1980s by economist Arthur Laffer,
the Laffer curve named for him, p. 307.
Much of wage consists of benefits. Not taxed.
Taxes induce more payment in untaxed benefits.
Effect on savings
A tax on interest and dividend income reduces the return from savings and affects saving.
Savings change during a lifespan, so we need to look at the life cycle model.
Intertemporal budget constraint.
Simplify with two periods, present and future.
Current income Y0 and future income Y1.
The interest rate is r.
The present value = Y0 + Y1/(1+r)
Consumption: C0 + C1/(1+r)
If consumption equals income,
C0 + C1/(1+r) = Y0 + Y1/(1+r)
C1 = [(1+r)/Y0 + Y1] - (1+r)C0
The budget constraint
The slope of the budget constraint is -(1+r)
One can save at rate r or borrow at rate r
The utility of present versus future consumption is u(C0,C1)
Optimal consumption is where the budget line is tangent to the indifference curve.
The slopes are equal.
MRS = muC0/muC1 = (1+r)
Effects of taxes on the yield from savings
There is an income and substitution effect like on wages.
The substitution effect reduces savings and increases present-day consumption.
The tax reduces lifetime income so will reduce present consumption.
C1 = [(1+r[1-t])/Y0 + Y1] - (1+r[1-t])C0
Another element in the effect is if the interest payments are tax deductible,
as it is with mortgages.
If you borrow on the equity of your house, the interest payment is tax deductible.
That reduces the cost of borrowing.
The substitution effect then increases current consumption.
To avoid reducing savings, the government has set up tax-sheltered accounts.
IRA, 401k, 403b, and others.
Traditional and Roth IRA.
Imputed rent from owner-occupied housing not taxed in US.
Is taxed in Spain, Sweden, Denmark.
Housing capital gains mostly untaxed.
Mortgage interest and taxes deductible.
Large subsidty to housing => higher land prices.
Taxation and risk taking
Entrepreneurs are the drivers of the economy, and they have an incentive to take risks when they get more profit. Taxing the profit reduces the incentive, and there is less economic growth.
There is also less innovation, fewer new products, less technological advance.
But losses are tax deductible, and losses offset gains.
So the income tax reduces the net loss.
The government is in effect a partner in the loss and gain.
Taxes on profits and gains reduce the expected value of a risky venture,
so some projects will not be done that would have been.
Reducing the loss actually induces excessive risk taking, which is wasteful.
Effect on tax avoidance, legal, and evasion, illegal
Since tax evasion is risky, the effect is similar to a tax on risk taking.
There is a safe legal asset and a risky illegal asset, such as unreported income.
Tax evasion can be limited either with increased enforcement, or
by taxing items that cannot be evaded.
P. 217: the marginal cost of public spending
The higher tax rates already are, the greater the marginal excess burden of additional taxes.
The current marginal excess burden is about 25% of the tax revenue.
A project financed by income taxes might be justified with a low tax rate but not a high tax rate.
Additional Costs of the Tax System
Compliance costs, administrative costs, and political costs must also be included.
Compliance costs are imposed on taxpayers; especially with income taxes.
Keeping records, filling out forms, looking up information, paying legal and accounting costs, setting up tax shelters, audits.
Over 5 percent of the tax revenue. Two billion hours of taxpayers’ time.
Sellers have significant costs for sales taxes for many jurisdictions.
Administrative costs borne by the government.
Political costs of seeking to change the tax code or prevent an unfavorable change.
p. 220: Earmarked taxes
From cows whose ears were marked to indicate ownership.
Earmarked taxes are designated for a particular use,
like gasoline taxes that are supposed to be spent on highways.
The extra toll amounts on the Bay Bridges are earmarked for bridge retrofitting.
Social Security taxes are earmarked for that program.
Earmarking reduces flexibility, but it secures funding for a program against political pressures.
Earmarking also makes the cost clearer.