1. The Haig-Simons definition of income is the net change in the individual’s power to consume during a given period. This criterion suggests the inclusion of all sources of potential increases in consumption and also implies that any decreases in an individual’s power to consume should be subtracted in determining income. Overall, it reflects the broadest possible base of income. Allowing capital losses of $5,000 to be deductible against other forms of income, rather than the current $3,000, would move the tax system more in the direction of the Haig-Simons criterion.
2. From a Haig-Simons point of view, the McCain proposal makes sense. According to Haig-Simons, all income should be taxed at the same rate, regardless of the use to which
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it is to be put. Under the status quo, income (in the form of capital gains) is taxed at a lower rate if it is donated to charity. Note that wage income that is to be donated to charity does not enjoy the same benefit.
Under the status quo, the tax price of a gift of appreciated property is 1 - t - tk*g, where t is the marginal tax rate on ordinary income, tk is the tax rate on capital gains, and g is the proportion of the gift that is appreciated property. With the McCain proposal, the tax price would be 1 - t. Thus, the tax price goes up. We expect charitable contributions to go down by an amount that depends on the elasticity of charitable contributions with respect to their tax price.
3. Suppose Jones buys the oil stock for $1,000 at the start of period 0. At the start of period 1, he has two options.
a. Hold the oil stock one more period, then sell.
b. Sell the oil stock, buy the gold stock and hold it for one period.
In both cases, it is assumed that all assets are sold, and any taxes paid at the end of period 2. What are the returns to option a)? At a 10 percent rate of appreciation, the oil stock is worth $1,210 after period 2, the capital gain is $210 and assuming a 29 percent rate applies to capital gains, the capital gains tax is 28 percent of
$210 or $58.80. Thus, Jones is left with $1,210 - $58.80 or $1,151.20 after tax.
If Jones follows strategy b), the value of the oil stock at the start of period 1 is
$1,000, the capital gain is $100, and the tax $28. Thus Jones has $1,672 left over to proceeds (V) from selling the gold stock at the end of period 1.
V = Value of gold stock – taxes
= (1+r)($1,072) –(.28)[(1+r)($1,072)-($1,072)]
= (1+r)($1,072) –(.28)r($1,072)
= $1,072 + .72r($1,072)
Setting V = $1,151.20 (same as oil stock):
$1,151.20 = $1,072 + .72r($1.072) ⇒ r=10.26%
Thus the gold stock must pay a “premium” of 0.26% (10.26% - 10%) over the oil stock in order to overcome the tax cost of realizing the capital gain.
4. Dear Newsweek: Your Wall Street editor does not understand the tax code. The bracket widths, exemptions, and deductions are all indexed and have been since the early 1980s.
In effect, this indexes wage income against inflation.
5. For an itemizer, a $500 tax deduction lowers the tax bill by t*deduction. Thus, for an itemizer with a 30% marginal tax rate, the tax bill is lowered by 30%*$500, or $150. A (refundable) tax credit, on the other hand, directly lowers the tax bill by that amount, in this case, $500.
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6. a. With a tax rate of t=0.3, and a nominal interest rate of i=0.13, the nominal after- tax rate of interest is (1-t)i=(1-0.3)0.13=0.091. With an expected inflation rate of π=0.08, the real after-tax rate of interest is (1-t)i-π=(1-0.3)0.13-0.08=0.091- 0.08=0.011.
b. If the expected inflation rate increased by 3 percentage points to π=0.11, and the nominal interest rate also increases by 3 percentage points to i=0.16, then the real after-tax rate of interest is now (1-t)i-π=(1-0.3)0.16-0.11=0.112-0.11=0.02. The real after-tax rate of return falls from 1.1% to 0.2%. This is because the tax system taxes nominal, not real, returns.
c. In general, consider two rates of inflation, π<π’. The key question is when taxes are present, by how much must the nominal interest rate increase in order to have the same real rate of return. This is calculated by equating real rates of return under different inflation rates (holding constant taxes): (1-t)i-π=(1-t)i’-π’. One can rearrange this equation: (π’-π)=(1-t)(i’-i), or (i’-i)= (π’-π)/(1-t). This can in turn be expressed as: Δi=Δπ/(1-t). Intuitively, the left-hand side of this final equation is the change in nominal interest rates that keeps the real after-tax rate of interest unchanged. It is equal to the change in the expected inflation rate divided by (1-t). Thus, returning to part 6b, for a 3 percentage point change in the inflation rate and a marginal tax rate of t=0.30, nominal interest rates would have to increase by approximately 4.3 percentage points.
7. Lowering the tax rate on the earnings of the secondary earner has better efficiency properties. By lowering the marginal tax rate, it reduces excess burden. Since the elasticity of labor supply for secondary earners is relatively high, the gain in efficiency should be substantial. In contrast, for most households, an increase in the standard deduction is “infra-marginal,” i.e., it does not affect the incremental returns from working another hour.
8. Proponents argued that letting nonitemizers take an additional deduction for charitable giving would stimulate giving. This is because the after-tax “price” of giving $1 to charity falls from $1 to (1-t)$1, where t is the marginal tax rate. The argument presented in the question, that “critics argued that a deduction was not necessary to stimulate giving because part of the standard deduction can be used for a charitable donation” have little in the way of argument. The price of giving remains $1. Although it is true that some giving is inelastically supplied, changes in tax-prices may stimulate giving. The Bush administration proposal would have lowered the price of giving for nonitemizers, who comprise about two-thirds of all tax returns. One suspects that the marginal tax rates that nonitemizers face, however, is relatively low compared to itemizers, so the after-tax price may not have changed very dramatically.
9. a. i. A family of four would receive four exemptions that totaled $12,200 (4*$3,050) in 2003, according to the figures on page 371 of the textbook.
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ii. Ignoring other features like the exemption phaseout, an increase in income of $2,500 leads to an increase in taxes of $750 with a marginal tax rate of 30% ($750=$2,500*30%).
iii. Personal exemptions are reduced by 2 percentage points for each $2,500 increase in AGI. Thus, the exemption falls from $12,200 to 98%*$12,200, and taxable income goes up by 2%*$12,200, or $244.
iv. The additional increase in taxable income of $244 increases the tax liability by 30%*$244, or $73.20.
v. The total change in tax liability, the effective tax rate, is ($750+$73.20)/
$2,500, or 32.928%.
b. i. With $100 of income initially, the family would owe 30%*$100, or $30 in taxes.
ii. According to the textbook (page 377), the phaseout on itemized deductions is at a rate of 3% for AGI above a certain threshold. The itemized deduction falls by 3%, or $3, for the $100 increase in income.
Taxable income goes up by $3.
iii. The $3 change in taxable income increase the tax liability by $0.90 (=30%*$3).
iv. The effective tax rate is ($30+$0.90)/$100=30.9%.
10. Of the $4,000 of earnings that Sam has, he is able to invest (1-tI)*earnings in the market, or (1-0.25)*$4,000=$3,000. Assume that when he saves the money in a taxable account, he has to pay taxes each year on the capital gains, and that those capital gains are treated as ordinary income and taxed at 25%. In this case, his after-tax rate of return is (1-tI)*r, or (1-0.25)*8%, or 6%. Thus, after 10 years of investment, the amount of money in the taxable savings account is $3,000*(1.06)10=$5,372.54. If he invests the money in a Roth IRA, the money accrues at the before-tax rate of return, and there is no tax liability at the end. Thus, the amount in the Roth IRA is $3,000*(1.08)10=$6,476.77. It turns out that the key difference between a traditional IRA and a Roth IRA is whether the income tax rate today differs from the income tax rate in retirement. Thus, the amount in the Roth IRA would be identical to that of a traditional IRA if tax rates 10 years from now were the same 25%.