Metaverse Liquidity Pool: AMM & Impermanent Loss

Pool Reserves

◆ MTC 1000.0▲ LAND 1000.0

x·y = k → 1000.0 · 1000.0 = 1,000,000

Swap

Swap amount (input token) 50

Pool fee 0.30%

External Market

External price of MTC (vs LAND) 1.00×

Live Readouts

Pool spot price

1.000 LAND/MTC

Last slippage

0.0%

Impermanent loss

0.0%

Pool value (in MTC)

2000.0

How it works

This models a metaverse DeFi liquidity pool exactly as a constant-product automated market maker (Uniswap-v2 style) works: two reserves, virtual currency MTC and virtual land token LAND, are held so that their product stays (almost) constant:

x · y = k
price(MTC in LAND) = y / x
dy_out = y - k / (x + dx_in·(1-fee))

Every swap moves the pool's reserves along this hyperbola. Because the curve bends, a larger swap gets a worse average price than a small one — that gap between the quoted spot price and the price you actually paid is slippage, shown live after each trade. The trading fee (default 0.30%) is added to the reserves rather than paid out, which is exactly how liquidity providers earn yield.

Impermanent loss compares holding the two tokens outright versus supplying them to the pool, once the external market price has drifted away from the pool's price. For a price ratio change r = P₁/P₀:

IL(r) = 2·√r / (1 + r) − 1

IL is always ≤ 0: an LP's position is worth less than simply holding the tokens whenever the external price has moved, because the pool's arbitrage-driven rebalancing sells the appreciating token and buys the depreciating one. Drag the "External Market" slider away from 1.00× to see it grow.

MTC → LAND / LAND → MTC — pick which token you're selling into the pool.
Swap amount — how much of the input token you send in; larger trades curve further along x·y=k and suffer more slippage.
Pool fee — the cut retained by the pool on every trade, compounding into the reserves.
Execute Swap — commits the trade: reserves update, the 3D towers and curve marker animate, and tokens flow between pools.

MTC reserve LAND reserve x·y=k curve / pool point

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