Automated Market Makers (AMM) in Blockchain / Solidity - Step-by-Step Execution

Concept Flow - Automated Market Makers (AMM)

User provides Token A and Token B

↓

AMM Pool receives tokens

↓

Calculate new token reserves

↓

Apply constant product formula: x * y = k

↓

Determine output token amount

↓

User receives swapped tokens

↓

Update pool reserves for next trade

The AMM takes tokens from the user, updates reserves using a formula, and returns swapped tokens, keeping the product of reserves constant.

Execution Sample

Blockchain / Solidity

reserveA = 1000
reserveB = 1000
inputA = 100
k = reserveA * reserveB
newReserveA = reserveA + inputA
newReserveB = k / newReserveA
outputB = reserveB - newReserveB

This code swaps Token A for Token B using the constant product formula in an AMM pool.

Execution Table

Step	Variable	Value	Calculation/Action	Explanation
1	reserveA	1000	Initial reserve	Starting Token A in pool
2	reserveB	1000	Initial reserve	Starting Token B in pool
3	inputA	100	User input	User adds 100 Token A to swap
4	k	1000000	reserveA * reserveB	Constant product remains fixed
5	newReserveA	1100	reserveA + inputA	Pool now has 1100 Token A
6	newReserveB	909.09	k / newReserveA	Calculate new Token B reserve
7	outputB	90.91	reserveB - newReserveB	User receives ~90.91 Token B
8	-	-	-	Swap complete, reserves updated

💡 Swap ends after calculating output tokens and updating reserves.

Variable Tracker

Variable	Start	After Step 3	After Step 5	After Step 6	Final
reserveA	1000	1000	1100	1100	1100
reserveB	1000	1000	1000	909.09	909.09
inputA	-	100	100	100	100
k	-	-	1000000	1000000	1000000
newReserveA	-	-	1100	1100	1100
newReserveB	-	-	-	909.09	909.09
outputB	-	-	-	90.91	90.91

Key Moments - 3 Insights

Why do we multiply reserveA and reserveB to get k?

Because the AMM uses the constant product formula x * y = k to keep the pool balanced, as shown in step 4 of the execution_table.

Why does outputB equal reserveB minus newReserveB?

Because the user receives the difference in Token B reserves after the swap, as calculated in step 7 of the execution_table.

Why do we add inputA to reserveA before calculating newReserveB?

Because the pool's Token A reserve increases by the user's input before recalculating Token B reserve, shown in step 5.

Visual Quiz - 3 Questions

Look at the execution_table at step 6, what is the value of newReserveB?

A 909.09

B 1000

C 1100

D 90.91

💡 Hint

Check the 'Value' column at step 6 in the execution_table.

At which step does the pool calculate the constant product k?

A Step 3

B Step 5

C Step 4

D Step 7

💡 Hint

Look for the step where k = reserveA * reserveB is calculated in the execution_table.

If the user inputs 200 Token A instead of 100, which variable changes first in the variable_tracker?

A reserveB

B inputA

C newReserveB

D outputB

💡 Hint

Look at the variable_tracker to see which variable records the user input first.

Concept Snapshot

Automated Market Makers (AMM) use a formula x * y = k to keep token reserves balanced.
Users swap tokens by adding one token to the pool.
The pool calculates the output token amount by maintaining k constant.
Reserves update after each swap to reflect new balances.
This allows decentralized token trading without order books.

Full Transcript

Automated Market Makers (AMM) let users swap tokens by interacting with a pool of two tokens. The pool keeps the product of the token reserves constant, called k. When a user adds some amount of Token A, the pool calculates how much Token B to give back so that reserveA times reserveB stays equal to k. This process updates the reserves and completes the swap. The key steps are: starting reserves, user input, calculating k, updating reserves, and determining output tokens. This method allows smooth token swaps without needing buyers and sellers to match directly.

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