1 Review questions

Indicate whether each statement is true, false, or uncertain, and give a brief explanation.

1. We should tax goods with inelastic demand.  Uncertain.   While goods with inelas- tic demand yield less excess burden,  they also tend to  be necessities like food and medicine that we may not believe should face higher prices.

2. Alvaredo et al.   (2013) find no relationship between top marginal tax rates and income inequality. False. Alvaredo et al.  (2013) find a negative correlation between top marginal tax rates and income inequality.

3. The vast majority of the behavioral response in Saez (2010) comes from self-employed individuals. That means that wage-earners don’t respond to kink points in the tax schedule.  False.  Wage- earners might respond, but we may not see the response in the short-run.

4. Behavioral changes to reduce tax liability are always illegal.  False.  Legal changes to behavior that reduce tax liability are considered tax avoidance, not tax evasion.

2 Problems

2.1 Income Taxation, the ETI, and the EITC

In the small fictional country of Waupaca, the hourly wage is $20 per hour before taxes. Citizens can work up to 8 hours a day, 250 days of the year.

(a) Put leisure on the x-axis and consumption on the y-axis. Draw the trade-off between

consumption and leisure for one year with a 0% tax and under a constant 15% income tax.

(b) Copy your image from (a). Draw a set of indifference curves where the income effect

of the tax dominates the substitution effect.

(c) Copy your image from (a). Draw a set of indifference curves where the substitution

effect of the tax dominates the income effect.

One way that governments make tax systems more progressive is through the use of tax credits. The Earned Income Tax Credit (EITC) is a large tax credit program in the US.

The government of the small fictional country of Waupaca wants to introduce an EITC- style tax credit. For the first $10,000 earned, the government issues a tax credit of $0.40 per dollar earned for a maximum credit of $4,000. For the next $10,000 earned, the credit amount stays constant at $4,000.  After $20,000 in pre-transfer earnings, the credit is reduced by $0.20 for every additional dollar earned until the credit is worth $0.

(d) Copy your graph from (a) but only include the line for a 0% tax. On this same graph, draw the consumption-leisure trade-off after the introduction of the tax credit. Make sure to note the number of hours of leisure associated with each kink as well as the amount of consumption. See answer to part (e) .

(e) Mark the portions of the graph of the tax credit in (d) where the labor supply effects of the tax credit are positive, negative, or ambiguous (relative to no tax). Explain why for each portion.

Phase-in:  negative income  effect  (more non-labor income  b/c  of transfer −→ negative impact on labor supply) , positive substitution effect  ⇒ ambiguous effect on labor supply

Plateau:  negative income effect (more non-labor income b/c of transfer −→ negative im- pact on labor supply) , no substitution effect  ⇒ negative effect on labor supply

Phase- out:  negative income effect (more non-labor income b/c of transfer −→ negative impact on labor supply) , negative substitution effect  ⇒ negative effect on labor supply

(f) In 2-3 sentences, explain why these kinks in the marginal tax rate might help us identify the elasticity of taxable income.

Standard  labor supply  theory  suggests  that kinks  in  the  marginal tax rate  will  lead to “bunching. ”  The amount of bunching can be directly related to the unknown input into the formula for the (compensated) elasticity of taxable income.

2.2 Tax Incidence

In class, we worked through the derivation of how the change in price faced by consumers changes with a change in the tax when sellers face the statutory incidence of the tax (that is, the tax in“on”sellers).

In this problem, we will work through the scenario where the tax in“on”consumers. Set-up:

• Consumer pays p + t

• Producer receives p

Consider the effect of going from no tax (t = 0) to a tax t > 0 for some small change t.

Our goal is to determine by how much does the price paid by the consumer change when we impose the tax.

(a) What is the equilibrium condition?

S(p) = D(p + t)

(b) Totally differentiate the equilibrium condition with respect to the tax, t.

S\ (p) = D\ (p)(1 + )

(c) Re-arrange the previous expression to solve for .

dp D\ (p)

dt      S\ (p) − D\ (p)

Define the elasticity of demand η D  = D\ (p) and η S  = S\ (p).

(d) Multiply all of the terms of the expression for by and re-write the expression as a function of η D  and η S .

dp η D

dt η S  − η D

(e) Note that the total price paid by the consumer in this case is p + t, where p is the amount received by the producer. To solve for the change in the total price paid by the consumer, calculate where dptotal  = p + t.

dptotal dp

dt         dt

η S − η D

(f) How does this compare to the result we get when the tax is“on”producers? Intu-

itively, what does it mean? Why is it important?

This is the same expression we get when the tax is “on” producers.  This result is known as the tax invariance proposition. Intuitively, it means that who bears the burden of a tax is independent of whether the statutory incidence of a tax is on producers or consumers. If true in reality, it is important because it means we do not need to worry about statutory incidence from a policy perspective (key phrase:  “if true. ”)