Office Hours: Costs of Inflation

Today's practice question is about expected inflation, taxes, and saving. We know that the government taxes any nominal interest you earn on a savings account. So, for this scenario, let's assume a realistic 33% tax rate. Now, if you're rational, you should care mostly about your real interest rate after taxes when deciding how much to save. So, in each case, we'll calculate the nominal rate of return after taxes. And then, most importantly, that real rate of return after taxes, which takes inflation into account. As always, check out our video on inflation before trying to solve this problem.

And one final note, before we get started. Recall that the real interest rate is simply the nominal interest rate minus inflation. In each of these cases, the nominal interest rate has actually adjusted for inflation, such that the real interest rate before taxes is 3%. In other words, inflation is expected. No surprises here. The real interest rate after taxes, though, which we'll calculate, differs from case to case.

So, let's tackle that first case. Your savings account offers a nominal interest rate of 6%, and inflation is 3% that year, fairly low. To make this more concrete, let's assume you saved $100. So, at the end of the year, you earned 6% on your $100, or $6 in interest. The government will take a third of your $6 in taxes, so you'll get to keep 2/3. of $6, or $4. You started with $100 and earned $4 after taxes, so your nominal rate of return is 4%.

Now, to calculate your real rate of return after taxes, the rate that actually matters, we have to adjust for inflation. Inflation is 3%. So, after a year, your initial $100 would be equivalent to $103. So, you gain $4 after taxes from interest, but three of those dollars are just making you break even, given inflation. So, your real gain after taxes is just $1. Given that you saved $100, we could also view this as a real return of 1% after taxes.

Just to recap, before taxes and inflation, you earned 6%. But after taxes and inflation, your real gain was 1%. It's a lot lower, but it is still positive. How about that next scenario, when inflation is 9% that year and the nominal interest rate on your savings account is 12%. We won't convert our calculation to dollars this time. So, to calculate the nominal rate of return after taxes, we'll multiply the nominal interest rate, 12%, by what proportion we'll actually get to keep after taxes, 2/3, which equals 8%. Now, for the real rate of return, the one that matters, accounting for inflation as well: 8% minus inflation, which is 9%, equals -1%, a negative rate of return. Surprisingly, you lose money by saving when there are moderate levels of expected inflation.

Now, it's time to get more extreme. Let's say inflation is 87% per year, and the nominal interest rate is 90%. Once again, the nominal rate of return after taxes is 90 times 2/3, or 60%. And the real rate of return after taxes? 60% minus inflation, which is 87%, equals -27%. Would you invest in a company that Offered you a -27% rate of return? No! So why would you put your money in a savings account with similar results? And keep in mind, just sticking your money under your mattress is even worse, because then you wouldn't be earning any interest.

So, you would lose even more in real terms. Honestly, I'm scared to do that last calculation, so I'll leave it as a practice question after this video. Just think about how you would respond in this situation. If inflation were, say, 900% per year, the money supply is increasing such that prices are rising daily, and even though it's expected high inflation, the tax system discourages savings. The rational person in this instance would try to spend any money she got as fast as she could. And sadly, this actually makes the problem worse. Because if everyone does this, money is turning over more quickly, so velocity has also increased. The quantity theory of money predicts that prices will rise even more.

So, the surprising takeaway here is that even moderate levels of expected inflation, like our example of 9% inflation, can still lead to financial intermediation failure when the tax system distorts the real rate of return on savings.