[UPDATE below with more (apparent) mistakes.]
I’ve been studying this chapter by Feldstein and Krugman on VATs/income taxes (from a 1990 NBER book). It’s excellent, as far as a mathematical model goes. I highly encourage academic economists to check it out.
I think I found a typo, if that motivates some of you to look at it. On the bottom of page 266 they write:
So in that equation (7), in the first two terms after the equals sign, should the superscripts be “1” instead of “2”?
I found two more equations that I think contain mistakes. They both come from page 274:
For equation (16), it seems they are missing the third term altogether? (On the previous page, it was established that L1 was the rebate from the government in period 1, so clearly the L2 in (16) is the rebate from the government in period 2. And what Feldstein/Krugman call “capital consumption allowances” seems to line up with the second term in (16), since this term represents the after-tax real return on the saved output carried forward from period 1.)
Now, looking at equation (18), I have three problems:
First, should the superscripts on the left-hand side be “2” not “1”?
Second, on the right-hand side, if we’re looking at period-1 Wealth and period-2 income separately, wouldn’t it be more natural to include the growth in W in the period-2 income? In particular, equation (16) included the real return to capital brought forward from period 1, so it seems the (1+r*) that is multiplying W in equation (18) is redundant. (I think that equation (16) represents income for the firm, whereas (18) is for the household, but it still seems like an inconsistent treatment of the timing of income.)
Third, even if we assume (inconsistently) that that I2 in equation (18) doesn’t include the real return on wealth created in period 1, then why is W being multiplied by (1+r*)? Shouldn’t we also account for the income tax?
In summary, it seems that there are several typos (if not outright errors) in this paper, but I still think it is a good example of using a mathematical model to address a question in economics. It shows the strengths and weaknesses of the approach. (It’s ironic that I set out to give Krugman his due, and ended up complaining about a bunch of typos.)