Stairway to Heaven or Highway to Hell: Liquidity, Sweat Equity, and the Uncertain Path to Ownership

Abstract

A principal contracts optimally with an agent to operate a firm over an infinite time horizon when the agent is liquidity constrained and has access to private information about the sequence of cost realizations. We formulate this mechanism design problem as a recursive dynamic program in which promised utility to the agent is the relevant state variable. By establishing that output distortions and the stringency of liquidity constraints decrease monotonically in promised utility, we are able to interpret the state variable as the agent’s equity in the firm. We establish a bang-bang property of optimal contracts wherein the agent is incentivised only through adjustments to his future utility until achieving a critical level of equity, after which he may be incentivised through cash payments, that is, through instantaneous rents. Thus the incentive scheme resembles what is commonly regarded as a sweat equity contract, with all cash payments net of costs (rents) being back loaded. A critical level of sweat equity occurs when none of the agent’s liquidity constraints bind. At this point, the contract calls for efficient production in all future periods and the agent attains a vested ownership stake in the firm. Finally, properties of the theoretically optimal contract are shown to be similar to features common in real-world work-to-own franchising agreements and venture capital contracts.