Depositing More Should Not Earn Less: Supplier Income Monotonicity and Rate Curve Design in Pooled Lending Markets

Abstract

In utilization dependent interest rate models, adding liquidity can reduce a supplier's total interest income even as the supplier's balance increases. A supplier holding a fraction $α$ of final pool supply keeps income nondecreasing with a marginal deposit exactly when $α(1+η)\leq1$, where $η$ is the elasticity of the borrow rate with respect to utilization. When the condition fails, the supplier can instead raise its income by withdrawing, which pushes utilization further up. On two public Drift markets, a lender held more of the pool than the curve protected in at least one hour in nine on SOL and one in thirteen on USDC. A protocol turns this into a design constraint by choosing, at each utilization, the largest supplier share it intends to protect. That choice caps the elasticity, and integrating the cap describes every admissible curve. Protecting the same share at every utilization gives a power law boundary, and protecting every fresh depositor gives a hyperbolic one. On a multiple kink USDT market, compliant repairs can lower or raise supplier income, because the constraint governs how income responds to a deposit and not the price level.