General equilibrium with contracts

This paper studies general equilibrium when workers in the economy are also consumers of final goods. Once a firm and a worker are matched, there is a standard moral hazard problem. However, the firm's profit depends on the price of the good the worker produces, and the price is determined by the total supply and demand in the economy. The worker's expected utility also depends on the number of units they consume and therefore depends on the price of the good. I characterize the set of equilibria and show that there is a unique equilibrium level of worker's outside option to price ratio. When the government changes minimum wage, the outside option for workers change through limited liability. In any equilibrium, the price responds proportionally to the change in minimum wage; the incentivized effort, the expected outcome, consumption and the expected utility of workers all remain exactly the same, and only the prices change as a result.