SMART CONTRACTS, DEFI & WEB3 SECURITY - Chapter 4, Exercise 1 Solution
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Working Out a Real AMM Swap: 50 ETH / 100,000 USDC Pool

PROBLEM
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A pool holds 50 ETH and 100,000 USDC. Using this chapter's own
constant product formula, work out roughly how many USDC a trader
receives for adding 5 ETH to the pool, and what the pool's implied ETH
price is immediately before and after the trade.

SOLUTION
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STEP 1: FIND k
k = x * y = 50 * 100,000 = 5,000,000

STEP 2: PRICE BEFORE THE TRADE
Implied ETH price = USDC / ETH = 100,000 / 50 = 2,000 USDC per ETH

STEP 3: THE TRADE
The trader adds 5 ETH to the pool, so the new ETH quantity is:
  50 + 5 = 55 ETH

To keep k constant at 5,000,000, the new USDC quantity must be:
  5,000,000 / 55 = 90,909.09 USDC (rounded)

STEP 4: USDC RECEIVED
The pool's USDC dropped from 100,000 to approximately 90,909.09, so the
trader receives:
  100,000 - 90,909.09 = 9,090.91 USDC (rounded)

STEP 5: PRICE AFTER THE TRADE
Implied ETH price = USDC / ETH = 90,909.09 / 55 = 1,652.89 USDC per ETH
(rounded)

ANSWER: The trader receives approximately 9,090.91 USDC for adding 5
ETH. The pool's implied ETH price was 2,000 USDC before the trade and
falls to approximately 1,652.89 USDC after it - a real, direct
consequence of the trade itself shifting the pool's own ratio, exactly
matching the mechanism this chapter's own 100 ETH / 200,000 USDC
example demonstrated at a different scale.

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WHY THIS WORKS AS AN ANSWER

This applies the chapter's own x*y=k formula with fresh, different real
numbers, correctly computing k first, then the new pool balance, then
the amount received, and finally the resulting implied price shift -
the same five-step process the chapter's own worked example used.