Automated Market Makers (AMM) in Blockchain / Solidity

Introduction

Automated Market Makers (AMMs) help people trade cryptocurrencies without needing a middleman. They use math formulas to set prices and let anyone buy or sell tokens easily.

You want to trade tokens on a decentralized exchange without waiting for a buyer or seller.

You want to provide liquidity to earn fees by adding your tokens to a pool.

You want to understand how prices change automatically based on supply and demand.

You want to build or use a decentralized finance (DeFi) app that needs token swaps.

You want to learn how blockchain apps handle trading without traditional order books.

Syntax

Blockchain / Solidity

function getAmountOut(amountIn, reserveIn, reserveOut) {
  const amountInWithFee = amountIn * 0.997;
  const numerator = amountInWithFee * reserveOut;
  const denominator = reserveIn * 1 + amountInWithFee;
  return numerator / denominator;
}

This function calculates how many tokens you get when you swap.

It uses a simple formula from the constant product model: reserveIn * reserveOut = constant.

Examples

Swapping 100 tokens when both reserves are 1000 returns about 90.73 tokens out.

Blockchain / Solidity

const amountOut = getAmountOut(100, 1000, 1000);
console.log(amountOut);

Swapping 50 tokens with different reserves shows how output changes with pool size.

Blockchain / Solidity

const amountOut = getAmountOut(50, 500, 1500);
console.log(amountOut);

Sample Program

This program shows how many TokenB you get when swapping 100 TokenA using an AMM formula.

Blockchain / Solidity

function getAmountOut(amountIn, reserveIn, reserveOut) {
  const amountInWithFee = amountIn * 0.997;
  const numerator = amountInWithFee * reserveOut;
  const denominator = reserveIn * 1 + amountInWithFee;
  return numerator / denominator;
}

const reserveTokenA = 1000;
const reserveTokenB = 1000;
const amountInTokenA = 100;

const amountOutTokenB = getAmountOut(amountInTokenA, reserveTokenA, reserveTokenB);
console.log(`Swapping ${amountInTokenA} TokenA gives you ${amountOutTokenB.toFixed(2)} TokenB`);

Important Notes

AMMs use a fee (like 0.3%) to reward liquidity providers.

The constant product formula keeps the pool balanced and prices fair.

Prices change automatically based on how much you swap and the pool reserves.

Summary

AMMs let you trade tokens without a middleman using math formulas.

They use reserves and a constant product formula to set prices.

You can calculate how many tokens you get from a swap with a simple function.

Practice

1. What is the main purpose of an Automated Market Maker (AMM) in blockchain?

easy

A. To enable token trading without a middleman using math formulas

B. To store user passwords securely

C. To mine new blocks in the blockchain

D. To create new tokens automatically

Solution

1. Step 1: Understand AMM's role

   AMMs allow users to trade tokens directly without needing a traditional exchange or middleman.

2. Step 2: Identify the key feature

   They use mathematical formulas and token reserves to set prices and enable swaps.

3. Final Answer:

   To enable token trading without a middleman using math formulas -> Option A

4. Quick Check:

   AMM = trading without middleman [OK]

Hint: AMMs trade tokens using formulas, no middleman needed [OK]

Common Mistakes:

• Confusing AMM with mining or token creation
• Thinking AMM stores passwords
• Assuming AMM creates tokens automatically

2. Which of the following is the correct formula used by a constant product AMM to maintain balance?

easy

A. x + y = k

B. x - y = k

C. x / y = k

D. x * y = k

Solution

1. Step 1: Recall AMM constant product formula

   AMMs use the formula where the product of token reserves remains constant.

2. Step 2: Identify the correct formula

   The formula is x * y = k, where x and y are token reserves and k is constant.

3. Final Answer:

   x * y = k -> Option D

4. Quick Check:

   Product of reserves = constant [OK]

Hint: Remember: AMM uses multiplication for constant product [OK]

Common Mistakes:

• Using addition or subtraction instead of multiplication
• Confusing division with the formula
• Mixing up variables and constants

3. Given an AMM with reserves x = 100 and y = 200, what is the new y reserve after adding 10 tokens to x and keeping k constant?

medium

A. 181.82

B. 220

C. 190

D. 200

Solution

1. Step 1: Calculate constant k

   k = x * y = 100 * 200 = 20000.

2. Step 2: Calculate new y after adding 10 to x

   New x = 100 + 10 = 110. New y = k / new x = 20000 / 110 ≈ 181.82.

3. Final Answer:

   181.82 -> Option A

4. Quick Check:

   New y = 20000 / 110 ≈ 181.82 [OK]

Hint: Divide k by new x to find new y quickly [OK]

Common Mistakes:

• Adding instead of dividing to find new y
• Using old y value without adjustment
• Forgetting to add tokens to x before calculation

4. Identify the error in this Python function that calculates output tokens from an AMM swap:

def get_output_amount(x_reserve, y_reserve, x_in):
    k = x_reserve * y_reserve
    new_x = x_reserve + x_in
    new_y = k / new_x
    return y_reserve - new_y

medium

A. The function returns new_y instead of the difference

B. The function uses addition instead of multiplication for k

C. The function does not account for swap fees

D. The function uses integer division instead of float division

Solution

1. Step 1: Review function logic

   The function calculates k correctly and finds new reserves after swap.

2. Step 2: Check for missing AMM details

   It does not include swap fees, which reduce the effective input amount.

3. Final Answer:

   The function does not account for swap fees -> Option C

4. Quick Check:

   Missing fees in calculation [OK]

Hint: Remember to subtract swap fees from input amount [OK]

Common Mistakes:

• Ignoring swap fees in calculations
• Confusing return values
• Using integer division in Python 3 (which is float by default)

5. You want to implement a function that calculates the output token amount from a swap on an AMM with a 0.3% fee. Given reserves x=500, y=1000, and input x_in=50, which code snippet correctly calculates the output amount?

hard

A. def swap_output(x, y, x_in):
fee = 0.003
x_in_with_fee = x_in + fee
k = x * y
new_x = x + x_in_with_fee
new_y = k / new_x
return y - new_y

B. def swap_output(x, y, x_in):
fee = 0.003
x_in_with_fee = x_in * (1 - fee)
k = x * y
new_x = x + x_in_with_fee
new_y = k / new_x
return y - new_y

C. def swap_output(x, y, x_in):
fee = 0.003
x_in_with_fee = x_in * fee
k = x * y
new_x = x + x_in_with_fee
new_y = k / new_x
return y - new_y

D. def swap_output(x, y, x_in):
fee = 0.003
x_in_with_fee = x_in / (1 - fee)
k = x * y
new_x = x + x_in_with_fee
new_y = k / new_x
return y - new_y

Solution

1. Step 1: Calculate effective input after fee

   The input tokens are reduced by the fee: x_in_with_fee = x_in * (1 - 0.003).

2. Step 2: Calculate new reserves and output

   Use constant product k = x * y, then new_x = x + x_in_with_fee, new_y = k / new_x, output = y - new_y.

3. Final Answer:

   Code snippet B correctly applies the fee and calculates output -> Option B

4. Quick Check:

   Subtract fee before adding input [OK]

Hint: Multiply input by (1 - fee) before calculation [OK]

Common Mistakes:

• Adding fee instead of subtracting
• Multiplying input by fee only
• Dividing input by (1 - fee) incorrectly