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Thinking Clearly about Capital, Interest, and Income

Mises Daily: Monday, November 08, 2010 by

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Nowadays, Austrian economists are most famous for their theory of the business cycle, as developed by Ludwig von Mises and Friedrich Hayek. However, they also made many contributions to the pure theory of capital and interest, most notably in the seminal work of Eugen von Böhm-Bawerk and later in that of Hayek. In the present article we'll see that these insights are relevant today, as mainstream economist Scott Sumner lashes out justifiably against absurd tax policies but, in the process, throws economic theory out the window too.

Sumner Not Sure How to Define "Income"

Although I won't have many kind things to say about him in this article, Scott Sumner is a very sharp mainstream economist who can pick apart Paul Krugman with the best of them. But recently on his blog, in a noble effort to criticize the US tax code, Sumner tied himself into knots over very basic financial and economic concepts.

Things started off badly right in the title of this blog post: "Income: A Meaningless, Misleading, and Pernicious Concept." Yikes! The very concept of income is meaningless and pernicious? In order to see what could possibly have generated such a title, we'll quote extensively from Sumner's post:

You can't imagine how enraged I get reading progressives talk about the "principle" that all forms of income should be taxed equally. … Or when they discuss Gini coefficients of inequality based on meaningless income data. …

Bear with me as I start from first principles; this is an important post. I will try to convince my progressive readers that they should favor complete abolition of all personal and corporate income taxes, as well as all inheritance taxes.

Suppose 2 brothers both make $100,000 a year. … [Also] assume it's possible to invest income at a real rate of interest that allow[s] one to quintuple one's wealth between age 25 and 65. (Say a 40 year zero coupon real bond yielding around 4%.) In this example let both brothers consume nothing but blueberries. One brother chooses not to save at all, the other saves 40% of his income. One eats $100,000 worth of blueberries today; the other eats $60,000 today and saves $40,000. [This one-time saving out of labor income grows at interest, so that a]fter 40 years the thrifty brother gets to eat $200,000 worth of blueberries. Both also get some social security at 65. Here's my question: In this society is there any economic inequality?

I don't see how anyone could say there is. Both have exactly the same wage income at age 25. Yes, they do different things with it, but that's their choice. At age 65 one has zero income outside social security, and the other has $160,000 in capital gains, which is generally considered "income." …

The mistake [for people who think there is income inequality] is assuming that blueberries in 40 year[s] are the same thing as blueberries today. Future blueberries only cost 1/5th as much, as they are much less valued than current blueberries. They are different goods just as much as watermelon and blueberries are different goods. That $160,000 gain is not "income" in the way most people think of the term, i.e. as some sort of goodie available for spending. Rather it reflects deferred consumption. The $200,000 received at 65 is exactly equal in present value to the $40,000 saved today. Indeed it is the very same wealth, simply measured at a different point in time. It is nonsensical to say the thrifty brother has income of $100,000 today plus another $160,000 at age 65, you'd be counting the same income twice.

I have emphasized the crucial point in the passage above, and Sumner himself, in a subsequent post, also summarized the moral of the above story like this:

Capital income is nothing like wage income — rather it is deferred consumption. Counting capital income and wage income is actually counting the same income twice.

Sumner's analysis is useful in many respects, but unfortunately he draws the wrong conclusion from it all. There is nothing "meaningless, misleading" or "pernicious" about the concept of income, whether labor income or capital income.

The Definition of Income

In terms of pure economic theory, income (in a particular time period) can be defined as the amount of consumption one can enjoy in the time period, without impairing the ability to generate future income. If we then define capital as the present value of consumption that will accrue in all future time periods, we can say that income (in a certain time period) is the maximum amount of consumption one can enjoy, without reducing the market value of capital from the starting period to the next.

A numerical example will illustrate these definitions. Consider a man who earns $100,000 in annual salary from his employer, and who has the option of putting money in a bank account where it earns 5 percent interest annually. The man starts out in year one with no money in the bank. The following table summarizes five years in the man's life:

Year:

1

2

3

4

5

Starting Bank Balance:

$0

$0

$10,000

$10,000

$6,000

Interest Income (5% of Balance):

$0

$0

$500

$500

$300

Labor Income:

$100,000

$100,000

$100,000

$100,000

$100,000

Total Income:

$100,000

$100,000

$100,500

$100,500

$100,300

Consumption:

$100,000

$90,000

$100,500

$104,500

$100,300

Saving (Dissaving):

$0

$10,000

$0

($4,000)

$0

Ending Bank Balance:

$0

$10,000

$10,000

$6,000

$6,000

In year one, the man earns no interest income. He consumes $100,000 — spending it on his apartment rent, going out to dinner, cruises, and so forth. But since his labor income was $100,000, his total financial capital remains unchanged at $0.[1]

In year two, once again the man has a total income of $100,000. However, this year he is very frugal and only consumes $90,000. He puts the other $10,000 in the bank. Because he has "lived beneath his means," the man's capital has increased from $0 to $10,000.

In year three, we can see the benefit of the previous period's frugality. Now, in addition to his salary of $100,000, the man has an additional source of income: the 5 percent interest he earns on the $10,000 in the bank. Therefore, his total income is $100,500. Now what does this really "mean" to a skeptic like Scott Sumner? It's quite simple: it means the man can consume $100,500 worth of goodies — fancy restaurants, tickets to the ballet, etc. — without impairing his bank balance.

In year four, the man lives above his means; he consumes more than his income. This is possible because of dissaving; the man draws down on his financial assets. Specifically, the market value of his bank balance drops from $10,000 to $6,000, which reflects the fact that the man consumed $4,000 more than his income this year.

In year five, we see the results of the previous year's dissaving. Because he has only $6,000 in the bank, the man earns only $300 in interest income. Thus, if he wishes to keep his capital intact (at the lower value of $6,000), the man can only consume a total of $100,300 this year.

Implications

This simple example illustrates the abstract definitions we earlier listed for income and capital. At this level, there is no distinction between labor income and interest income. Yes, they aren't identical concepts — one is from labor, the other from interest — but they are both forms of income. To say that only labor income is "really" income, while interest income is actually just deferred consumption, would make the accounting impossible and would lead to absurdities.

In the comments section of his first post, I asked Sumner if he had a problem with the standard definition of income. I reminded him that it is the amount of consumption that one could afford, without reducing the value of capital. Sumner replied, "I do not object to your definition. … I guess 'meaningless' was a bit strong, but what possible use is there for a concept that measures how much consumption one could do [without] impairing one's wealth?"

This reply actually flummoxed me; it's akin to asking what possible use there is for the concept of profit. Specifically, a household needs to calculate its income, in order to know if it is "living beyond its means." We can make the analysis more esoteric if we wish. For example, one of the key issues in Austrian business-cycle theory is that people during the boom period enjoy a false prosperity — a high standard of living — because they are unwittingly consuming their capital. These crucial issues are dependent on the basic definition that Sumner finds useless.

Clearing Up the Confusion

Many libertarians loved Sumner's analysis (and the similar approach that Steve Landsburg took), because it blows up the case for taxing interest and capital gains. After all — as Sumner showed — we can have two identical people with the same opportunities for either current consumption or investment, and the one who saves will end up having a much higher lifetime income. So why should the frugal person be taxed more, simply because he chooses to consume his labor income "over a lifetime" rather than blowing each paycheck as soon as it comes in the door?

To be clear: I agree with Sumner (and Steve Landsburg) that these types of thought experiments are useful to show the problem with typical handwringing over "income inequality" and the related pleas for progressive income and wealth taxation. My problem is Sumner's rejection of the standard definition of income and his claim that interest income isn't really income, but rather a form of deferred consumption.

By the same token, I could challenge Sumner's own argument for a tax on consumption. Imagine two identical people who could each hold a $100,000-per-year job. Person A goes to work, and spends his entire income on goodies each year. Because the government imposes a Scott-Sumner-approved 11 percent tax on consumption, this man pays $10,000 to the government, and actually only consumes $90,000 worth of goodies.[2]

On the other hand, person B decides to be a drifter. He only works occasionally at odd jobs; he spends most of his days hitchhiking, watching the sunset, and working on his great American novel. He doesn't cheat on his taxes, though: out of the $10,000 in annual income that he earns, he saves none of it, sends $1,000 to the government, and consumes the remaining $9,000 in goodies.

I could very easily condemn this hypothetical consumption tax, and along Sumnerian lines. After all, the two men had equal abilities at the start of their adulthood. Person B could have chosen to work in the office and earn enough money to spend $90,000 each year on consumption. But instead, person B chose a different path. So why in the world should the government tax him far less than it is taxing the "equivalent" person A?

So far, so good. I am showing that the (immoral and inefficient) consumption tax cannot hold up to scrutiny; it isn't really true that people who "consume" more are necessarily "richer" and therefore able to pay more, as Scott Sumner and other advocates of the consumption tax seem to think.[3]

Mises Academy

But what if I went further? Suppose I went on to argue, "Indeed, the very concept of labor income is meaningless, misleading, and pernicious. In our example, person A earned ten times as much 'labor income' as person B, but there is no reason to suppose that person A somehow has a better life, since person B could have made the same choices. Indeed, 'labor income' is really just forfeited leisure. The drifter could have devoted his hours to office work, but instead he chose to 'purchase' $90,000 worth of his time from himself. Therefore, to count 'labor income' as a form of freebie flow of wealth is to count the same hours twice."

Now, regardless of how one feels about the validity of a consumption tax, does anyone want to go so far as to say that a paycheck isn't really a form of income after all? I submit that Sumner made an analogous mistake in his own analysis. Just because we can imagine scenarios in which an income tax (that includes interest and capital gains) is patently unfair, does not mean that interest income therefore isn't "really" income. Rather, it simply means that the conventional calls for progressive income taxes are misguided.

Income vs. Capital

If we step back and look at the big picture, I think Sumner's basic mistake is that he is trying to use income when what he really should be using is financial capital or wealth. Let's go through one last numerical example to see why.

Once again, suppose we have two initially identical people, who both start out with $100,000 in the bank. The first guy, Prodigal Paul, withdraws the whole sum and consumes it immediately — he really lives it up for a week. After his amazing binge is over, Paul has no more assets, and that is that. So his "total consumption," measured in present dollars, is clearly $100,000.

But now consider Frugal Freddy. Rather than consuming anything in the present, Freddy waits. After one year, the bank balance has grown to $105,000. At the beginning of the second year, then, Freddy takes out $5,000 and consumes it. Freddy does this for 50 years straight — we're assuming the interest rate remains at 5 percent throughout — and then withdraws the principal of $100,000 and consumes that too.

Although it's not as obvious, the present market value of Frugal Freddy's lifetime consumption — measured at the start of our experiment — is also $100,000. Indeed, we can imagine Frugal Freddy withdrawing his $100,000 in the beginning (just like Prodigal Paul), but instead of buying present consumption goods, he instead arranges for merchants to sell him claim tickets to future consumption goods at various intervals. In other words, Prodigal Paul might have bought a steak right now for $100, but Frugal Freddy instead gives the restaurant owner only $95, in exchange for a ticket that says, "Entitles the bearer to one steak in the year 2011."

Since Prodigal Paul and Frugal Freddy both start out with $100,000 to work with, and since (in principle) they could both enter the market on day one and spend all of it arranging for their preferred streams of consumption, then clearly the present market value of their lifetime consumption streams must be equal. This is why Sumner wants to conclude that they both have the same level of economic well-being, and that any tax that fell more heavily on Frugal Freddy would be unjust.

"Income is not a stock variable (applicable at one point in time); rather it is a flow variable, applicable over a certain period of time."

However, there is something odd here. Even though both men have the same lifetime consumption (measured in present-value terms at the starting point), Frugal Freddy has a much higher lifetime income, even measured in present-value terms at the starting point. Prodigal Paul has no income at all, in any time period; so his lifetime income is clearly zero. However, Frugal Freddy earns $5,000 in annual interest income for 50 years. This lifetime income stream has a present market value (at the starting point) of more than $91,000.

Thus we see Sumner's complaint: Even though there is a very legitimate economic sense in which these two men have equal "means," one of them has a lifetime income of $0, while the other has a lifetime income — again, measured in present-value terms at the beginning — of more than $91,000. So doesn't this prove that income is a meaningless, misleading, and pernicious concept?

No, it doesn't, and there are two main reasons: First, Sumner is using the wrong concept for his goal. The correct measure is that Prodigal Paul and Frugal Freddy both start out with the same financial capital or, in a word, wealth. Prodigal Paul chooses to consume his wealth in one fell swoop, whereas Frugal Freddy spreads his consumption out over 50 years. But both men start out year one with the same amount of financial capital or wealth, and that's why they can afford to sell their wealth to acquire different streams of consumption that have the same market value (measured at the start).

Second, the concept of income is still useful because it gives guidance period-by-period. This is the source of Sumner's confusion. He wants a single number at the start of the process and he's unhappy with income because it doesn't fit the bill. Yet income is not a stock variable (applicable at one point in time); rather it is a flow variable, applicable over a certain period of time.

Even if Frugal Freddy withdraws his $100,000 from the bank at the same time as Prodigal Paul, and then trades it away for various claim tickets to steaks, haircuts, apartment rentals, and so forth over the next 50 years, the concept of income is still quite useful. It shows Freddy what his options are if he changes his plan at some point during the 50 years. Even if he has exchanged his $100,000 in the beginning for a collection of claim tickets, it is still the case that Freddy's accountant can compute the market value of his actual consumption year to year. If Freddy decides to alter his course, he could sell his unused claim tickets (which would have a higher spot price than what he originally paid for them) and rearrange his consumption plan.

In any given year, the accountant could tell Freddy the total market value of his remaining claim tickets. If Freddy consumed tickets with a market value of more than 5 percent of this amount, then next period his accountant would inform him that the total value of his unused tickets had fallen.

Most importantly, the accountant's reliance on market prices, and the related calculations of wealth and income, would allow Freddy to rationally respond in the face of surprises. In the real world, Freddy wouldn't want to commit himself to a stream of consumption over a 50-year period, because he wouldn't be sure what the future would hold. That is why market prices, and the related accounting techniques, are so important.

Conclusion

Capital and interest theory, and its relation to income, is a very complex area of economics. It is also one in which the Austrians have made major contributions. Contrary to Scott Sumner, the concept of income is perfectly fine, used properly. Interest and capital gains are income — albeit different types of income — just as wages are.[4] We shouldn't toss out an economic category just because the politicians and envious public have used it improperly to justify a tax.

Notes

[1] Technical note: In this simple example, we are assuming that the man's total financial capital is equal to his bank balance. Strictly speaking, this means that we are classifying the man's capital as the present value of the future streams of just interest income. Some economists might include the man's labor income too in this calculation, in which case his "total capital" would include not just his bank balance, but also his "human capital." Then we would have to worry about the man eventually retiring, and how his current paycheck was actually more than just pure labor income, but also a form of (human) capital consumption. But to keep things simple, we are ignoring these complications, and have kept the paycheck at a steady $100,000 throughout the analysis.

[2] The actual tax rate to achieve this outcome would be 11.111… percent.

[3] Things are even worse for Sumner, who actually advocates a progressive consumption tax, i.e., one where the rate itself is higher, depending on the amount of consumption.

[4] Murray Rothbard agrees that capital gains are a form of income. See pages 533–34 of the Scholar's Edition of Man, Economy, and State.