Automated Market Makers (AMM) in Blockchain / Solidity - Mini Project: Build & Apply

Automated Market Makers (AMM) Simulation

📖 Scenario: You want to understand how a simple Automated Market Maker (AMM) works in a blockchain environment. An AMM allows users to trade tokens automatically using a liquidity pool without needing a traditional order book.In this project, you will simulate a basic AMM that holds two tokens and uses the constant product formula to determine prices and trades.

🎯 Goal: Build a simple Python program that models an AMM liquidity pool with two tokens, calculates the price based on reserves, and simulates a token swap.

📋 What You'll Learn

Create a dictionary to represent the liquidity pool with exact token reserves

Add a variable for the swap fee percentage

Write a function to calculate the output amount of tokens for a given input amount using the constant product formula

Print the amount of tokens received after a swap

💡 Why This Matters

🌍 Real World

Automated Market Makers are used in decentralized exchanges on blockchains to enable token trading without traditional order books.

💼 Career

Understanding AMMs is important for blockchain developers, DeFi engineers, and anyone working with decentralized finance applications.

1

Set up the liquidity pool reserves

Create a dictionary called liquidity_pool with these exact entries: 'TokenA': 1000 and 'TokenB': 1000 to represent the initial reserves of each token.

Blockchain / Solidity

# Create the liquidity_pool dictionary with TokenA and TokenB reserves
# Your code here

Hint

Use curly braces to create a dictionary with keys 'TokenA' and 'TokenB' and values 1000 each.

2

Add the swap fee configuration

Create a variable called swap_fee and set it to 0.003 to represent a 0.3% fee on swaps.

Blockchain / Solidity

liquidity_pool = {'TokenA': 1000, 'TokenB': 1000}
# Set the swap_fee variable to 0.003
# Your code here

Hint

Assign the decimal 0.003 to the variable swap_fee.

3

Write the swap calculation function

Define a function called calculate_swap_output that takes three parameters: input_amount, input_reserve, and output_reserve. Inside the function, calculate the amount of output tokens received after applying the swap fee and using the constant product formula: output_amount = (input_amount_with_fee * output_reserve) / (input_reserve + input_amount_with_fee), where input_amount_with_fee = input_amount * (1 - swap_fee). Return the output_amount.

Blockchain / Solidity

liquidity_pool = {'TokenA': 1000, 'TokenB': 1000}
swap_fee = 0.003

# Define calculate_swap_output function below
# Your code here

Hint

Use the formula given and remember to apply the swap fee before calculating output.

4

Simulate a token swap and print the output

Use the calculate_swap_output function to calculate how many 'TokenB' tokens you get when swapping 100 'TokenA' tokens. Store the result in a variable called tokens_received. Then print the exact string "Tokens received: {tokens_received:.6f}" using an f-string to show 6 decimal places.

Blockchain / Solidity

liquidity_pool = {'TokenA': 1000, 'TokenB': 1000}
swap_fee = 0.003

def calculate_swap_output(input_amount, input_reserve, output_reserve):
    input_amount_with_fee = input_amount * (1 - swap_fee)
    output_amount = (input_amount_with_fee * output_reserve) / (input_reserve + input_amount_with_fee)
    return output_amount

# Calculate tokens_received for swapping 100 TokenA and print the result
# Your code here

Hint

Call the function with input_amount=100, input_reserve=liquidity_pool['TokenA'], output_reserve=liquidity_pool['TokenB'], then print with 6 decimals.

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