Harry Truman famously asked for a one-handed economist since all of his seemed reluctant to decisively answer anything: “on the one hand,” they’d tell him, but “on the other…”

When asked whether an income tax makes people work more or less, the typical economist gives the sort of answer that would have grated on Truman like a bad music critic.

If, however, we change the question slightly and make it more realistic, it’s possible to give a decisive answer to the question. Income taxes do reduce overall labor supply. This is something that economists James Gwartney and Richard Stroup explained in the pages of the American Economic Review some 30 years ago. And last week, the CBO’s much-discussed report on the ACA and labor-force participation illustrated their point nicely.

The Standard, Two-Handed View

Let’s begin with the standard way that economists answer the question.

On the one hand, they say, an income tax encourages people to work more. This is because of what we call the “income effect.” You see, the tax makes people feel poorer. And as a result, they feel compelled to work harder in order to maintain something close to their pre-tax standard of living. Another way to put it is that leisure is a normal good meaning that people prefer to consume less of it when they are poorer and since the tax makes you feel poorer, you consume less leisure.

On the other hand, however, an income tax encourages people to work less. This is because of what we call the “substitution effect.” You see, the tax makes non-work, or leisure, less expensive. And as a result, people feel compelled to take more time off since it will cost them less in forgone income.

Whether people work more or less as a result of an income tax depends on which of these two countervailing forces dominates.

It’s enough to drive a president to distraction.

The One-Handed View

As Gwartney and Stroup point out, however, “it is invalid to generalize from the individual work-leisure analysis to the economy as a whole.” Why? Because the government doesn’t just tax; it taxes and spends. And even though the income and the substitution effects work against each other on the taxing side, they work in the same direction on the spending side.

Let’s say that the government takes the revenue it taxes from me and gives it to you in the form of a means-tested insurance subsidy.

On the one hand, the subsidy has an income effect that makes you feel wealthier. As a result, you feel compelled to work less since you don’t need to work as hard in order to stay close to your pre-subsidy standard of living. Put another way, since leisure is a normal good, you choose more of it now that you feel wealthier. Notice that the income effect that you feel when the money is spent offsets the income effect that I feel when it was taxed. The income effect of the tax makes me work more, but the income effect of the subsidy makes you work less.

What about the other hand? What about the substitution effect? If everyone gets the subsidy irrespective of income, then there is no substitution effect. The cash grant doesn’t affect relative prices so all one is left with is the income effect. More realistically, the subsidy will likely be means-tested the way TANF payments and ACA insurance subsidies are. In this case, as you earn more, the government will reduce your subsidy. In this case, the substitution effect complements the income effect. Just as the income effect of the subsidy makes you work less because you feel you can afford more leisure, the substitution effect of the subsidy makes you work less because it makes work look more expensive and leisure look less expensive.

In summary: when the government taxes the population, the income effect makes people work more while the substitution effect makes them work less. But then when the government spends this money on transfers, the income effect makes people work less, offsetting the income effect on the taxing side, leaving only the substitution effect. What’s more, if the subsidy is phased out as incomes rise (which most subsidies are), then a substitution effect on the expenditure side rears its ugly head, encouraging even less work.

That’s why the CBO’s report should be no surprise to anyone who has read Gwartney and Stroup.

And of course, this isn’t just theory. Empirical papers such as those by Edward Prescott, Michael Keane; Ohanian, Raffo and Rogerson; Davis and Henrekson; Cardia, Koshoya and Ruge-Murcia; and Nada Eissa corroborate the theoretical story that Gwartney and Stroup tell.

Here it is in diagram form

Let’s begin with a standard labor-leisure tradeoff model. The horizontal axis measures hours in leisure while the vertical axis measures consumption. Assume that you can make $10 an hour selling trinkets online. If you do nothing but make trinkets, you can earn $240 per day allowing you to consume $240 per day (for simplicity, let’s assume no savings). And if you make no trinkets, you can spend 24 hours in leisure, permitting $0 in consumption. If you connect these two points, you get your budget line, indicated below in red; it shows all of the feasible combinations of consumption and leisure.

You presumably value consumption and you presumably value leisure. Moreover, when you are working a lot, you value another minute of leisure more than when you are working a little. With this information, we can trace out an indifference curve. A single indifference curve shows all of the combinations of labor and leisure that bring you the same amount of satisfaction. Any one indifference curve is part of a “family” of such curves, so that any point above and/or to the right of the indifference curve would put you on a “higher” indifference curve (making you happier) and any point below and/or to the left of the curve would put you on a “lower” indifference curve (making you less happy). The diagram shows three indifference curves in blue.

The combination of leisure and income that you choose is known as the equilibrium. It is the point at which you are able to select your highest indifference curve (solid blue) given your budget constraint.

(click on the images to see up-close)

Now consider an unrestricted cash transfer, shown in the diagram below. This extra money pushes your budget constraint out, allowing you to reach a higher indifference curve. Notice the “kink” in the budget constraint at the bottom right; though the subsidy allows you to have more cash, no government program can give you more time in the day. Since leisure is a normal good, the income effect of this transfer causes you to choose more leisure and less work. Your total consumption is now the sum of your income and your transfer payment. In this case, there is no substitution effect because the cash transfer is unrestricted and doesn’t alter the relative price of leisure and work. If you take an extra hour off work, it will still cost you $10.

Finally, consider a conditional means-tested cash transfer. The transfer is phased-out as incomes rise. Let’s say that each extra dollar you make, reduces your transfer by $0.50 and that at some point, it is completely phased out. In this case, you still have the income effect, causing you to feel wealthier and therefore encouraging you to consume more leisure. But because the transfer is phased out as your income rises, you also have a substitution effect. Another hour of leisure only costs you $5 instead of $10 (it reduces your income by $10, but raises your cash payment by $5). If you want to think of it another way, the substitution effect means that you face an implicit marginal tax of 50 percent: Each extra dollar earned reduces your net-of-transfer consumption by $0.50. This makes the budget constraint look more “flat,” and creates another kink in the constraint right at the point where the subsidy first kicks in. In this case, the flatter budget constraint causes you to work even less than you did with the unrestricted cash transfer.

This is why economists like Milton Friedman and Veronique de Rugy often say that in an ideal world, the most efficient welfare program would offer a guaranteed income for everyone irrespective of income. Such a program has no substitution effect.