As many have observed, within a system of wage-labor, a rational worker (at least, one that does not expect a promotion) will work hard enough to avoid being fired. Within a system in which the worker can expect the full profits of their labor, a rational worker would work harder — and, further, one would expect that this would vary continuously as one mixed the two conditions.

That is to say, if:

P is the worker’s actual productivity

A is their productivity when they only get wages, as within a capitalist firm

A+B is their productivity when they get wages AND get their share of the profits, as within a cooperative (though, I believe, a cooperative would actually have greater productivity than this — the benefits of greater information-sharing through the internal alignment of incentives)

and x is the share of the profits that they actually are getting within whatever system they are actually in

Then one would expect:

If we assume that this is a capitalist firm in which the owner is voluntarily allowing some profit-sharing, then we would expect the owner to choose x such that:

being the owner’s cut of the worker’s productivity, is maximized.

Given these definitions and assumptions, it is possible to mathematically prove that the decision of firms within an industry to not share profits is only evidence that 100% profit-sharing (i.e., as in a worker cooperative) would multiply worker productivity by up to (but no greater than) two.

This means that allowing individual firms to decide on what they will share with their own workers represents a miscalibration of norms and incentives within the market, leading to a large economy-wide reduction in worker productivity, which leads to a reduction in incomes for both firms and workers.

Essentially, a lack of profit-sharing is the result of a set of choices that are individually entirely rational, but lead to everyone being worse-off. Therefore, there is a strong argument for using government regulation to mandate profit-sharing.