Today I’ll give the solution to another of the problems from my honors exam:
Question 5. Rank these taxes in order of how much you’d dislike paying them:
- A tax on consumption
- A tax on wages
- A tax on income (including wages, interest and dividends)
Assume that the tax rates are adjusted so that your total tax bill is the same in each case.
First a clarification: As I noted in the original post, the questions posed here are translated from the original economese into English. This one lost a little in the translation. Instead of saying “Assume…your total tax bill is the same in each case”, I should have said “Assume…the present value of your tax bill is the same in each case.” This means, for example, that if the interest rate is 5%, then paying $1 today counts as the equivalent of paying $1.05 a year from today.
Next, an observation: Several readers thought that if two different tax policies lift the same number of dollars from your pocket, there’s no reason to prefer one over the other. The easiest way to see that that’s wrong is to consider an extreme example: Under policy A, you pay zero dollars per year. Under policy B, you pay $100,000 tax every time you wash your feet. Either way you’ll pay zero, because if the government enacts policy B, you’ll stop washing your feet. But even though both policies cost you the same zero dollars, you’ll still prefer A if you care about your hygiene.
As this extreme example shows, taxes hurt you in two ways: First, they take money from you, and second they discourage you from doing things you want to do. By assumption, the three taxes in the problem are all equally bad on the first count, so the question becomes: Which tax do you most dislike on the second count? In other words, what does each tax discourage and how much do you care?
Start with the first two taxes: A wage tax discourages work. A consumption tax discourages consumption. Which is worse? Answer: There is no difference, because discouraging work is the same thing as discouraging consumption. We work, after all, to consume. More work means more consumption; more consumption requires more work. You can’t discourage one without discouraging the other. So the wage tax and the consumption tax are equally bad.
In case you’re not convinced by that, here’s a link to a numerical illustration.
Next, although the question didn’t ask about this, let’s think about a tax on interest. Like the others, this tax discourages work—because one reason you work is to earn income that you can save at interest. And because the tax rates are all adjusted to take the same amount from you, this tax discourages work roughly as much as the others do. But after it’s done discouraging work, the interest tax hits you again by discouraging saving. That’s a double whammy, and it makes the interest tax more painful than either the wage or consumption tax.
Finally, what about an income tax? An income tax is halfway between a wage tax and an interest tax; it’s therefore worse than the wage tax and better than the interest tax.
Although these arguments are correct, you probably shouldn’t trust them, because it’s all too easy in economics to make specious verbal arguments that sound more convincing than they deserve to. That’s why we insist that our students learn the skill of translating these arguments into graphs or equations, where it’s easy to check their soundness (and easy to identify the hidden assumptions that have crept in).
So a full-credit answer to this question requires some of those graphs or equations. But even without the technicalities, if you saw your way through to the right conclusions for the right reasons, you’re a natural economist.
Hmmmm … it seems to me that since my only utility comes from consumption, the “washing my feet” argument doesn’t apply. I derive no benefit from “saving” per se, like I do from foot-washing … the only purpose of saving is to consume more later.
So since the income tax winds up taking the same (discounted) amount from me as the other taxes, and I lose no consumption (such as foot washing), it has to work out the same. Doesn’t it?
Mathematical example: I earn $10. After a 15.5 percent tax, I’m down to $8.45. I earn interest of 4.225. Now I have $12.675. But I pay a 15.5 percent tax on the $4.225 interest, which is about 67.5 cents (not exactly, but close enough). I’m still left with $12 worth of apples.
Total tax paid: $1.55 last year, and 67.5 cents this year (discounted to 45 cents last year). $2 tax after discounting, same as the wage tax or the consumption tax.
(Of course, under this assumption, if my preference changes to apples this year, I’m better off, because I have $8.45 worth of apples instead of $8. But by your assumption, if my time preference changes that drastically, the tax adjusts back to 20% so as to continue collecting the same amount.)
So I’m confused. What am I missing?
Please allow me 3 unrelated short comments in a single entry.
1. Phil has a point: if you say that my lifetime tax bill is constant, the literal interpretation is that I can do whatever I want and still pay the same amount. The literal interpretation must be wrong, unless it is meant as a trick question; but the question would be clearer if it specified that the **minimum** lifetime tax bill is constant.
2. Is there a diagram related to this question, like there was for the Yukon question, or do we have to rely on the numerical examples alone?
3. Does the equivalence of wage and consumption taxes also apply in the case of a heterogeneous population? (heterogeneous in terms of preferred time pattern of consumption.) If Tom prefers delayed gratification and Harry prefers instant gratification, then naively it seems possible that Tom is worse off with a wage tax and/or Harry is worse off with a consumption tax (since interest rates and/or tax rates adjust to take into account both of their consumption patterns).
It certainly is useful to compare different kinds of taxes and the incentives they provide to people. I’ve long thought we should eliminate or drastically reduce all dividend taxes and drastically raise taxes on capital gains.
We currently tax capital gains and dividends at the same rates. Isn’t this ludicrous? What if we raised tax on capital gains significantly, and lowered the tax on dividends. Wouldn’t this have the remarkable effect of encouraging people to hold onto their investments and encourage stockholders to get CEO’s who were actually interested in making their companies profitable (so they could pay a dividend), rather than currently where we get CEO’s who can spin a good story to drive up the stock price so the stockholder can sell (and therefore has no long term interest in the company). I bet companies would be more socially responsible as well, since stockholders would by necessity be taking the long term view.
As to the argument that low capital gains encourages capital investment, there has to be a better way to do it. Most of the money that changes hands in the stock market is doing just that, changing hands not being invested in new ventures. Why do we encourage that?
Any other thoughts on why this would (or wouldn’t be a good idea)?
Phil: In your example, you do all your consumption in the future. In that extreme case (and in the other extreme case where you do all your consumption in the present) the income tax can be equivalent to the wage tax. But in the usual case where you split your consumption between the two periods, the shift from one tax to the other will cause a shift in the division of your consumption that leaves you worse off in the case of the income tax. I’ll try to post a diagram later today to make this clearer.
Howard: A tax on capital gains *is* a tax on (expected future) dividends, because capital gains are caused by changes in the stream of (expected future) dividends. So to a first approximation, it really doesn’t matter whether you tax the dividends or the capital gains. (It’s not quite that simple because capital gains reflect only *unexpected* changes in the dividend stream.)
PS—I’d have to think about this more, but my early-morning thought is that the capital gains tax is worse because it has all the negative effects of taxing dividends while also discouraging the transfer of assets (which I know you were listing among the advantages, but I’m not sure why asset transfers are undesirable).
Snorri:
1) The question would be incorrectly stated if it specified that the *minimum* lifetime tax bill is constant. The tax bills we are equating are the tax bills you actually pay after you optimize your consumption stream, subject to the tax policy.
2) I’ll try to post a diagram later today.
3) The equivalence is independent of any other taxpayers. If the rates are adjusted so that your tax bill (in present value) is equal in all three cases, then the result applies. Of course, it is probably impossible to adjust the rates so that the equality condition applies for both Tom and Harry.
Snorri and Phil:
With some trepidation, I’ve posted a diagram at http://www.thebigquestions.com/tc.gif .
This diagram is incomplete because it only shows the effects of various taxes on savings choices, not on labor choices. But it’s the differing effects on savings that really differentiate these taxes.
My trepidation follows from the fact that this diagram is unavoidably pretty technical. If you’ve recently sat through a microeconomics class, it should all look familiar. But if not, I’m afraid it might confuse more than it enlightens. Use it if it helps.
OK, I think I’ve got it. The interest tax increases the “price” of tomorrow’s consumption relative to today’s. That makes me “buy” less of it.
By stipulation, my taxes are the same, but I lose additional utility because the only way to keep my total tax bill from rising (as stipulated) is to shift some of my consumption to the present. That obviously makes me worse off, or I would do it even without the tax.
Phil: You’ve got it.
Phil -very close. It is not that you will shift your consumption to the present in order to keep your tax bill constant. While the equilibrium will almost surely be more current consumption, the government is setting the tax rate to equalize your taxes paid (say to generate $100, so that it can balance its $100 spending budget). In this equilibrium, you would prefer to shift some extra consumption into the future if it could be done in a tax-neutral shift, but you don’t prefer to do it with the tax in place. However, with the consumption or wage tax, you are content with your mix of present and future consumption. Since the total tax bill is the same, by construction, you are less happy with the income tax because it gives you less freedom to optimally allocate your consumption.
Different Phil: I absolutely agree with your explanation, but I think the first Phil’s post can be read as saying essentially the same thing. Govt revenue is fixed all along Phil’s “wage tax” budget line. Therefore tax rates are always adjusted to keep him on this line. When he’s offered the entire line (via a wage tax) he chooses his favorite point P. When he’s subject to an interest tax, the rate is set so he’ll choose another point QQ on that wage tax line, with more present and less future consumption. (“The only way to keep my total tax bill from rising…is to shift some of my consumption to the present”.) He must be worse off at Q than at P because P was optimal. (“That obviously makes me worse off, or I would do it even without the tax.”)
I think thedifferentphil is assuming that I am *deliberately* trying to keep my taxes the same. That wasn’t what I meant.
Either it’s a coincidence that my taxes wind up the same, or the government has analyzed my indifference curve and deliberately chose the rate that would keep the total tax paid the same.
Phil: I repeat; you’ve got it.
Steve: thank you for the answers. Let me say that it is a privilege to be able to get explanations from someone whose writings I have been reading with great interest for over 10 years (irregularly, I admit).
WRT my 1st question: looking at the diagram (thanks for that, as well), I see that there is indeed a difference between the minimum tax bill and the tax bill paid after optimizing my temporal pattern of consumption.
WRT to my 3rd question: I was just trying to persuade myself that I am not irrational in preferring a consumption tax over a wage tax. From what you say, maybe I am not irrational after all.
Steve, I think that the specification for a constant tax bill makes this problem less clear than the standard economics case. There is an asymmetry. Consider the interest tax from your diagrams, with income of 10 units in period 1 and a 50% interest rate.
1. Start with the interest tax where a present value of 2 units is paid in taxes. Then switch this over to a wage tax of 20% that collects the same money. Your diagram shows that utility will rise with this 20% tax, relative to the original equilibrium with the interest only tax. As a person changes between present and future consumption, this wage tax will not have to be adjusted to maintain the 2 units of PV tax revenue.
2. Start with a wage tax of 20% that collects 2 units of tax revenue off of the 10 units of income. Suppose that the person chooses to consume 2 units now and 9 in the future (the tangency of the indifference curve). Now, switch to an interest tax that collects 2 units of income. Suppose that this involves a 75% tax on interest. At a present consumption of 2 units, 8 units can be invested, earning 4 units of interest. The person pays 3 units in tax, which has a PV of 2) and can consume 9 in the future. This is the same consumption mix as with the wage tax. If the person considers switching to 0 consumption in the present, the tax rate will have to be 60% and if he switches to 4 units in the present, the interest tax rate will have to be 100%. Both of those options leave him with the same present-future consumption mix as the 20% wage tax. Thus, the budget line for a tax revenue constant interest tax must be the same as the wage tax. This means that the person has the same trade off options with such an interest tax as with a wage tax, and that means that he is not disadvantaged with the interest tax, relative to the wage tax.
So, for the argument to be symmetric in its treatment, their needs to be the threat of higher total PV taxes paid with increases in savings or an income tax will also break down into being equivalent to a wage tax too.
Re capital gains and dividends…
I know that in theory, the value of a stock is supposed to be approximately the present value of the stream of future income it generates, but in reality most companies don’t pay out dividends anymore and most investment is not done with the thought of ever receiving such a payment…didn’t many of the ills of our current setup arise in parallel with this shift over the last 40 years (not arguing causation but worth thinking about?)
So I don’t quite understand. In the extreme, if we taxed capital gains at 100% and dividends at 0% would not that change behavior. Wouldn’t investors be pressing companies to change their businesses to actually earn a profit and pay it out? Wouldn’t we be less inclined to hire flim-flam sweet talking CEO’s whose value is talking up the stock price and more likely to hire CEO’s who actually can run a business (to produce high dividends in the here and now rather than high stock prices based on speculation on the future, which never seems to happen anyway)? Would not people hold onto their investments for the long term and encourage companies to be good citizens, rather than sell at the first sign of trouble like they do now?
Steve, thanks for your patience…read your book 2x already and have given away 2 copies so far as gifts…
> Answer: There is no difference, because discouraging work is the same thing as discouraging consumption
Hold on: How about the time value of money & the ingenuity of man!
Picture this: I would prefer to make a bundle and save the better part of it. Next thing onj the family agenda: move out to a low-consumption-tax country for a cool beer during sunset.
How about that?
;-)
I don’t think the numerical example given is necessarily correct. It implicitly assumes that the entire cost of the consumption tax is born by the consumer, which is not always true.
It is not necessarily the case that a wage tax and a consumption tax are equivalent. If I care about leaving a bequest, then discouraging consumption is not the same as discouraging work.
Without making assumptions about the elasticities of labor and consumption, I think the only claim you could make is that an income tax is worse than a consumption tax.
I take back my previous post – my points do not hold because we assume that the present-value tax burden is the same under all three tax plans.
Here I strongly disagree with you. Even if the effect is the same, the actual impact on how I *feel* about them (which is what you asked) is very different if a tax is hitting me at the point of sale. What I dislike about a consumption tax is knowing, at the moment I choose to consume, that that will be taxed. I’d much rather have an income or wage tax even if its effect on my consumption amounted to the same thing.
Similarly, I prefer paying a flat monthly rate for all of my telecommunications services rather than, say, a per-call rate, EVEN IF I KNOW that the per-call rate would actually have cost me LESS every single month of the past N years. The feeling of being able to make a call whenever I want without considering its direct impact in how much I’m paying, is a real benefit, and is worth money to me.
Transaction costs? Collecting a consumption tax at the register is easier for me than having to hire an accountant at the end of the year to figure out my income tax.
Obviously the structure of these taxes could minimize the transaction costs, but I think that tax efficiency is overlooked far too often.
The wage tax and consumption tax are equivalent only under the condition that the total discounted taking is guaranteed to be the same.
Unfortunately in the real world this is never the case and in the real world I think I would prefer the wage tax because it is taken as a portion of my productivity. When I am forced to no longer be productive (injury, retirement, etc) I can consume from my savings without fear of escalating tax rates.
Howard Messing,
That’s a point that I’ve thought a lot about. I’ve suspected that moving away from valuing stocks by the “present value of the future revenue stream” has been a problem and that tax rules (capital gains taxes decrease the longer a stock is held?) would help.
However, I’m not an economist and, having come up with this independently on my own, I suspect that it can’t be that simple. Anyone care to point out how I might have it all wrong?
I took a different and apparently wrong approach.
What would I have to give up in each case to pay $0.00 in tax?
A tax on wages means I would have to give up work. That’s fine, I have a large portfolio.
A tax on all income means I would have to stop working AND stop earning interest on my portfolio (I suppose by donating my dividends and gains to charity). That’s fine, I have a large enough port folio to live comfortably off of until I die.
A tax on consumption means I have to stop spending. Worst possible scenario. Hands down. No comparison.
Triumphantly,
Benky
I’m still stuck on the original example.
“Under policy A, you pay zero dollars per year. Under policy B, you pay $100,000 tax every time you wash your feet. Either way you’ll pay zero, because if the government enacts policy B, you’ll stop washing your feet. But even though both policies cost you the same zero dollars, you’ll still prefer A if you care about your hygiene.”
The example seems to be in conflict with the specification: “Assume that the tax rates are adjusted so that your total tax bill is the same in each case.”
Let’s assume I wash my feet every day. Then since the tax rates are adjusted so that my total tax bill is the same, the tax rate for foot washing has to be adjusted to 0.
On the other hand, if the tax rates are set based on current practice and not adjusted as I adjust my activities (as in the example) then I prefer the tax consumption. I can reduce my consumption and increase my income (thereby accumulating more money) without paying more tax. If I eventually chose to spend the accumulated money, I then pay tax, but to a great extent one can enjoy having money (because it generates power) without actually spending it. One could, for example, buy and run a business that affects the country. That’s not consumption. One could also spend one’s money running for public office. A lot of that is not consumption. Or one could contribute to a non-profit organization. That’s not consumption.
I’m sorry for coming late and I hope you’re still responding to comments – I’m having trouble seeing how there’s not an excluded middle falacy in your explanation equating work and consumption that changes the answer.
As you identify in your next paragraph, we don’t work only to consume – there’s investment. It’s a relationship between three things, not two. You can trade your effort for money (wage), spend your money on goods and services (consume), or lend your money in hope of a larger return (invest). Discouraging consumption doesn’t discourage work, since work is still useful for investment, which creates additional income without more work, which mitigates the additional cost on consumption caused by the tax – so discouraging consumption encourages investment, and wouldn’t discourage wage earning.
It seems the last choice would still be the least preferable, because like you say income tax discourages both investment and work. The wage tax alone would be preferable to that, since you’re still free to shunt consumption into investment to build a stockpile of wealth that can become a source of income that eludes the tax. This makes the wage tax the most personally preferable, even, because it’s the only one you can ultimatly avoid entirely, by increasing your investment return to the point you can consume what your desire without having to earn a wage at all to do it.
SL: Suppose your investments return a rate of 50% a year (just for illustration).
Then every dollar you spend today is $1.50 less you can spend next year.
With a wage tax, that fundamental tradeoff remains. You have fewer dollars to spend, but you’re still trading off a dollar of consumption today versus $1.50 of consumption in the future.
Likewise with a (permanent) consumption tax. The consumption tax raises all post-tax prices by the same percentage, so it remains the case that a dollar spent today is $1.50 not spent tomorrow.
That’s why the wage and consumption tax are equivalent. They leave the basic tradeoff untouched.
The income tax, by contrast, changes the rate at which consumption today can be converted to consumption tomorrow (by taxing the return on your investments).
For example, if the tax reduces the after-tax interest rate to 25%, then a dollar spent today means forgoing $1.25 spent tomorrow, instead of $1.50. The income tax *does* change the basic tradeoff. That’s why it’s not equivalent to the other two.
The only way to be sure this is all correct is to translate it into graphs and equations. That’s a standard textbook exercise but probably a little more technical than most blog readers want to see.
Much of the confusion here is the specification for how the tax will be adjusted. The standard textbook case looks at differing tax instruments that generate the same tax revenue. Consumers are assumed to make choices on investments and the timing of their consumption based on the fact that they face a tax on either wages or consumption or income, but they are not told that their tax rates will be reduced as they do more of the taxed activity to guarantee identical tax bills -that is different. Take away that guarantee and just compare different tax regimes that collect the same revenue and we are back at the textbook.
This was a good (and straightforward) question from a micro perspective. I was wondering if there are any good reads that you know of from a macro perspective of the tradeoffs between wage and consumption taxes.
I think I remember that Huckabee was advocating replacing the income tax with a federal sales tax. What are some of the pros and cons of this from a policy perspective?
I think there are sound policy reasons to disagree with the pure incentive style argument. The poor generally take all of their income from wages, but the rich have more investments. It is extremely regressive to tax wages directly.
From your argument –
Consumption must be optional, or else it would not be possible to forgo spending the $1 today on consumption to gain the benefit of $1.50 tomorrow
Greater capacity for consumption in the future must also be a goal, or else there would be no incentive to not spend $1 today in order to be able to spend $1.50 tomorrow.
Wages are not necessary to gain $$ for consumption, since $1 invested can created an income of $0.50, or $100 get you $50, etc. even if your wages are $0.
The tax on $0 is $0. This is not equivelent to a tax on consumtion, where the tax will always be a positive number fraction of the value consumed.
Given all these premises, the goal to maximise future consumption is best satified where there is an option to minimise $$ lost to taxation. Ideally, to eliminate it entirely
The wage tax is the only option that offers that possiblity.
To graph it, I think you’d need an assumed minimum level of consumption, wage, investment rate of return, and tax rate, to plot out the optimum starting wage you’d have to work to be able to reduce wages to zero in the minumum mount of time while maximising consumption across time.
I read the answers, and can’t pretend to have fully understood them. Put me down in the “not a natural economist” column. I was interested to see Cos say that he prefers an income tax because he does not want his choice to consume taxed at the point of consumption – just like he pays a flat fee for his phone bill each month.
I also pay a flat fee for my phone bill because I don’t like having to decide to spend money at each instance of using those services. But I *feel* like I’d rather have heavier consumption taxes and lower income taxes, because then I would have more control over when and how I was taxed (for instance, paying a higher tax rate for luxury goods and vices). In my head, that would encourage me to save more, which would be good for me but probably not for the economy.
Sierra:
I have no idea what “good for the economy” means, but if it means “good for your neighbors”, then for God’s sake, save more. The more you save, the less you consume, and the less you consume, the more goods are available for your neighbors. I’ll be blogging about this in a special Christmas post sometime in the next week.