We analyze dynamic capital allocation and risk sharing between a principal and many agents, who privately observe their output.

The state variables of the mechanism design problem are aggregate capital and the distribution of continuation utilities across agents. This gives rise to a Bellman equation in an infinite dimensional space, which we solve with mean-field techniques.

We fully characterize the optimal mechanism and show that the level of risk agents must be exposed to for incentive reasons is decreasing in their initial outside utility.

We extend classical welfare theorems by showing that any incentive- constrained optimal allocation can be implemented as an equilibrium allocation, with appropriate money issuance and wealth taxation by the principal.

This paper studies executive pay with fairness concerns: if the CEO's wage falls below a perceived fair share of output, he suffers disutility that is increasing in the discrepancy. Fairness concerns do not always lead to fair wages; instead, the firm threatens the CEO with unfair wages for low output to induce effort. The contract sometimes involves performance-vesting equity: the CEO is paid a constant share of output if it is sufficiently high, and zero otherwise. Even without moral hazard, the contract features pay-for-performance, to address fairness concerns and ensure participation. This rationalizes pay-for-performance even if effort incentives are unnecessary.

I develop a model of screening with imperfect competition. The model has a unique equilibrium in pure strategies, which I characterise in closed form. I apply the model to the credit market and show that decreasing competition can be a Pareto improving policy. It alleviates the credit rationing that stems from adverse selection and reduces the maturity or interest rate spread between contracts. Similarly, I show that increasing the marginal lending costs can reduce credit rationing and contract characteristics spreads and can lead to a Pareto improvement. The welfare impact depends on the level of competition and which type of contracts (e.g., long versus short maturity contracts, high versus low Loan-to-Value or loan amount) are mostly affected by the marginal cost change. This result has new implications for capital requirements and monetary policy.