AbstractOutlines conditions under which the interest of a whole organization is best served by its central management allocating more funds or resources to a sub‐unit or sub‐centre than is optimal (on average) under certainty, or budgeting fewer funds or resoruces than this. Slack is efficient in the former case and organizational strain in the latter one, a possibility neglected by Leibenstein in his theory of organizational slack and X‐efficiency. The solution to the problem is simplified, in comparison to Hart's and Theil's approach, by using random net benefit functions. Optimal budget bias is shown to depend on rates of change of marginal net be