You can prove results in computability on economic systems. There are classes of problems that are insoluble in a given economic system. In a system such as capitalism where money is held by individuals and spent at discretion in order to maximize the holder’s return, there are two: “refactorings”, which make systems more efficient but have no direct short-term benefit, and “synergies”: problems that raise the standard of living of an entire group significantly more than they raise the standard of living of any given individual. Money is not zero sum because new value can be created, but spending decisions (taken individually at a single point in time) are zero sum, because you have a fixed amount to allocate among a collection of spending choices.

Game theoretically, a rational player in a capitalist economy will always try to spend money in a way that provides the greatest return for himself, monetary or otherwise. A player with knowledge of other player’s strategies will attempt to tie his own monetary gain to the monetary gain of as many other individuals as possible given his resources (this is, for example, where VCs came from). However, this is not the same as providing a benefit to the group as a whole; the holder must reach out and touch everybody directly, because only individuals can make spending decisions. (Corporations, for the purpose of this exercise, can be treated like wealthy individuals, since a corporation’s members usually have common motives).

It’s possible (indeed, easy) to construct a problem which has little individual benefit to the individual members of the group while having an overall benefit to the group’s welfare: for example, reducing carbon emissions, or cutting the use of pesticides in produce to prevent bee populations from collapsing, or becoming a space-faring civilization while there are still few extraterrestrial resources to exploit. These problems all require major changes in behavior, which require investment (as in physics, no Work gets done in the economy without an expenditure of energy/capital), but their benefit to individuals does not justify the investment, even though their benefit to the group does.

These problems are literally outside of what a rational capitalist economy can solve (similar arguments can be constructed for other economic systems). Since we inhabit a mixed economy, and since not all players behave rationally in a game-theoretic sense, the lines are fuzzier in the real world. But the rational strategy will always point to the mean behavior of the system.

Intriguingly, you can bin the ranges of problems available to be solved into classes (much like we do in computational complexity), and use class coverage as a measure of an economic system’s efficiency.

Should we continue to inhabit a mixed economy, the government has then found a just task to take up: aggregate economic interests so that efforts which provide the greatest benefit to group welfare also provide individual returns (and then recoup the difference proportionally from the groups that benefit most, preventing a Robin Hood economy from emerging). This would then increase the coverage of soluble problems within the economy (and the diversity of economic activity taking place), and quantitatively increase its efficiency if measured according to the paragraph above.