How can an economy pay for all the products it produces? How can the totality of an economy pay for all the products it produces, if the initial amount of money in the system (before the profits on all of the products is realized) is less than the amount of money after all of the products are sold (at a profit)? The arithmetic does not seem to make sense. Any suggestion out of this riddle?
This is not really a riddle.
First, amount of money in economy is not constant. The amount of money economy has access to is typically growing thanks to policy of central bank/government. For example, you can see from Fred data that amount of money in the US measured by $M2$ increases over time (you can check similar statistics for almost any other country you want save for few that don’t publish it).
However, even if amount of money would be fixed that wouldn’t cause any issue. A price level in an economy is determined by the output and other factors so economy can’t really run out of money.
For example, following Mankiw Macroeconomics 8th Ed money market equilibrium can be described by:
$$MV=PY$$
Where $M$ is money stock, $V$ velocity of money (how often one banknote is used), $P$ is price level (aggregate prices) and $Y$ real output (this is only most simple representation of money market, in more complex models expectations of these quantities matter as well but for this explanation this simplified version will more than suffice).
Hence, if the amount of goods and services increases in the economy ($Y$ goes up), even if $M$ is fixed either $P$ can drop or $V$ can increase (or some combination of those two) to offset $Y$ and make sure that the amount of money in economy is sufficient to purchase or goods and services.
Consequently, economy will always be able to pay for what it produces. Heck, money is strictly speaking not even necessary - people could just barter with each other - money just helps transactions to run smoother.