The Impact of Firm Size on Dynamic Incentives and Investment

Recent empirical studies conclude that small firms have higher but more variable growth rates than large firms. To explore the effect of this size-dependence regularity on moral hazard and investment, we develop a continuous-time agency model with time-varying firm size. Firm size is a diffusion process with two features: The drift is controlled by the agent's effort and the principal's investment decision, and the volatility is proportional to the square root of firm size. We characterize the optimal contract when both parties have CARA utility. The firm improves on production efficiency as it grows, and wages are back-loaded when firm size is small but front-loaded when it is large. Furthermore, there is under-investment in a small firm but over-investment in a large firm