Management quality drives firm performance and aggregate productivity, yet the supply of managerial talent remains poorly understood. A key friction is that hired managers cannot fully appropriate the surplus they generate, unlike entrepreneurs who own their firms, creating a wedge between private and social returns to management. Here we develop a general equilibrium model to quantify how this corporate governance friction distorts talent allocation between entrepreneurship, management, and employment. Using the universe of Hungarian firms and CEOs (1986--2022), we exploit the transition to capitalism—when the count of enterprises increased from 21,000 to 115,000 in three years—to identify the parameters of the model. We find that managers capture only 60\% of the surplus they create, resulting in too few professional managers and too many less-productive entrepreneurs. Eliminating this friction would raise GDP per worker by 4\% through improved occupational composition. Uniform subsidies fail to correct the misallocation, raising GDP by only 0.1\%. Our results show that management interventions' aggregate effects depend critically on targeting the specific friction between hired managers and entrepreneurs rather than expanding the overall pool of business leaders.