Econ 309 Introduct to Taxation Notes
I. Public Finance, short form
a. Markets are great
b. But sometimes markets fail: Externalities, Public Goods, etc.
c. Maybe some role for government might improve things
d. Requires collective choice
i. Problem I: Collective choice mechanisms often give bad results
ii. Problem II: Principal-Agent issues: On the margin, elected officials and bureaucracies may care more about holding power and gaining benefits than about concerns of the electorate.
iii. Hard to have a government without taxation, and taxation usually creates DWL.
e. What is the relationship of government to its citizens? Servant or master? Useful tool or overlord? This makes a difference when thinking about how tax systems should run. Example: US Revolutionary War.
II. How are tax systems?
a. Note that this discussion ignores the wonderful, rare exception of Pigouvian negative-externality taxes. Alas, most tax collection creates DWL rather than reduces it.
b. From an efficiency standpoint, the ideal tax is “Lump sum”
i. Everyone pays the same and there are no distortion effects at all.
ii. Fixed resource grab
iii. Unrelated to behavior and so creating no distortions in actions, no DWL,
iv. Federal government would require about $10,000 lump sum from every American
v. In practice, this can be very hard on the poor, seen as “unfair”
c. Supply & Demand model with taxes is the simplest way of thinking about taxation, but other models (particularly on labor supply) will be considered
d. Role of taxes: Collect revenue to finance government operations.
e. Why do normal people hate taxes? Income effects. (OK, bad government spending would create negative income effects, but good government spending should create good income effects.)
f. Why do economists hate taxes? Substitution effects, (Marginal Effects)
i. Ideally tax system would be “neutral”
ii. Neutral means has no effect on behavior, so creates no DWL
iii. Exception: Environmental and “sin” taxes are intended to discourage behavior viewed as harmful
g. What would we hope our tax system would be like?
i. How should the tax system treat richer people?
ii. How should the tax system treat married people?
h. Mancur Olson: Natural constituency for cutting taxes – an easy call, not so with spending programs
i. Problems of “rent seeking behavior”, “inframarginal effects”
ii. Ricardian rents = Seeking increased payment for something you would have done anyway
III. How should a tax system be?
a. What would we hope our tax system would be like?
b. How should the tax system treat richer people? Vertical equity?
c. How should the tax system treat people with similar abilities to spend? Horizontal equity?
d. How should the tax system treat married people? Conflict of the two above?
e. Simplicity! Clear rules! Stabile rules over time (Transitional Equity)! Low DWL (Efficient)! Collects revenue! Enforceable!
IV. Tax history
a. Egypt, Mesopotamia, China, Bible – ancient records
b. Smith, Malthus, Ricardo, Mill – finance government and transfers.
c. American colonies: Stamp Act, “Taxation without Representation is Tyranny!”, Boston Tea Party (1773, odd story really, Hancock and smuggling)
d. US: Started with tariffs, property and d excise taxes (whiskey!), fees. Income tax an illegal “specific tax”, an issue between rich and poor states.
e. Wars change thinking, at least temporally.
i. Civil, Spanish American, WWI, WWII.
ii. Imagine an MTR of 92%!
iii. Loopholes help though. Health insurance.
iv. Economic historian J.R.T. Hughes: “Wars permanently add another digit to the size of government.”
v. A strong tax system is a powerful weapon of war because of the way it can gather resources for the effort.
f. US federal tax system has been remarkably stable in its share of GDP since WWII, about 20% of GDP.
i. Rising state and local taxes
ii. Rising payroll taxes (FICA) to support Social Security and Medicare (but these programs bring in more taxes than they currently generate in spending so this surplus finances a deficit between other taxes and government spending, but this won’t continue)
iii. Declining corporate income taxes
V. Income tax definitions
a. Haig-Simons comprehensive income definition: Income is the ability to increase consumption. (Includes benefits.)
b. Marginal tax rate (MTR): Change in taxes owed for a given change in income, tend to be higher for higher incomes, hugely important for efficiency
c. Average tax rate (ATR): (Taxes paid)/income, hugely important for “fairness”
d. For a single earner. (Note: There is an implicit 0% tax rate on the first several thousand of income as standard deductions, $3,500 for personal exemption and $5,350 for the standard deduction for those who don’t itemize their tax deductibles.)
e. Gross income (GI) = Wages + salaries + capital income (?) + interest + dividends + rental income + business income
f. Adjusted Gross Income (AGI) = GI – Deductions (IRAs, home interest, alimony paid, etc.)
i. Tax deductions reduce taxable income
ii. Tax credits reduce taxes owed.
iii. In the 33% tax bracket, $1 of a tax credit reduces taxes by the same amount as $3 of tax deductions.
g. About half of gross income gets taxed in the federal income tax system!
h. Big deductions and “Tax Expenditures”: Employer provided health insurance ($146 B), Home mortgage interest ($80 B), total = $872 B >> budget deficit
VI. Tax “fairness”
a. What the heck does fairness mean?
i. Benefits principal – People should pay for the benefits they get.
1. Taxes as user fees?
2. “Taxes are the price we pay for a civilized society.” Oliver Wendell Holmes, Jr., 1904
ii. Ability to pay criterion?
1. Tax rich more?
2. Tax deductions for having dependents, mortgage interest, state & local taxes?
b. Progressive tax systems have a higher ATR at higher incomes (rich pay a larger share of their income in taxes)
c. Proportional tax systems have the same ATR at all incomes
d. Regressive tax systems have a lower ATR at higher income (rich pay a lower share of their incomes in taxes)
e. How do we compare progressivity of two tax systems?
i. Suppose people earning income Y0 pay tax T0, and income Y1 goes with tax payment T1. Y0 < Y1, T0 < T1.
ii. Two possible measures of how progressive a tax system is:
1. Measure 1 = (Change in ATR)/(Change in Income)
= (T1/Y1 – T0/Y0)/(Y1-Y0)
2. Measure 2 = (% change in taxes)/(% change in income)
= [(T1-T0)/T0]/[(Y1-Y0)/Y0]
3. If both taxes were to go up by 20%, would the system become more progressive? It depends upon the measure.
f. Fairness of a system: Progressivity definitions?
i. Lorenz curves, Gini coefficients
ii. Michael J. Graetz, Distributional Analysis of Tax Policy, “Distributional Tables, Tax Legislation, and the Illusion of Precision”, The AEI Press, 1995.
g. User fees and Benefits Principal– dorm cable, Libertarian fetish. Tolls, park admissions, gas taxes (supporting roads). Can conflict with Horizontal and Vertical equity.
VII. Tax incidence: Who bares the burden of the tax?
a. “Simple market” tax effects on Q, PSuppliers, PDemanders, DWL, Tax Revenue
b. “Tax wedge” is not wedge-shaped, but is just the amount of the tax, that is, the difference between what buyers pay and sellers receive.
c. Commodity taxes: Unit versus ad valorem
i. Unit tax = Fixed dollar amount per unit of product. (5 cents per can) Shifts curve by the amount of the tax (if on supply, raises supply; if on demand, lowers demand). Easy to draw, so I’ll usually use this.
ii. As valorem tax = Fixed percentage of sale price of product. (5% sales tax). Rotates supply curve counter-clockwise (outward) around its horizontal intercept, or alternatively rotates the demand curve counter-clockwise around its horizontal intercept.
iii. Comparison: A unit tax on cars would be the same dollar amount on all cars, but an ad valorem tax would be more dollars on a more expensive car.
d. Gruber’s Three Rules of Tax Incidence
i. Statutory burden of a tax is not the same as who really bears the burden of the tax.
1. Statutory incidence = Who the law says must write the check to pay the tax.
2. Economic incidence = Who loses resources due to the effect of the tax.
3. Example: Sellers can often shift some of the burden of a tax to customers by raising prices.
ii. The side of the market (suppler or demander) the tax is levied upon is irrelevant for the distribution of the tax burden.
iii. Parties (suppliers, demanders) who are inelastic bear a lot of the burden; parties that are elastic shift their behavior to avoid it.
1. “Tax avoidance” = changing behavior to avoid taxes, source of DWL, legal
2. Steve Landsburg: “If your behavior cannot effect your taxes, then your taxes will not affect your behavior.”
3. “Tax evasion” = Not paying the taxes owed, ILLEGAL.
e. Incidence is all about who suffers from a tax. From the standpoint of politicians, lawyers, or accountants, this is a simple question. Who does the law say has to pay the tax? This is called statutory incidence. However, the issue is much more complex than those knuckleheads realize. There is what is known as tax shifting which is when the statutory burden of a tax is pushed onto someone else. These people who get hit with the true burden of the tax suffer its economic incidence. So those employer mandates for health insurance that politicians talk so much about may have had a statutory incidence on firms but an economic incidence on workers.
f. A unit tax is a tax of a set amount on a unit of output. An example would be a tax of 5 cents on a can of beer. The tax would be the same on a can of Pabst's Blue Ribbon (dirt cheap with emphasis on the dirt) as it would be on a can of expensive Beck's. An ad valorem tax is like a sales tax. If it was 10%, then if Pabst's sold for 10 cents before the tax, then with tax it would sell for 11 cents with the tax (assuming inelastic demand). If Beck's sold for $1.50 per can, with tax it would sell for $1.65. A unit tax on suppliers raises the supply curve by the amount of the tax. An ad valorem tax on suppliers rotates the supply curve upward from the point where it hits the horizontal axis. For graphing simplicity, I will generally work with unit taxes since it's easier to draw a parallel shift. (The Pabst verse Beck's example is a little misleading because they are supposedly different goods, although both taste terrible to me.)
g. As you may recall from previous studies in economics, elasticity of supply and demand figure in here somehow. As a rule of thumb, the more inelastic is supply or demand, the more of the burden of the tax will be borne by the inelastic sector.
h. Note however, that our analysis here assumes "partial equilibrium." That is, we are thinking about only one market, but this can be very misleading. It could well be that introducing a tax on beer will cause me to give up drinking beer and switch to drinking orange juice. Here I avoid paying any tax, yet since I clearly bear some incidence of the tax, that is I'm worse off, because I prefer to start my day with Pabst rather than orange juice.
VIII. Tax Incidence and Market Structure
a. Profits tax, input tax, output tax.
i. Profits tax interesting for monopoly and oligopoly since they often have non-zero profits.
ii. Input tax interesting for pollution (tax use of coal), payroll taxes. Will be considered in later weeks.
iii. Input tax
b. Perfectly competitive firms have no profits, so can’t be taxed on them. Taxes on output just shift costs.
c. Monopoly: Tax on output treated as shift in costs, changing point where MR = MC.
d. Oligopoly: Same as monopoly.
IX. Mathematical Example
a. Demand: PD,Gross = 110 – Q
b. Supply: Marginal Cost = $10
c. Perfect Competition: Tax of $10 on demand shifts demand down by 10. Tax of $10 on supply shifts MC up by $10. Same result.
d. Monopoly: Goal is to maximize profits
i. Max(Profit,Q) = Max[(PD – MC)*Q] = Max[(110-Q-MC)*Q]
ii. With tax T imposed on demanders, Max[(110-Q-T-MC)*Q]
iii. With tax T imposed on suppliers, Max[(110-Q-(MC+T))*Q] Same!
iv. Tax increases DWL here, but there is a social benefit of tax revenues. Is it worth it?
v. With profits tax (1-T’), monopoly’s goal is to maximize (T’)*Max(Profit, Q), which is the same basic optimization problem as before, so profits tax doesn’t seem to change anything.
e. (Just for example, we won’t do Cournot in this class this quarter) Cournot Duopoly: Goal is for each firm to try to maximize its own profits, given what the other firm is doing. Quantity competition and a Nash equilibrium, neither firm can improve its profits by unilateral change. Firm One produces q1, Firm Two produces q2, both get the market price which is determined by the total amount Q = (q1 + q2)
i. Demand: PD,Gross = A – B*Q = A – B*(q1 + q2) = 110 - (q1 + q2)
ii. Goal for each firm: Max (P-MC)* qi, i = 1,2.
iii. In equilibrium w/o taxes, q1 = q2 = (A-MC)/(3*B) = (110-10)/3 = 33.33.
Price = 110-(33.33+33.33) = 33.33
Profit for each firm = (P-MC)* q1 = ($33.33-$10)*33.33 = $777.78
iv. With tax T imposed on demanders, qi = (A-T-MC)/(3*B)
v. With tax T imposed on suppliers, qi = (A-(MC-T))/(3*B)
vi. With profits tax (1-T’), goal for each firm: Max (P-MC)* qi, i = 1,2. Same problem as before!
X. Imperfect competition and taxation
Demand: P = 100 – 3*Q
Marginal cost of production = $10
If this market is perfectly competitive, P = $10, Q = 30, DWL = 0, Profits = 0.
If the market is a monopoly and there are no taxes, P = $55, Q = 15, DWL = 0.5*($55-$10)*(30-15) = $337.5, Profits = ($55-$10)*15 = $675.
If the market is a Cournot duopoly, each firm makes q= (100-10)/9 = 10, so market quantity Q = 20, P = $40, each firm makes profit ($40-$10)*10 = $300 for a total market profit of $600, and market DWL = 0.5*($40-$10)*(30-20) = 150.
a. What would be the new market Q, profit, DWL, and tax revenue if there were a $5 unit tax put on the monopoly?
b. What would be the new market Q, profit, DWL, and tax revenue if there were a $5 unit tax put on the Cournot duopoly?
(Hint: q = (100-MC-T)/9)
c. With the monopoly, what would be the DWL and tax revenue from a 30% profits tax?
d. With the Cournot duopoly, what would be the DWL and tax revenue from a 30% profits tax?
XI. So…profits taxation looks like a great way to raise revenues without DWL…but…there are dynamic issues that screw this up. Damn!