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# Why the Asymmetry between the Income and Consumption Taxes?

In what was, I think, the only math course I took in college, the professor said: “when you are trying to solve a problem, look for the asymmetries and ask: why? Asymmetries happen for a reason, and if there is no reason, then the asymmetry shouldn’t be there.”

It is a staple of tax theory that the income tax touches both labor and investment income whereas the consumption tax touches only labor income.

Why this asymmetry?

## The Conventional Account

The standard explanation sheds no light on the question. It goes like this.

Suppose that you work for a period l at wage w, invest the resulting income of wl at interest rate r, and then spend the proceeds.

Under an income tax of rate t, you will pay twl in tax on your labor income, leaving you with wl-wlt=wl(1-t) remaining to invest. Your investment will grow to wl(1-t)+wl(1-t)r=wl(1-t)(1+r), but the interest earned on the investment, wl(1-t)r, counts as income as well, so it, too, will be taxed at rate t. You will therefore pay twl(1-t)r in additional tax, leaving you with wl(1-t)(1+r)-twl(1-t)r=

to spend after all taxes have been paid.

By contrast, under a consumption tax, you will be able to invest all of your labor earnings, wl, to obtain wl(1+r) after your investment pays out. Assuming that the income and consumption tax rates are the same, you will then pay tax twl(1+r) when you go to spend your income on consumption items, leaving you with a total of wl(1+r)(1-t)=

The expressions for the income tax and the consumption tax both have a tax term, 1-t, applied directly to labor income, wl, suggesting that they both tax labor income in the same way. But the expression for the income tax also applies the same 1-t term to the rate of return on investment, r, which the expression for the consumption tax does not. This suggests that the income tax taxes investment returns whereas the consumption tax taxes only labor income.

Indeed, if we construct an expression for an income tax that applies to labor income but not to investment income, we end up with our expression for a consumption tax.

We start with labor income wl and then apply a tax of twl, as we did in analyzing the original income tax, to obtain wl(1-t). This amount is again invested to obtain wl(1-t)(1+r). But now we are done—we do not apply a tax on investment returns. The result,

is identical to the expression that we obtained for the consumption tax.

We must, then, conclude that a tax on consumption taxes only labor income whereas the income tax taxes both labor income and investment income. (The table at the end summarizes after-tax value under this and a number of other scenarios that I will discuss.)

Why this asymmetry?

It is not intuitive.

A consumption tax is a tax on money going out, whereas an income tax is a tax on money going in. If everything that comes in must eventually go out, should not the income tax and the consumption tax be identical?

If the money the worker spends on consumption was generated in part through financial investments, shouldn’t a tax on everything he spends (i.e., on consumption) end up taxing the return on investment as well as labor income?

If there is no good reason for an asymmetry, then it should not be there.

If it should be there, then we have not really understood tax policy until we have understood why the asymmetry is there.

It turns out that the conventional account of the difference between consumption and income taxation both ignores a broader symmetry between the two approaches and is equally mum regarding a good reason for the asymmetry.

## A Latent Symmetry

Our method will be to try to find—or construct—symmetry between the income and consumption taxes. If we can figure out what we need to make the treatments symmetrical, we can then ask whether the absence of the things that are needed for symmetry is justified.

### Comparing Workers with Rentiers

The first thing to realize is that the conventional account jumbles the tax treatment of labor income together with that of investment income. It tells the story of a laborer who starts with labor income and then invests it, suggesting that all income originates in labor. It starts with wl.

But not all of us are so unfortunate.

Some people don’t work—don’t have to work—because they get all of their income from financial investments.

The money they invest is so great that the return it throws off is large enough to make them prefer not to work for labor income.

There’s an old word for such people: rentiers. As Piketty has shown, they are making a comeback.

To avoid any quirks in tax treatment created by jumbling the experience of the rentier together with that of the worker, let’s consider the worker who gets all of his income from labor and the rentier who gets all of his income from investments—rather than consider a worker who plays rentier with his labor income, as in the conventional account.

Let’s look first at the rentier and the income tax.

The rentier has some financial endowment—call it p for property—which he grows to p(1+r)=p+pr through investment. At this point, the income tax is applied to his interest income, pr, and he is taxed the amount tpr. This leaves him with p+rp-tpr=

We see that the effect of the application of the income tax to investment returns reduces the after-tax growth rate of the investment from r to r(1-t).

Now let us consider the experience of the workers under the income tax when he does not invest his earnings in financial assets.

In that case, the worker earns wl, pays tax on it, and does not invest, ending with

The income tax treatment of the worker clearly differs from that of the rentier. We should be surprised that they do.

The income tax taxes both labor income and investment income at the same rate t, and here we have a rentier who has generated only investment income and a laborer who has generated only labor income. Shouldn’t the two be taxed in the same way?

The answer holds the key to our problem.

We can find it by continuing to try to construct symmetry between the treatment of the rentier and the worker.

One way to do that would be by eliminating the 1 term in the parentheses in our expression for the rentier’s after-tax income. That would give us pr(1-t), which is analogous to the expression for the worker’s after-tax income, lw(1-t).

But doing that would not make any sense. Eliminating the 1 is equivalent to making the claim that when you invest an amount p you obtain interest on your investment, pr (which is then taxed to obtain pr(1-t)), but not the return of the amount you invested, p.

But that’s not how finance works. When you invest an amount, you don’t lose your capital and gain only the interest paid on it. Instead, you get your capital back, plus interest.

We can also create symmetry by adding a 1 to the expression for the worker’s after-tax income, to obtain

Here is where things get interesting.

### Labor as Capital

Adding that 1 in makes the claim that labor income, wl, is equivalent to the interest paid on an investment of working hours l. The worker invests l by working, and that investment grows into l(1+w)=l+wl, the worker’s l hours of work plus labor income wl.

But the “labor capital” that the worker has invested, l, is not taxed, only the return on that capital, wl, is taxed, just as, in the case of financial assets, the capital, p, is not taxed, and only the return on capital, pr, is taxed. As a result, the worker pays twl on value of l + wl, and ends up with l+wl-twl=l(1+w(1-t)), our symmetrized expression for labor income.

That is, with this change, the wage, w, becomes the analogue of the interest rate, r—it becomes the rate at which labor is compensated, just as r is the rate at which investment is compensated. And the number of hours worked, l, becomes the analogue of the dollar amount invested, p—it becomes the amount of labor with which the worker is endowed, just as p is the amount of investment capital with which the rentier is endowed.

But what does it mean to say that a worker invests l hours of labor and receives those l hours plus a return equal to labor income in exchange?

Of course, if one works l hours, one never gets those hours back again. Perhaps one receives the satisfaction of having worked l hours of honest labor alongside one’s income on that labor.

Or the l hours represent one’s ability to work over a given period of time, and, as this ability does not diminish from one period to the next, at the end of each period one starts over afresh with the same amount of hours on hand to invest in labor.

We do not need to resolve this question, however, because, for purposes of comparing consumption and income taxation, the nature of a labor hour matters only to the extent that this affect’s the hour’s exchange value. But labor hours have no exchange value.

Labor hours cannot be transferred.

One’s labor time is personal to oneself.

Only I can can expend my hours on work because only I have those hours.

You can pay me for my work—that’s the return that you pay me on my investment of my time in laboring for you—but you yourself cannot work my hours. If I could transfer my hours to you, then you could work 24 or 48 or 72 hours in a single day, for you could work my hours and your own ours and the hours of others.

But that, of course, is impossible.

I am a capital asset that only I can use.

Because labor hours cannot be transferred, they have no price. They cannot be exchanged for cash, cannot be spent on consumption goods or services, and cannot be taxed.

When we speak of financial investment, we speak of p(1+r) and when we speak of labor, we ought to speak, analogously, of l(1+w).

That is, we should think of labor hours in the same way as we think of financial assets, and we should therefore think about the taxation of labor income in the same way as we think about the taxation of investment income.

When we tax investment income, we don’t tax the financial asset that is invested—we don’t tax “savings”—but only the interest on that asset—the return on investment.

Just so, when we tax labor income, we don’t tax the labor asset that is invested—those labor hours—(how can we?) but only the interest on that asset, which is the interest rate—here called the wage—applied to the asset in the form of hours worked. That interest on the labor asset is otherwise known as labor income.

Thus the rentier’s after-tax investment value is p(1+r(1-t)) and the worker’s after-tax investment value is, similarly, l(1+w(1-t)).

But in the case of the worker we don’t write down l(1+w(1-t)) and instead write down wl(1-t) because the fact that l is not transferable, has no cash value, can’t be spent on consumption, and can’t be taxed causes us to forget that it is there.

Financial capital is a transferable thing—it’s dollars and cents, or things that can be exchanged for them—-and we can and do tax it and consume it. The existence of p is therefore constantly before our mind’s eye and we do not omit to write p(1+r(1-t)) rather than, analogously to the worker’s case, pr(1-t).

But what does this hidden symmetry between the income tax as applied to the rentier and the income tax as applied to the worker tell us about the asymmetry that we set ought to conquer, which is the asymmetry in the consumption tax treatment of labor and (financial) investment?

It shows why the asymmetry exists.

### Eliminating the Asymmetry by Treating Labor as Capital

For if we acknowledge that labor income is the return on an investment of labor time, and if it were possible to transfer one’s endowment of labor hours, l, so that it could be taxed or consumed, just one’s endowment of financial assets, p, can be taxed or consumed, then the consumption tax would no longer be equivalent to a tax on labor income; it would differ both from a tax on labor income and from a tax on investment income and would differ from both in the same way.

Thus the asymmetry between the consumption tax treatment of labor and investment income would be eliminated.

If we acknowledge that labor income is the return on labor hours, and if one’s labor endowment were transferable—and so taxable and consumable—then a worker who generates labor income but does not invest in financial assets would generate value equal to l(1+w) from working and then pay tax tl(1+w) on this value, leaving the worker with consumption equal to

But, as we have already seen, under the income tax, the worker’s after-tax value would be l(1+w(1-t))—it would differ from value under a consumption tax in that the factor 1-t would be applied to the wage instead of to the entire investment.

And precisely the same would be true of the income and consumption taxes with respect to financial investments.

We have already seen that under an income tax the rentier’s after-tax value would be p(1+r(1-t)). Under a consumption tax, the rentier would invest p, obtain p(1+r), and then pay the consumption tax on that amount, leaving p(1+r)(1-t). Thus, here again, the difference would lie in the application of the factor 1-t to the interest rate (the analogue of the worker’s wage) in the case of an income tax. The table at the end summarizes these results.

It follows that, as a general matter, we cannot say that the consumption tax taxes labor income but not financial income.

The conventional account is not generally true.

The consumption tax is neither a tax on labor income nor a tax on financial income.

Rather, in principle, it is a tax on wealth—it taxes both the return on capital and the capital itself, whether that capital is labor capital or financial capital.

Because all wealth—the capital and the return on capital—must, ultimately, be consumed.

We also see from this analysis that the income tax and the consumption tax are not the same, whether applied to labor income or financial income. The income tax taxes the return on capital whereas the consumption tax taxes both capital and its return.

The answer to the question how a tax on what goes in can differ from a tax on what goes out is that what goes in is not just income but rather wealth—capital plus returns thereon—and so an income tax will not fully cover it. Thus the tax on what goes out—the consumption tax—which does cover everything that goes out, will differ from the income tax.

## The Untransferability of Labor Hours as the Source of the Asymmetry

So much for the general structural symmetry of the income and consumption taxes. We must now ask why the conventional account finds asymmetry.

Is the conventional account simply mistaken, or is there a reason why, in practice, we must depart from the general structure?

It turns out that we have already encountered the answer. There is a good reason why, in practice, there is asymmetry. That reason is the untransferability of labor hours.

We cannot, in fact, say that under a consumption tax the after-tax value enjoyed by a worker is l(1+w)(1-t), because that equals l(1-t)+w(1-t), implying that the tax authority taxes tl labor hours, and the worker consumes l(1-t) labor hours.

But that’s impossible, because those hours can’t be transferred, either to the government or anyone else.

Unlike the rentier, who, at the end of the day, spends both his investment capital and his returns on consumption, the worker cannot spend his labor hours on consumption because he cannot trade them. He generates cash for consumption only through the returns he generates on his labor, which are paid to him in dollars or other tradable commodities.

His value after application of the consumption tax is, therefore, his labor income—his return on his labor hours—wl, less a tax twl on those returns, or wl(1-t), plus his labor capital, l, which he still holds, even if he cannot trade or consume it. So it is l+wl(1-t)=l(1+w(1-t)).

But that makes the consumption tax identical to the income tax—the same identity found by the conventional account. For we have already seen that under the income tax, he is left with l(1+w(1-t)), and as the income tax touches only labor income, wl, the fact that he cannot transfer his labor hours does not change the analysis.

Financial assets are consumable, however, and so the nonconsumability of labor hours counsels no change to our expression for the rentier’s value after application of the consumption tax. It remains p(1+r)(1-t) and so remains different from the expression for the rentier’s value after application of the income tax, p(1+r(1-t)).

So far from failing to tax financial capital, the consumption tax in fact does tax it—p(1+r)(1-t)=p(1-t)+rp(1-t), so financial capital, p, is reduced by 1-t—and it is the fact that the consumption tax taxes financial capital, while not taxing labor capital, that accounts for the difference in the way the consumption tax treats the two forms of endeavor.

Thus the nontransferability of labor introduces the asymmetry between the treatment of labor and investment income by the consumption tax that we see in the conventional account—and this is evident even without telling the story about the reinvestment of labor income in financial assets through which the conventional account makes this point.

The conventional account does not, of course, say that the worker’s after-tax value is l(1+w(1-t)), but rather that it is wl(1-t)(1+r). That is because the conventional account doesn’t recognize that labor hours are labor capital—or doesn’t care whether they are, because they are nontransferrable—and so doesn’t bother to write down the 1 in l(1+w) when it writes down the worker’s starting income. The conventional account omits the 1 and writes down wl instead. According to the conventional account, the worker’s wealth is exclusively his return on labor capital.

And, as already noted, the conventional account goes on to imagine the worker playing rentier and investing his labor income in financial assets. Thus, in the case of the consumption tax, the worker’s income is invested in financial assets and grown to wl(1+r) before being taxed down to wl(1+r)(1-t). So, in the conventional account, wl is in effect substituted for p in our expression for the rentier’s after-tax value of p(1+r)(1-t).

Similarly, in the income tax context, we have labor income of wl that is taxed down to wl(1-t) and then ploughed into financial investments. So wl(1-t) is substituted for p in our expression for the rentier’s after-tax income, p(1+r(1-t)), to obtain wl(1-t)(1+r(1-t)), the familiar result of the conventional account in the case of an income tax.

We can now restate what we have learned in terms of the conventional account.

The fact that after-tax value under a consumption tax in the conventional story has the same form, wl(1+r)(1-t), as a tax on labor income (that is then invested tax free), wl(1-t)(1+r), is not due to any failure on the part of a consumption tax to tax investment returns. After all, wl(1+r)(1-t)=wl(1-t)+wlr(1-t), so investment returns wlr are taxed down to wlr(1-t).

Rather, it is due to the fact that labor time, l, is not taxed under a consumption tax. If it were, then, adding 1+r terms (to reflect financial investment) to the expressions we generated for the worker above, we would find that the after-tax value expression under a consumption tax would be l(1+w)(1+r)(1-t), whereas the expression for a tax on labor income that is then invested tax free would be l(1+w(1-t))(1+r), which is a different quantity. It is only by deleting the first 1 to be found in each expression that they collapse into each other. (Equivalently, we could render labor hours untaxable—pulling the first 1 in the case of the consumption tax out of the parentheses—as we did above, and achieve the same result.)

## Taxing Capital Would Restore Symmetry

Let us return to our simpler comparison of the tax treatment of worker and rentier in which the worker does not plow his earnings into financial assets.

Our understanding of the source of the asymmetry in consumption and income taxation helps us see how to eliminate it.

We have seen that the key to the asymmetry is that the consumption tax taxes capital and the income tax does not, but labor capital is untaxable, so the consumption tax and the income tax collapse into each other in the case of labor income—but not in the case of financial income.

The way to make the income tax equivalent to the consumption tax is, therefore, to redefine the income tax to apply to financial capital.

Make the income tax a wealth tax.

That would make the consumption tax as applied to investment income the same as the income tax, and the consumption tax and the income tax would, then, be equivalent both when applied to labor income and when applied to investment income.

Because no amount of redefinition of tax rules can make labor hours transferable, such a wealth tax would not apply to labor capital, and so the income tax as applied to labor income and the consumption tax would continue to be identical for practical purposes.

But now the income tax as applied to financial investments would be identical to the consumption tax, for now the rentier would pay tax both on p and his return rp, and so he would have his investment outcome, p(1+r) less tax tp(1+r), or p(1+r)(1-t), and the consumption tax on the rentier’s investment outcome would be the same as the income tax that he pays—tp(1+r)—leaving the rentier with the same after-tax value of p(1+r)(1-t).

This situation is slightly more complicated when we translate this insight back into the conventional account, because in the conventional account the worker is also the financial investor.

The conventional account’s expression for the income tax applied both to labor and financial income, wl(1-t)(1+r(1-t)), differs from that for the consumption tax, wl(1+r)(1-t), in two ways.

One is that the second 1-t term is applied directly to r rather than to the entire expression. The fix of taxing financial capital solves this problem. The worker’s financial capital—wl(1-t)—would, then, be taxed alongside the return on that capital, rwl(1-t), and so we would have after-tax value of wl(1-t)(1+r)(1-t), bringing the expression closer to that for the consumption tax.

But that still leaves the first 1-t term as an extraneous term. That term is present because the worker uses his labor income for purposes of financial investment and his labor income is taxed when it is earned. In effect, the worker who invests would be taxed twice under a wealth tax. Once when he generates labor income and again when he converts that labor income to financial capital and invests it.

This is the sort of problem we were able to ignore in comparing the experience of the worker with that of a separate rentier.

The income and consumption taxes can be brought into equivalence by recognizing a deduction for labor income that is invested in financial markets, in which case the worker will invest wl instead of wl(1-t), and the worker’s after-tax income will therefore become wl(1+r)(1-t)—identical to that for the consumption tax.

Labor income that is earmarked for investment is properly treated as investment capital, and so it should be taxed after it is invested, not when it is first acquired. If we tax labor income that is earmarked for investment, then we should tax all financial assets at the time that they are acquired—that is, before they are invested—and then again when the investment pays out.

The proposed fix to the asymmetry in consumption taxation—taxing financial capital and deducting labor earnings that are invested in financial markets—has a name: it is called a “cash-flow consumption tax.” The fact that it is called a consumption tax and not a wealth tax, even though it is collected when cash flows in rather than when it flows out, is an acknowledgement that this sort of tax on inflows is equivalent to a tax on outflows.

## The Radicalism of the Consumption Tax

Defenders of the income tax (as presently defined) like it because it taxes more. Under the conventional account, after-tax income under the income tax is wl(1-t)(1+r(1-t)), which is less than after-tax value wl(1+r)(1-t) under a consumption tax because an additional 1-t term is applied to the interest rate, r, under the income tax.

But after-tax income is lower under the income tax only because, under the conventional account, labor income is taxed once before it is invested, and that happens only because the conventional account assumes that a financial investor’s source of income is labor.

For the rentier, the situation is reversed. We have already seen that the rentier subject to an income tax ends up with p(1+r(1-t)) in after-tax income whereas the rentier subject to a consumption tax ends up with p(1+r)(1-t). In the latter expression, the 1-t is outside of the parentheses—reducing the entire magnitude contained in the parentheses—and so after-tax income is lower than in the case of the income tax. That is because the rentier pays tax on his financial capital, not just his returns.

Because the consumption tax is a wealth tax; it is more radical than the income tax.

The truly rich, who do not work but live off of their financial assets, do worse under a consumption tax than under an income tax.

It is only the worker, who scrapes together savings to invest in financial markets, who ends up being taxed more heavily under the income tax than under the consumption tax.

That same math teacher who taught me to question asymmetries also liked to call out students who weren’t paying attention in class. “Are you an angry young man?”, he would ask.

I’m not.

But I would like to tax the rentier’s capital.