The Demand and Supply of Favours in Dynamic Relationships

We characterise the optimal demand and supply of favours in a dynamic principal-agent model of joint production, in which heterogenous project opportunities arrive stochastically and are publicly observed upon arrival, utility from these projects is non-transferable and commitment to future production is limited. Our results characterise the optimal dynamic contract, and we establish that the principal's supply of favours (the production of projects that benefit the agent but not the principal) is backloaded, that the principal's demand for favours (the production of projects that benefit the principal but not the agent) is frontloaded, and that the production of projects is ordered by their comparative advantage, that is, by their associated efficiency in extracting (for demanded projects) and providing (for supplied projects) utility to the agent. Furthermore, we provide an exact construction of the optimal contract when project opportunities follow a Markov process.