Some comments on my post on Social Security challenged me to bet. Here is a bet I am willing to make. It concerns the following proof.

1. national output = national income (note that is true by definition in a closed economy, but in an open economy you can in theory earn income on other countries’ output. Let’s ignore the open-economy case here and assume a closed economy.)

2. national income = labor income + capital income + rental income + other

3. capital income = income accruing to shareholders of public companies + interest income + income of privately-held companies + other

4. Leaving out pathological examples that make certain types of income negative, it is impossible for something on right-hand side of one these equations to become larger than the left-hand side. For example, it is impossible for income accruing to shareholders to exceed all of capital income.

5. Therefore, income accruing to shareholders of public companies can never exceed national output.

6. If income accruing to shareholders grows faster than output indefinitely, then eventually income accruing to shareholders must exceed national output.

7. Therefore, income accruing to shareholders cannot grow faster than output indefinitely.

I will bet that you can find nothing wrong with that proof.

Many relevant time horizons are shorter than “indefinitely.” Shorter time horizons may present investors with the opportunity to earn income that grows more quickly than the economy over the relevant time horizon. You are always welcome to make a bet on that by buying mutual fund shares. I have some myself, although these days my portfolio is lighter on U.S. stocks than usual. For Social Security., though, the time horizon you want to think about is pretty long.