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

Paper: arXiv 2610.36899

Authors: Ahzam Khan, Cavey Cool

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel and critical insight into pooled lending market design, backed by rigorous mathematical derivation and empirical validation on real-world data. The methodology is clearly explained, and the provision of Lean 4 formalizations and analysis code significantly enhances reproducibility.

Research Flowchart

  flowchart TD
    A[Research Goal: Understand Income Monotonicity in Pooled Lending] --> B{Key Problem: Can adding liquidity reduce supplier income?};
    B --> C[Methodology: Analyze supplier income dynamics with utilization-dependent rates];
    C --> D[Model Input: Supplier share α, Borrow Rate Elasticity η];
    D --> E[Analysis: Derive condition for non-decreasing income: α(1+η) ≤ 1];
    E --> F[Empirical Data: Drift Markets (SOL, USDC) & Multiple Kink USDT Market];
    F --> G[Computational Check: Identify hours where α(1+η) > 1];
    G --> H[Outcomes: Income monotonicity failure observed; Protocol design constraint derived; Admissible rate curves (power law, hyperbolic) described; Impact of repairs on USDT market];