rateAtTarget evolution over the elapsed window
Fixed protocol constants: target utilization 90%, curve steepness 4x, adjustment speed 50/year, rateAtTarget bounded [0.1%, 200%] APR.
| Metric | Value |
|---|
Why the curve remembers, instead of resetting every block
A kinked Aave-style model recomputes the rate from scratch on every block using only current utilization — it has no memory. Morpho's AdaptiveCurveIRM adds a second layer: the anchor point itself (rateAtTarget) is a piece of state that persists between interactions and keeps climbing or falling for as long as utilization sits off the 90% target, at a speed proportional to the size of that gap. That's deliberate — a market that's been running hot for two weeks should charge more than one that just ticked over 95% a minute ago, even at identical utilization, because sustained demand is a stronger signal than a momentary spike. See Aave vs Compound vs Morpho to compare this against the static kink model side by side.
Reading the two-layer rate, not just the headline APY
The instant borrow APR you see quoted on a Morpho market UI is the product of two independent numbers: rateAtTarget, the slow-moving anchor that only this calculator's "days elapsed" field lets you evolve, and the curve multiplier, a fast-moving function of the current utilization error that reacts instantly to every deposit or withdrawal. At exactly 90% utilization the multiplier is always 1.0x — the instant rate equals rateAtTarget exactly, no matter what. Move above 90% and the multiplier climbs linearly up to 4x at 100% utilization; move below and it falls to 0.25x at 0% utilization. That asymmetry (4x headroom above target, only 0.25x below) is intentional: it lets the model punish over-borrowing far harder than it rewards under-borrowing, because liquidity risk only bites in one direction.
The exponential drift compounds on top of that multiplier. Because rateAtTarget updates continuously as startRate × e^(speed × elapsed) where speed itself scales with the utilization error, a market stuck at 95% utilization doesn't just sit at 4x the anchor forever — the anchor itself roughly doubles every 10 days, so the effective instant rate compounds on top of an already-elevated multiplier. That's a materially different risk profile from Aave's static kink: on Morpho, "utilization has been high for a while" is itself priced in, separately from "utilization is high right now." A borrower checking only the current multiplier and ignoring how long the market has been off-target is missing half the picture — and the average rate actually charged over any accrual period is a trapezoidal blend of the start and end rateAtTarget, not just the instant snapshot at either end.