Why would a temporary extension of the high-end Bush tax cuts be a highly ineffective form of stimulus? Coming into this economic crisis, I thought every macroeconomist understood why temporary tax cuts do little to boost demand, especially if those tax cuts are for people with high incomes. But as with so much else, this seems to be one of these economic insights that has been lost in our intellectual Dark Age. So what I thought I’d do is lay out, briefly, the basic logic.

So, how do we think about consumer spending choices? The origins of modern theorizing lie with none other than Milton Friedman, who argued that we should think of consumers as maximizing expected welfare over their lifetimes. Lots of reasons to doubt whether that’s a good description of actual behavior, but it’s a starting point. If we think of people as living for just two periods, the picture looks like this:

Here Y represents income in the two periods; there’s an indifference curve representing preferences; and there’s a budget line running through Y, reflecting the assumption that people can borrow or lend at a real interest rate r. In this case the individual shown would choose to consume at C.

Now suppose that we give this person a temporary increase in income — that is, a rise in period-1 but not period-2 income. This leads to the following figure:

The income point shifts to Y’, directly to the right of Y; this shifts the budget line out; and in general, we’d expect the consumer to increase consumption in both periods, as indicated by the move from C to C’. But this means that first-period consumption rises by less than the rise in income: part of the temporary tax cut is saved.

And if we bear in mind that the two-period representation is shorthand for a multi-period reality, with this year’s income only a small part of the present-discounted-value of all years’ incomes, we would expect most of a temporary tax cut to be saved.

What could change this picture? Well, we’ve assumed that individuals can borrow or lend at the same rate. But what if they can’t borrow, or can do so only at a substantially higher rate than the rate at which they can lend? If they’re in this position, the budget line becomes “kinked”, as shown in this picture:

As I’ve drawn it here, the no-borrowing constraint is binding — that is, if this person could borrow at the rate r, he would, because his current income is low compared with future income. But he can’t, so consumption is right at the kink.

Now what happens if a person in this situation receives a temporary rise in income? The budget line shifts out, again — and the kink moves directly to the right, taking consumption with it. So whereas someone who can borrow and lend freely will spend very little of a temporary rise in income, someone who is liquidity-constrained — wanting to spend more right now, but unable to borrow — will spend all of that temporary rise.

That’s why unemployment benefits are an effective demand stimulus: the unemployed are highly likely to be suffering a temporary income loss but be unable to borrow cheaply. It’s also why tax cuts for working-class families may have some traction: a fair proportion of those families will be people having a bad year, but without assets or borrowing capacity to draw on.

But temporary tax cuts for people with high incomes are likely to be highly ineffective: there are people with incomes over $250,000 who are having a temporary bad time and have neither assets to sell nor the ability to borrow, but they’re very much the exceptions to the rule.

And that’s why extending the high-end tax cuts is such a bad idea: it would deliver very little bang for a very large number of bucks.