The nature of the bonus function under market socialism and the implications of such functions for a comparison of income distributions under socialist and capitalist economic systems are examined. It is shown that when efficiency is required, when enterprise shutdown rules are taken into account, and when information is decentralized, the bonus will be equal to the profits of the enterprise. Lange's social dividend must be zero. Hence, contrary to previous claims, one can make no strong conclusions when comparing the degree of inequality of the income distribution under competitive capitalism and market socialism.