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Liquidity pool dynamics

Liquidity pools are the dispenser contracts of the protocol that holds ASAs. Each pool holds a specific ASA. This paragraph explains how the utilisation ratio U influences the interest rates.

Utilization Ratio

The pool's Utilization Ratio, *U,* is defined as the ratio between the total borrows and the total liquidity, calculated as the sum of the total deposits:

$U = \frac{Total Borrows}{Total Liquidity}$

The protocol leverages the *U* to maintain the pool balance among all deposits and borrows. Generally, if *U* tends to 1, the available capital becomes scarce, resulting in a possible problematic situation of unavailable funds for depositorâ€™s withdrawal requests.

$U$

carries a high value, the protocol will exhibit a low borrowing capacity, as well as a low redeem capacity. Therefore, the borrow interest rate, and consequently, the deposit interest rate both increase to disincentivize new loans and incentivize new deposits. So, when On the contrary, if

$U$

moves lower, the protocol, on that specific pool, will offer lower returns on deposited capital, so it must incentivize new loans. Therefore, the borrow interest rate and consequently the deposit interest rate will both decrease to incentivize new borrows and disincentivize further deposits.So the protocol implements these rules:

- High$U$--> high interest rates --> incentive deposits
- Low$U$--> low interest rates --> incentive borrows

Impact of Utilization ratio on interest rates

The relation that links the

$U$

and the interest rates is a semi-linear formula made up as follows:- from zero to a safety threshold$U_{opt}$, the rate follows a linear growth with a gentle scope.
- from the safety threshold to 1 (100% utilization), the course is linear but with a steeper slope.

For precisely modelling the

$U$

behavior, four values are defined as follows:(*Uoptimal*$U_{opt}$) indicates the optimal utilization*ratio.*Once$U$reaches this value, it is necessary to encourage deposits, and drastically reduce loans. This is done by increasing the slope of the line, thus resulting in a high increase in both the borrow and deposit APRs.(*Base*$R_0$) is the line intercept representing the initial borrowing rate, when$U=0$.(*Slope 1*$R_1$) and(*Slope 2*$R_2$)respectively, indicate the slope of the interest rate function before and after the*,*$U_{opt}$.

Behaviour of the interest rate as the Utilisation Ratio varies

Parameters of the example above

Value

Optimal Utilization Ratio (

$U_{opt}$

)80%

Base (

$R_0$

)1%

Slope 1 (

$R_1$

)4%

Slope 2 (

$R_2$

)60%

Token parameters

Uopt

R0

R1

R2

RR

EPSILON

ALGO

0.7

0

0.11

3

0.1

1

gALGO

0.7

0

0

0

0.1

1

USDC

0.85

0

0.09

1

0.1

1

USDt

0.85

0

0.09

1

0.1

1

goBTC

0.6

0

0.08

3

0.1

1

goETH

0.6

0

0.08

3

0.1

1

gALGO3

0.7

0

0

0

0.1

1

Planets

0.6

0

0.07

3

0.1

1

ALGO/gALGO PLP

0.7

0

0

0

0.1

1

ALGO/USDC TMP1.1

0.7

0

0

0

0.1

1

ALGO/USDC PLP

0.7

0

0

0

0.1

1

ALGO/gALGO3 TMP1.1

0.7

0

0

0

0.1

1

ALGO/gALGO3 PLP

0.7

0

0

0

0.1

1

USDC/gALGO TMP1.1

0.7

0

0

0

0.1

1

USDC/USDt TMP1.1

0.7

0

0

0

0.1

1

USDC/USDt PLP

0.7

0

0

0

0.1

1

goBTC/gALGO PLP

0.7

0

0

0

0.1

1

goBTC/gALGO PLP

0.7

0

0

0

0.1

1

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Utilization Ratio

Impact of Utilization ratio on interest rates