Understanding Taxation Effects on Income and Savings Strategies

School
University of Toronto**We aren't endorsed by this school
Course
MGAB 2020
Subject
Economics
Date
Dec 10, 2024
Pages
2
Uploaded by BrigadierLightningToad19
Short Answers to 2015 Exam #2Note: These are sketchy answers only – for full marks on the exam, you would usually be required to provide more detailed answers. 1a) [Imposing a 50% tax on a before-tax wage rate of $20 generates an after-tax wage rate of $10. The after-tax budget line runs from (4000, 0) to (0, 40,000), The individual ends up maximizing utility at point C with 22000 hours of leisure, 2000 hours of work, and 20,000 units of good C.]Revenue = tw(hrs of work) = $10x2000 = $20,000[The equal utility lump sum tax moves the consumer to the budget line running from (2800, 0) to (0, 56,000). This corresponds to a lump sum tax of $24,000]Excess burden = $4,000b) Income effect is A to B. Substitution effect is Bto C.The substitution effect causes the consumer to work much less at C than at B, and the reduction in work effort reduces the revenue raised by the tax on wages. You could also argue that the income effect is associated with the lump sum tax, which has no excess burden.2. Inside the RRSP, the initial $15,000 grows to $15,000(1.05)30= $64,829.14 ( = $64,800 using the approximation provided in the problem). When the taxpayer cashes this in after 30 years, the taxes are 40% of this, leaving 60% for the taxpayer to spend. So consumption = .6($64,829.14) = $38,897.48( = $38,880using the approximation provided in the problem). PDV of taxes = .4($64,829.14)/1.0530= $6000(you get the same result using the approximations in the problem).Outside the RRSP, you start with $9000. The interest rate of 5% is taxed at 40%, so the after-tax interest rate is 3%, which is the rate at which the savings grow after paying taxes. So after 30 years, the individual has $9000(1.03)30= $21,845.36( = $21,870using the approximation provided in the problem). This is the consumption after 30 years (no further tax is due). PDV of consumption is $21,845.36/1.0530= $5054.52 ($5062.50 using the approximation), so PDV of taxes = $15,000 − $5054.52 = $9945.48($9937.50using the approximation from the problem). 3a) Under realization, the asset accumulates without taxation for 20 years. After 20, years, it is worth $100,000(1.10)20= $672,745.00 ($673,000using the approximation from the problem). The capital gain is $572,745.00 ($573,000using the approximation from the problem). The tax on the capital gain is 60%, so tax= .6($572,745) = $343,647 ($343,800 using the approximation from the problem). So the amount available forconsumption is $672,745 − $343,647 = $329,098($329,200using the approximation from the problem). . The PDV of the taxes is $343,647/(1.1)20= $51,080.94($343,800/6.73 = $51,084.70 using the approximation from the problem).Under accrual, the taxpayer pays tax each year, so the after-tax rate of return is 10%(1 − t) = 10%(.4) = 4%. After 20 years, the taxpayer has $100,000(1.04)20= $219,112.31($219,000using the approximation).To get the PDV of taxes, first get PDV of Consumption = $219,112.31/(1.10)20= $32,569.65 ($32,540.86 using the approximation).PDV Taxes = $100,000 – PDV Consumption = $67,430.35($67,459.14using the approximation).b) Taxation on realization is inequitable since it treats income from capital gains more generously than income from bonds (which, by definition, are taxed on accrual basis). Thus, if two taxpayers have exactly the same wage income and exactly the same amount of money to invest, but one invests in an asset that generates capitalgains while the other invests in an asset that generates interest, the one with capital gains will be treated more favourably and will pay fewer taxes (approximately $51,100 under realization vs. $67,400 under accrual, in present discounted value terms). Yet the two taxpayers are in exactly the same economic position, and have exactly the same capacity to pay taxes. So taxing them differently violates horizontal equity.1
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At the same time, taxation on realization is also inefficient. Because capital gains are taxed less than interest income, taxpayers with money to invest are given an incentive to invest in assets that produce capital gains andare, in effect, penalized for choosing assets that generate interest. This distorts the decision on which assets to buy, and it also distorts the decision by companies between retaining earnings and paying dividends. Realization also generates an advantage that increases the longer the taxpayer holds the asset. This generates alocked-in effect, discouraging taxpayers from selling assets, even when it makes sense otherwise to do so.4a) Your friend is clearly wrong, and does not understand the concept of a tax bracket. The higher marginal rate when you move into a higher tax bracket only applies to the extra dollars in that tax bracket, not to all earnings. In class, we described this as the “Scrooge McDuck Fallacy”, but you might want to remember that no one else I know calls it that!4b) In a strange way, your friend is right if he is only concerned with what he has when his paycheque arrives, and ignores the future tax refund that will arrive when he files his income tax. But if he is rational and takes into account his future tax refund, the $300 will be deductible from earnings in computing taxable income. Because taxable income will be lower by $300, federal taxes will be reduced by 15% of $300 (or $45) and provincial taxes will be reduced by 5.05% of $300 (or $15.15). So the true cost to your friend of the $300 in union dues is $300 − $45 − $15.15 = $239.85 (that is, about $240).2
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