The Least Painful Tax

advilSome taxes are more painful than others. It’s not as simple as “the more you pay, the more it hurts”. Consider these two taxes, for example:

  • Tax A: Shoes are taxed at $0 per pair.
  • Tax B: Shoes are taxed at $100,000 per pair.

Under Tax A, everybody pays zero. Under Tax B, nobody buys shoes and everybody still pays zero. But Tax B is more painful, because it leaves us barefoot.

That’s of course an exceptionally simple example, but the same point arises in much subtler contexts. The pain caused by a tax is measured not just by what you pay, but also by what you do to avoid paying more.

So let’s try something more interesting:

  • Tax A: A tax of 50% on all wages.
  • Tax B: A tax of 40% on all wages and interest

To make the comparison fair, suppose your total tax bill happens to be the same under either policy.

In class today, I proved to my students that under that assumption, you’ll always prefer Tax A. (Of course someone else with different tax bills might disagree). I fear, however, that I was not my usual crystal clear self. So partly for the benefit of the students and partly for the benefit of anyone following along at home, I’ll reproduce the key diagram here.

Before I show you the diagram, I’ll note that the result follows from the joint application of two principles:

Principle I says you should never double tax anything, and Principle II says that to avoid double taxes you must avoid interest taxes. This argument, of course, proves nothing, because stating a principle doesn’t make it true. The diagram below, however, proves all. This is an indifference curve diagram of the sort that is standard fare in intermediate-level economics courses. If you’ve never taken such a course, this might not be the diagram for you.

Share/Save

40 Responses to “The Least Painful Tax”


  1. 1 1 Bennett Haselton

    Steve,

    I’ve thought about it but there seems to be a logical error in the way the graph is used to argue that a wage tax is better.

    Here’s the problem: If you have tax A and tax B (and their “menu of options” lines have different gradients, as above), and your current behavior is already optimal under tax A, and the government proposes to switch to tax B at a rate such that under your CURRENT behavior your tax bill will be the same, then you will always favor switching to tax B. This is because after the government switches to tax B, your tax bill will initially be the same, but your current behavior will no longer be optimal under tax B (because the gradient of the “menu of options” has changed, so it’s no longer tangent to the indifference curve at your current point). That means you’ll always be able to move somewhere else on the menu of options, and always make yourself better off.

    But, if the government had started with tax B, and was proposing to switch to tax A at a rate such that your tax bill would initially be the same, you’d favor *that* switch, too, by the same reasoning.

    Note that there is no paradox here like “But then you get stuck an infinite loop of always preferring A to B and B to A!” First you’re optimal under tax A, and the government switches to tax B at a rate so that your tax bill is the same. Then you make yourself better off by making yourself optimal under tax B, and you have a *new* tax bill. Then the government offers to switch back to tax A at a rate such that your *new* tax bill remains the same — but that’s a different rate than the tax A that you started with.

    In other words, you could use your graph above to show that if you *started* with a wage tax, and your behavior was already optimal under the wage tax, and the government proposed to switch to an income tax such that your current tax bill would be the same, then you would favor that switch from a wage tax to an income tax.

    Am I missing something?

  2. 2 2 Steve Landsburg

    Bennett:

    This part is right:

    If you have tax A and tax B (and their “menu of options” lines have different gradients, as above), and your current behavior is already optimal under tax A, and the government proposes to switch to tax B at a rate such that under your CURRENT behavior your tax bill will be the same, then you will always favor switching to tax B.

    But that’s not the experiment we’re considering. The experiment we’re considering is a switch to tax B at a rate such that *government revenue is unchanged* (in present value). This requires the rates to always be adjusted to keep you on the same “isorevenue line”, where the isorevenue lines are all parallel to the initial budget line.

    That, I think, is what you’re missing.

  3. 3 3 Harold

    This is interesting, as I would probably have assumed that if you pay the same under both tax systems you would be indifferent to which one was used. Just to work it out in my mind. The “future” axis is the point where your investment has doubled. In the 40% tax regime, you have been left with 60, so in the future you have made 60, taxed at 40% = 24, so total = 120-24=96.
    So *if you pay the same tax under both regimes*, the 50% wage tax allows you to balance your consumption between future and present in a way you prefer to the 40% income tax.
    Could you explain how to decide the position of the green dot? I think the red dot is fixed because we you have defined the graph as applying to the individual who pays the same under both regimes, thus the indifference curve must pass through both points. I think this is similar to Bennet Hassletons point: this graph applies only to the individual who’s preference for future and current consumption is such that they choose to consume at such a level that they are taxed equally under both regimes. Can we say if this has any applicability for the rest of us?

    The diagram is not to scale, so the difference between the two indiference curves is smaller than it appears. Therefore it might take only a small interfering factor to remove the preference. This could be the difficulty of separating wages from capital income as discussed previously. This would push the tax rate up a bit for wage tax compared to income tax.

    The menu of options assume an ability to choose between 100% consumption today and 100% consumption tomorrow. This does not seem realistic.

  4. 4 4 Steve Landsburg

    Harold:

    this graph applies only to the individual who’s preference for future and current consumption is such that they choose to consume at such a level that they are taxed equally under both regimes. Can we say if this has any applicability for the rest of us?

    To a certain extent, yes. Here’s why: The natural question is—what is the least painful way to raise a given amount of govt revenue? Therefore it is natural to hold govt revenue fixed throughout the problem. Fixing total revenue means fixing the tax bill of the average taxpayer. So this graph will not apply to all taxpayers, but it will apply to Mr. (or Ms.) Average.

  5. 5 5 Steve Landsburg

    Harold:

    Could you explain how to decide the position of the green dot?

    Start with the wage-and-interest tax, represented by the red line. You choose the red dot. The govt then switches to a wage-only tax, represented by the green line. To raise the
    same amount of revenue, they set the tax rate so the green line goes through the red dot. There is then a unique indifference curve tangent to the green line; this determines the location of the green dot.

  6. 6 6 Bryan

    I would like to make sure I’m getting all of your discussion here.

    Suppose there is a person who gets no utility from future apples. That person would be better off with the 40% income tax, correct?

    But if a person gets no utility from future apples, the wage tax and the income tax could not differ in percentage terms since you also require the different tax schemes to have the same revenue.

    This is why it is true that even people who have high discount rates would still prefer a wage tax.

    Also, I found this article in support of a “Tax Rate Lottery” where the very rich get their tax rate determined randomly. The author claims that this would encourage the rich to work more since they don’t know what their tax rate would be.

    I’m positive that he is wrong, but I figured you would be able to prove it more rigorously that I did.

    http://curiouscapitalist.blogs.time.com/2010/08/30/what-if-tax-rates-where-set-by-lottery/?xid=rss-topstories&utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+time%2Ftopstories+%28TIME%3A+Top+Stories%29

    http://huntitwithforksandhope.blogspot.com/2010/08/tax-rate-lottery.html

  7. 7 7 thedifferentphil

    The confusion here is that the green wage tax budget line is everywhere isotaxrevenue of 50 period 1 apples, while the red income tax budget line has a different tax revenue at every point, with 50 apples only at its intersect with the green line. Thus, the framework only works to clearly show the preference of an isotaxrevenue wage tax to one possible way to raise 50 apples of tax revenue from an income tax. One way to go the opposite direction would be to compute all possible income tax rates that could generate 50 present value apples in tax and then plot out all of the points of 50 present value apple tax revenue based on these tax rates. If they lie below and to the left of the green indifference curve, then the reverse thought experiment of not preferring a switch from wage only to income tax would be proved.

    The problem ultimately is one of a Robinson Crusoe type person is on an island. He has 50 small chickens that he can eat now, or allow each chicken not eaten in period 1 to grow to a larger double-sized chicken in period 2. He needs to acquire a critical medicine from a ship that will come to the island, and the ship’s captain says that the medicine will cost him either (1) 50 small chickens in period 1 (wage tax), or (2) x% of small chickens in period 1 and x% of the extra meat that he gets from allowing the remaining (1-x%) of chickens fatten up into period 2. The present value of a period 2 large chicken is one period 1 small chicken. So, the x will be chosen so that he the ships captain will get 50 chickens, some small in period 1 and some large in period 2. Does Robinson prefer (1) or (2)? Is that a fair restatement of the problem?

  8. 8 8 Steve Landsburg

    Bryan: Yes, if in this scenario you were a person who never ate future apples, then the two tax rates would have to be the same in order to keep govt revenue equal across the two policies.

    I’ll try to find time to look at the links you included. I have a busy few days coming up.

  9. 9 9 Steve Landsburg

    Bryan: Okay, I *did* find time to follow your links. Your blog post at http://huntitwithforksandhope.blogspot.com/2010/08/tax-rate-lottery.html is excellent. I haven’t double checked every detail of your argument (though it all looks plausible) but I think you’ve got all the main points exactly right.

  10. 10 10 Harold

    Mr (or Ms) average can mean lots of different things. Here we are keeping total revenue the same. So I presume this is the person for whom total earnings by those who earn more than him = total earnings by those who earn less than him. (This is distinct from the person who earns the median wage, where total number of higher earners = total number of lower earners). This is likely to be a few rich people and lots and lots of poor people.

  11. 11 11 Michael

    On Principle II (Any tax on interest is a double tax) — if wages were not taxed at all, would a tax on interest still be double taxation?

    Second, is it double taxation if you tax wages and rent, or interest and rent?

    (I have to apologize, since I’m under the influence of antihistamines this morning, and my thinking is a bit fuzzy. :) )

  12. 12 12 Steve Landsburg

    Harold:

    So I presume this is the person for whom total earnings by those who earn more than him = total earnings by those who earn less than him

    Correct.

  13. 13 13 Bennett Haselton

    To clarify, when you say:

    “The experiment we’re considering is a switch to tax B at a rate such that *government revenue is unchanged* (in present value).”

    Does that mean:

    (a) that government revenue will be unchanged if you leave your behavior exactly as it was before the tax plan switch (which, of course, means that government revenue will change after you re-optimize under the new plan),

    or

    (b) that *after* you re-optimize your behavior under the new plan, government revenue will be the same as it was before the tax switch, when you were optimized under the old plan?

    It sounds like I thought you meant (a) but you actually meant (b).

  14. 14 14 Steve Landsburg

    Bennett: I definitely meant (b), and I agree that it appears that you thought I meant (a).

    Let me add that it’s hard to see any circumstance in whch (a) would be an interesting scenario to contemplate.

  15. 15 15 Bennett Haselton

    Ah OK. I think I just didn’t think carefully about the line: “We assume both taxes raise equal revenue for the government. This means the red tangency sits on the green line.”

    I assumed that meant that the green line was chosen such that the tax bill would be the same under your current behavior. Of course that’s true, but I failed to see that it’s a special property of the wage tax that your tax bill is the same even after you *change* your behavior!

    So would it be more intuitive to emphasize it not as “a tax where everything is taxed at the same rate”, but rather “a tax where you pay the same tax bill everywhere on your frontier of possibility”?

    Then you can prove your original claim without graphs: Suppose your behavior is optimized for the income tax, and the government switches to a wage tax such that your bill is the same under your current behavior. By the special property of the wage tax, your tax bill will also be the same after you change your behavior, and your current behavior is (probably) no longer optimal under the wage tax, so you can change behavior and make yourself better off.

  16. 16 16 Bennett Haselton

    p.s. could you make the same argument in favor of replacing a wage tax with a lump sum tax (which may vary per person), as you did in “Fair Play”?

    You’ve already optimized your behavior under the wage tax. So the government imposes a lump sum tax of the same amount. They get the same revenue, but now your behavior is no longer necessarily optimal under the lump sum tax, so you change your behavior and make yourself better off.

    (Basically the same as your example here, except that instead of keeping income fixed and choosing between present and future consumption, you’re choosing between present income and present leisure.)

  17. 17 17 Paul

    I don’t see why the red tangency should lie where the red and green lines cross. These lines cross do not cross at the point in which revenue from the taxes are equal. They cross at the point in which a hypothetical taxpayer’s present and future consumption is equal under both tax regimes. At a 40% income tax rate the governmental revenues would be equal to a 50% wage tax when the taxpayer has $35 dollars of present consumption and $40 of future consumption and this point is not on the green line.

    I drew a chart to scale in Excel which you can view here: http://flic.kr/p/8DvnMQ and it is not as obvious in this chart which tax leads to a higher indifference curve. I also drew on the chart a line which represents the various possible income tax rates that would generate equal revenue to a 50% wage tax. It extends from the lowest rate of 29% in which present consumption is zero and future consumption is $120 to the highest tax of 50% in which present consumption is $50 and future consumption is zero. (Note: I drew it as a straight line, but technically I think it should be a curve, albeit a very flat one.) It is not obvious to me that the points along this line do not lie on higher indifference curves, although it is beyond my competence to actually draw those curves.

  18. 18 18 Cornelius McFudgemuffin

    What is cap gains tax? you could buy an option at for half an apple with the right to buy an apple at zero.

    What about this model:

    There was a vairance in the income distrubtuion and people with earnings below a! (in my discrete example it could be 26) do not have acces to capital markets and thus can not shift their income between time periods.

    Ex.
    There are two types of people: one with 25 apples every period and one with 75 apples a period. It is an economy where the rich can invest some apples to get interest next period but the poor can not. This transfers the tax burden from the poor to the rich. Allowing the poor a better standard or life. No?

    PS i understand you had a one period model here, I am not sure if my multi period mode makes a difference.

    I have not worked in out with maths and paper yet…

  19. 19 19 Soomin Lee

    I have a question about the graph.
    Between the x value of orange dot and 60, the orange line is always
    placed above green line. If indifference curves are drawn on the both lines, wouldn’t the indifference curve that is tangent to the orange line above the indifference curve that is tangent to the green line? Therefore, the orange line is happier between the orange dot and 60 on the x value?

  20. 20 20 blink

    I am a little confused by the assumption that “both taxes raise equal revenue for the government.” Does this mean present value of the taxes or simply the sum of the amount collected? While I think you intend present value, I do not see anywhere that states this.

  21. 21 21 Bennett Haselton

    Paul: It took me a while to see this, but actually, where the lines do cross, I think the revenues from the two tax plans should be equal. Here’s why: where the lines cross, under both plans, you’ve spent all of your money (since in either case you’re on the possibility frontier). And in both cases, you’ve purchased the same number of each good, and by assumption, the prices of each good are the same under either tax plan. Therefore you spent the same amount of money on pre-tax sales in either case. The rest is all tax revenue, so that must be the same in both cases as well.

  22. 22 22 Steve Landsburg

    blink: yes, i mean present value

  23. 23 23 Jonathan Campbell

    Soomin: Yes, in the range you mention, the orange line is happier than the green line. However, the government’s tax revenue is lower, so it is not a fair comparison. In order to make it an apples-to-oranges comparison, you must compare situations along isorevenue lines, which are parallel to to current consumption line.

    It turns out that wage tax lines are parallel to the current consumption line (since both present and future consumption levels are just scaled down by the amount of the tax). Thus, comparisons can only meaningfully be made along wage tax lines, and so, for any non-wage tax line, you can always simply draw a wage tax line that crosses it (at the non-wage tax regime point of max utility, i.e. the orange point), and then move along that line to a new point where utility is higher.

    At least that is how I understand it.

  24. 24 24 Harold

    Quick follow up to the “average” point. The above graph applies to the mean income. Most income statistics are expressed as median income. In the USA the median houshold income is about $45,000. The mean is about $65,000. Approximately 2/3 of households earn less than the mean.

  25. 25 25 vivek

    There is a problem here. The budget lines will only look like that if the Govt is using the tax revenue to pay off reparations or foreign creditors. If the Govt. is using revenue for
    1) transfers- in which case lower savings may be compensated by, for example, Social Security pensions and other benefits such that the inter-temporal budget line develops kinks. Indeed, strategic dis-saving by people approaching retirement to qualify for means-tested benefits could pose a problem for U.K fiscal policy.
    2) Public, merit and other positive externality goods then the rate of return of savings might increase. Obviously the reverse may also be the case- if Govt. spending is wasteful and has a crowding out effect.

  26. 26 26 Steve Landsburg

    Vivek: Assuming the funds are used the same way under either tax (which certainly seems to be the right assumption for this exercise), then both budget lines are affected in the same way, i.e. both shifted up or down by the same amount, so the same analysis should apply.

  27. 27 27 Steve Landsburg

    Jonathan Campbell: This is exactly correct.

  28. 28 28 vivek

    So, if this is a 2 time period economy, such that I retire next year, I earn 100, assuming the interest rate is 100% I have savings of 25 yielding interest income of 25 which taxed at 40% yields 10 which together with my tax on earned income of 40 yields the Govt 50.
    However, for some reason (as per the diagram showing my upper consumption bound on the y axis) in the second period my presumably interest only income of 100 plus savings of 100 (actually 125) is nevertheless being taxed at 50% (why?)
    For the moment, let us suppose it is a lump-sum poll tax demand from a Benthamite omniscient tax man, equal to 100.
    If the Govt. is taxing for transfers to pensioners via means tested social security payments such that those with savings over x get nothing and those with less than x get a transfer of y then the budget lines have to be changed to show this.
    My income plus savings i.e. 50 plus 25 is my upperbound on present counumption which is 75. Assume that the social security transfer is 100 with a means-test of 10 in savings then my upperbound for future consumption is my current income of 100 plus savings of 25 less dis-saving of 15 (so as to qualify for means tested benefit) which doubles because the interest rate is 100% yielding 230. Add 100 as the mandated transfer and you have 330. 100 is taken away by the lump-sum tax. This gives an upperbound of 230. Now this sort of change in gradient in favor of future consumption normally leads to greater saving whereas, here, it depends on dis-saving.
    The 40% tax makes greater sense as it is levied on both earned and undearned income and like any marginal tax has greater allocative inefficiency than a lump-sum tax.
    But that’s hardly news.
    No doubt there’s something I’m not getting.

  29. 29 29 Harold

    I may be stretching the model too far here, but does it make any sense if you cannot choose the full range of options? (100 current or 200 future or anything inbetween?) I am thinking that you need to spend some (say 20) of your 100 apples today. So with no tax you perhaps have an option of 100 current apples, or 20 current apples and 160 future apples or anything inbetween. With 50% wage tax, you can have 50 current or 20 current a plus 60 future apples. With 40% income tax you can have 60 current or 20 current plus 64 future apples.
    This is just cutting off the lines, (you can see more cleasrly on Paul’s diagram) and in this example they do not meet, so it is not possible to optain the same tax income.

    However, if you must spend 10 apples today, this correponds to the point where the lines cross. The revenue can therefore be the same, but there is no line for the tangent to meet

    I conclude that it makes no sense to restrict the diagram in this way, but I am not quite sure why.

  30. 30 30 Steve Landsburg

    Vivek:

    So, if this is a 2 time period economy, such that I retire next year, I earn 100, assuming the interest rate is 100% I have savings of 25 yielding interest income of 25 which taxed at 40% yields 10 which together with my tax on earned income of 40 yields the Govt 50.

    I don’t understand this. With the 40% tax rate, if you earn a 100, you pay $40 tax. That leaves $60. You assume that you save $25,
    which means that you spend $35 in the present. You earn $25 interest, paying $10 to the government. So the government receives
    $40 in the present and $10 in the future, which has a present value of $45, not $50.

  31. 31 31 vivek

    My bad.
    I didn’t read the conditions properly. I thought the tax receipt to the Govt from you remained the same, of course it can do by adjusting the tax rate. (However, if one can do that then why not just have a lump sum tax which has no excess burden?) Also dis-saving does not arise as this is a 2 period economy, so your 100 is your whole endowment.
    Sorry!
    Still, if the interest rate was very low and the only goods were tinned products, you’d be better off with the 40% tax which yields 6o tins as the best outcome.
    This is an interesting case and would really focus the student’s mind. I guess, I find it counter-intuitive because I imagine that savings are mainly precautionary and so I imagine the excess burden of a tax, even a double-tax, on saving would be lower than one on income.

    It may be that if transfers are means tested for savings, debt is non-recourse and so on then,a double tax on savings would be a case of the Govt. steering you to do the rational thing and make hay while the sun shines.

  32. 32 32 vivek

    Sorry! In a tinned food economy you can always escape a tax on savings so, for equal revenue to the Govt., the tax rate in B would be the same as A. Since only B taxes interest, A would always be preferred. The crucial point is that tax rates can be changed to yield equal revenue. It’s a zero sum game if interest rate is zero. For positive interest rates A is always better because it permits an economic activity at the margin which would not otherwise have taken place.
    Very interesting gedanken. I can’t understand why I took so long to get it.

  33. 33 33 Paul

    I think I see now what my mistake was. I need to reduce the amount the government receives from taxing interest by half to adjust for it’s present value. If you do that then the red dot does lie on the green line. If you do this you will also notice that the line which shows all the various income tax possibilities that result in a present value of $50 of revenue to the government is identical to line showing all the possible combinations under a 50% wage tax. However, I’m still not sure how that leads to the conclusion that the wage tax will necessarily lie on a higher incidence. For every point along the wage tax line there is a possible income tax line that crosses at that point given a the right income tax rate. If the argument is then that no matter where the income tax line crosses there is a point farther up on the wage tax line that would be of higher preference value, I don’t see how this proves anything as there is another possible income tax that goes through that point as well. Further, there is the point where both lines cross the Y axis (roughly 38% income tax) where there is no possible combination of present/future consumption that leads to a higher preference. Surely at that point there is no preference one way or the other.

  34. 34 34 Steve Landsburg

    Paul:

    If the argument is then that no matter where the income tax line crosses there is a point farther up on the wage tax line that would be of higher preference value, I don’t see how this proves anything as there is another possible income tax that goes through that point as wellIf the argument is then that no matter where the income tax line crosses there is a point farther up on the wage tax line that would be of higher preference value, I don’t see how this proves anything as there is another possible income tax that goes through that point as well

    But (unless you’re pushed all the way to an axis) the configuration must look as in the diagram I posted. If you first find the red tangency and then draw a green wage tax line through that tangency, you are not holding govt revenue fixed (in present value). In order to hold govt revenue fixed, the green and red dots must both lie on the green line. That nails down everything else about how the picture must look.

    You’re right that you could draw a different red income tax line through that green point. But if you did that, the taxpayer would choose a different point on that line (lower and to the right), and the govt would get less revenue — making this experiment irrelevant to the policy question at hand, which holds govt revenue fixed (in present value).

  35. 35 35 vivek

    Paul
    Indifference curves are irrelevant here. That’s what confused us. The requirement of equi-revenue means that if at time 1 you decide to spend everything, the Govt simply increases the tax to 50%-AT THAT VERY TIME- so the two taxes are the same except B is potentially worse because it also taxes interest. Provided the interest rate is non zero positive, A is always better than B. A trivial, purely verbal, result.

    I found it interesting because Economics got in the way of seeing this for the simple verbal argument it is. I guess as we grow older we tend to do that a lot. I’m guessing, the Prof’s students
    spotted this a lot quicker.

  36. 36 36 vivek

    Maybe the point the Prof is making is that we should be looking at economic activity rather than incidence of the tax. Clearly, for a positive interest rate there is an economic activity- fuelled by saving- that will diminish if interest is taxed. Then a tax on interest leads to less output- there is an excess burden. This is not to say that such a tax might not increase saving if a negative (Permanent)Income effect swamps the inter-temporal substitution effect- i.e. poorer people need more precautionary balances or, simply, subsistence in time 2 requires larger savings to generate the needed income. Under both assumptions the tax-payer is worse off and a dead weight loss arises without any fall, or even with a rise, in economic activity.

    I still think a double tax on savings makes sense if the Govt. is doing something with revenue to make savings more prodctive. Alternatively, if through transfers the Govt. is removing a source of uncertainty or providing a source of income that eliminates the income smoothing function of savings then such a tax would be justified. The scenario here is, individual agents are underconsuming because it they can’t see the big picture- viz. how everybody could be a lot better off, have consumption smoothing, lower uncertainty, etc by Govt. action.
    Let us take a simple subsistence economy where savings are held in bullion. The Govt. decides to tax bullion and invest the proceeds in irrigation or building a port or other such infrastructure. The Govt. also offers bonds as way of holding savings. Tax the bond income by all means. An economic service has been provided and its beneficiaries should have a tax incidence proportional to the benefit received.
    Put another way, take a sort of caricature Japan with a ‘shoe-box’ effect- i.e. more profitable to put your money in a shoe-box than invest it. The Govt. lets you buy bonds and uses the money in some way with a negative rate of return. Surely the burden should fall on the bond-holders who get a safe way to hold savings?
    Under these sorts of scenarios, Govt is extracting a rent rather than reducing Econ. activity.
    Another reason to ‘double’ tax savings could have to do with missing markets w.r.t. non fungible assets such that no other means exists equalise the marginal rate of tax on different types of economic activity.
    I wonder if there is any work on reverse engineering taxation by looking at shadow prices and decomposing agents into their relationships with the incidence falling there rather than on ‘income’ or ‘capital’ as currently defined. I guess there must be.

  37. 37 37 Vivek

    Steve Landsburg is a very bright mathematician but he is popularising an old fallacy re. double taxation of savings.

    ‘A tax on wages is (among other things) a tax on capital gains, because your capital gains are proportional to your savings and a tax on wages reduces your savings. Capital gains, therefore, are taxed in advance at exactly the same rate as earned income. The capital gains tax (along with any other tax on capital income) sits on top of that. And it’s only the total that matters.’

    This line of argument is fallacious.

    Suppose I get a job as a Prof of Econ, or a janitor. As a result of being a Prof. , or janitor, I’m offered a second job- as a consultant to Rightwingnutjobs’r'us. Clearly, it is because of my being a Prof., or having damaged my brain by breathing in the fumes of powerful cleaning fluids, that I’m getting the gig as a consultant and you can hardly call it work- I mean, all I have to do is shoot my mouth off which I’d do for free anyway.

    So like IT IS LIKE TOTAL DOUBLE TAXATION DUDE if my douceur from Rightwingnutjobs’r'us is taxed as income. I mean, like I dun already paid taxes on my salary as a Professor or janitor- and it is only because of the brain damage I sustained or induced in that role that I got this bonus from Rightwingnutjobs’r'us.

    Indeed, because my job as a Prof is only possible because I got an education- which Daddy paid for out of his post-tax income- so taxing my professorial or janitor’s (the janitor studied Post Colonial Theory) salary is like DOUBLE TAXATION dude.

    Prof. Landsburg is using precisely this argument against a tax on interest income or capital gains.

    Notice (apart from seigniorage) there is no tax on cash under your mattress. The moment you invest it however there is a new economic activity. That this activity continues to occur while you’re sitting on the toilet- on the analogy of a Professor of Econ, or janitor, fouling the air by giving vent to her views on behalf of Rightwingnutjobs-r-us- is why it is taxed albeit at a much lower rate than payments made for services rendered by the august institution last mentioned.

    The Govt. may or may not be providing institutional and legal support for the existence and functioning of markets and corporations. Nevertheless, it is entitled to tax any economic activity which becomes measurable and fungible to a greater or lesser extent by reason of occurring through the market.

    In this post the brilliant Prof has offered a ludicrous Indifference curve analysis to support his view.

    Imagine 2 tax regimes

    A. 50 % income tax

    B 40% tax on both income and interest

    However, constrain the above such that Govt. receives equal revenue by adjusting tax rate.

    What happens? Well, if you try to escape tax on interest by just not saving and spending all you have the Govt. simply raises the tax rate AT THAT VERY TIME PERIOD to 50%. In other words the real situation the Prof is describing is

    A- a Tax on income of 50%

    B- a Tax on income of 50% plus a tax on interest of 50%

    Of course, if interest rate is non zero- in other words if some economic activity occurs as a result of savings- then A is always better than B.

    But why stop there? Let our knowledge increase

    Let us prove swans are swans and geese are geese!

    Or if that enterprise somehow lacks in verve

    Clutter things up with an indifference curve!

  38. 38 38 vivek

    Since coming across this post- and, I confess, having shown myself to myself as an idiot- I’ve been looking at a general equilibrium model (closed economy- with tax revenue=transfers) for this type of mutli-period economy- as well as a special case of a dynamic, not standard game theoretic, but ‘mimetic-field’ (such that preference formation is ‘learned’) theory such that you get some quantum game like phenomena.

    Result? Urm…I’m embarassed to say this, specially coz the Prof reckons Hindus think Judaism is wrong, but his 2 Principles mentioned in this post are ‘halachah vein morin kein’- if you know the principle you can’t, to be adhere to the principle, act upon it except to its Divivne-retribution-requiring violation.

    The utterly brilliant Prof, who writes with such clarity and to an effect of utter hilarity, is misguided by stuffy old Brouwerian intuitions re. the nature or necessity of the continuum between ‘two-ities’.
    I may mention that Andrei Weil almost lost his life because of a Gandhian mis-reading of the Gita- he ran when he should have accepted conscription. This very brilliant Prof. (who moreover is a master of written English) ought to run rather than accept conscription in a sort of Ayn Rand Libertarianism as dead as John Birch.
    Ideas of Liberty are what change when you have it. Resurrecting fallacies from a century ago is not the way forward.
    Okay, this post suckered me- but I’m 47 and left the L.S.E 28 years ago. Still, it’s Not the sort of stuff we expect from you Prof.
    Mathematically speaking, if Econ can be modelled- there must be a higher order generalization from symmetry that looks at constraints upon possible matrices or repertoires of interaction. What is that higher order generalization?
    That’s what we want to know Sir.

  39. 39 39 vivek

    If the Prof. had studied Econ rather than Maths
    a) he wouldn’t be the ignorant, deeply provincial, booster that his videos depict him as
    b) he would have looked at the ‘dual’, the shadow-price- of that which his mathematicism imposes upon him.

    This is a guy who says he knows poetry coz he don’t write it. I don’t do math but I read it- all of it I can lay my hands on. The advantage is with me, almost infintely less smart though I am, unless of course the good Prof is a Straussian ‘noble liar’.

    What the Prof. is doing is deeply damaging to Libertarianism. He’s all over the place with ‘statistical lives’ and the other thing whose names escapes me, where essentially his argument boils down to begging the question- viz the convexity and continuity properties of an entirely notional Indifference curve.
    I got over that sort of silliness when I was 17 coz I was in the 2nd year at L.S.E. I have economic intuitions, the Prof has silliness.
    What a waste of, I will not say a fine Mathematical mind (can’t find anything interesting there) but the futile semi-literary gifts of a meretricious mathematical flaneur.

  40. 40 40 vivek

    The odd thing here is that the Prof. responds to unconsidered comments- i.e. one’s that don’t spot how his initial condition specifying legerdemain begs the question- though, he must know any comment other than this are witlessly wrong. Who will bet he won’t respond to my comments- though they are right?
    Why is this disgrace to Libertarianism peddling such sophistries?

    Does he know something I don’t? Is Libertarianism really founded upon Nineteenth Century fallacies?

    Landsburg’s Libertarianism gives the lie to the inscription on the Liberty Bell. Go talk to a Rabbi, Landsburg, he’ll explain the allusion.
    A lot of mathematicians have foolish views.
    Landsburg is one of them.
    Pity. But there it is.

Comments are currently closed.