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Adjustible Rate Everything

January 14th, 2013
money, inflation

When I wrote about inflation before, people pointed out that inflation is different from swapping currencies because debts aren't updated. Imagine I lend you 10 credits to buy a house. If we decide that credits are an awkwardly large unit of money and switch to a new one, millicredits, at a 1000:1 exchange rate, you'll pay me back 10,000 millicredits and all is well. If instead of switching currencies we have 100,000% inflation, you'll still pay me back 10 credits but I have majorly lost out.

This is all true, but it ignores interest rates. When lending money people ask for more money back than they gave. Why?

The chance that the borrower won't pay the money back. If you're lending money to a many people and think each has a 1 in 10 chance of failing to pay you back, then you could give them $1000, ask for $1111 ($1000 / 90%) in return, and wrongly [1] expect to have the same amount of dollars come back in as went out.
If you expect the $1000 you lend me will be worth only $900 when I pay it back, you'll ask me to pay you back $1111.
You could do many things with your money; I need to make it worth your while to lend to me instead of doing one of those other things.

So you still want to buy a house, I still have 10 credits. I like you and trust you and decide I'm ok with treating your risk as 0% and taking a 0% return. But there might be inflation so we decide that when you pay me back you'll account for inflation. As before hyperinflation happens, but now you pay me back 10,000 credits instead of 10 and I'm happy.

But are you happy? You borrowed 10 and were asked to repay 10,000! How could I expect you to manage that? Well, you're paying me back by working your job at Techsyscorp, and you make 5 credits a year at the time I lend you the 10 credits for your house. Without inflation, if you paid me 1/10th of your salary every year [2], in 20 years I'd have my money back. With inflation you still pay me 1/10th of your salary every year and in 20 years I've been fully repaid. That you paid me back a nominal 10,000 credits [3] instead of 10 doesn't matter.

This is basically an adustible-rate mortgage (ARM). We can do the same thing for saving money, with inflation-indexed bonds (ex: TIPS). If high inflation were a fact of life we would stop approximating inflation as 0% everywhere and start inflation-indexing everything, including loans. Computers being fast and convenient, this is a little annoying, but not too bad. So again: why does inflation matter?

[1] If you lend money to me, John, and Mary, who work together at Techsyscorp and then it turns out that the accounting department got confused and paid all our money to a Nigerian prince, all three of us might lose our jobs at the same time. Our failures to repay weren't independent; some events could leave all of us unable to pay you back all at the same time.

[2] Assuming no raises. Raises don't change the underlying idea; they just make the fraction of your income you're paying decrease in a way that obscures the point.

[3] Well, you actually paid me less than 10,000 credits if we had 1000% inflation over the 20 years because some of your payments were when we had had less inflation so far. But this doesn't matter; I've still been continuously repaid

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