A fixed supply in a growing economy: the Bitcoin demonstration

The PaSta whitepaper argues that when a currency's supply is fixed and its economy grows, each transaction has to become a smaller slice of the supply. Bitcoin is the natural test case. This page rebuilds that chart from public chain data and corrects two things the original analysis skipped: newly minted coins, and what happened to the real size of a transaction.

Data through from the blockchain.com charts API (daily: price, confirmed transactions, estimated transaction volume with change outputs removed, coins in circulation, unique addresses, fees). Monthly medians of daily values from 2011. Generated , commit . Reproduce with the commands at the bottom.

1. The coarse model

Take a coin with a fixed supply. Each person wants to hold about the same real amount of money and makes about the same real purchases. If the number of people doubles, the same coins have to serve twice the real economy, so each coin must buy twice as much: price per coin doubles and the number of coins in a typical transaction halves. Price goes up with users; coins per transaction go down as one over users. That is all the model says.

Price per coinCoins per transaction

Toy: fixed supply, users grow 1x to 100x

both axes logarithmic; everything relative to the start

2. Bitcoin, raw: price up, coins per transaction down

This is the whitepaper's chart. Price on top; below it the average transaction size in BTC, computed as estimated transaction volume divided by the number of transactions (estimated volume strips out change outputs, which would otherwise inflate every figure).

Bitcoin price, USD

monthly median, log scale

Average transaction size, BTC

estimated volume / transactions, log scale

3. Correction one: minted coins

Bitcoin's supply is not fixed yet. It roughly tripled over this period (M to M coins), so part of any fall in "BTC per transaction" is just each coin being a smaller share of a bigger pile. The clean quantity is the share of circulating supply moved per transaction. Adjusting makes the fall larger, not smaller, so the original chart understated the effect, as the whitepaper suspected.

BTC per transaction (raw)Share of supply per transaction (adjusted)

Raw vs. supply-adjusted transaction size

both indexed to January 2011 = 1, log scale

4. Does the toy fit? Slice of supply against number of users

If the coarse model is right, the share of supply per transaction should fall as one over the number of users: a straight line of slope minus one on log-log axes. Using daily active addresses as the user count, that is what the early years show. After 2017 the relationship disappears, because active addresses stopped growing while the economy kept growing: block space ran out and activity moved to exchanges and off-chain systems.

2011 to 2016, fees near zero2017 onward, block space scarceToy: slope exactly minus oneFit to all data

Share of supply per transaction vs. active addresses

monthly medians, log-log

Elasticities by era (slope of log y on log x; minus one means exactly inverse)

5. Correction two: what a transaction was actually worth

The whitepaper reads the falling BTC size as transactions tracking purchasing power. If that were the whole story, the USD size of an average transaction would be roughly flat. It is not. It rose from tens of dollars to thousands. Coins per transaction fell about 40% as fast as the price rose (elasticity ), and the other 60% shows up as much larger real transactions (elasticity ). The fee chart says why: once block space became scarce, small payments were priced off the chain and the on-chain average came to reflect large transfers between exchanges and large holders.

Average transaction size, USD

monthly median, log scale

Fee per transaction, USD

monthly median, log scale

Table view: yearly medians

6. What this means for PaSta

Supported. Fixed supply plus a growing economy does shrink the coin size of transactions, and the effect is stronger once minted coins are accounted for. In the years before block space ran out, the share of supply per transaction fell almost exactly as one over the number of users, which is the coarse model's prediction. The deflation signal the whitepaper wants to read is real.

Not supported. Average transaction size was not a clean gauge of purchasing power. The real value of an on-chain transaction moved by two orders of magnitude for reasons that had nothing to do with the coin's value: fee pressure, batching, and the network's shift to a settlement role. This is the same confound the simulator flags as the granularity problem. A payments coin without a block-space cap would suffer less of it, but Bitcoin's history cannot show how much less.

Update: the median tells a different story. Everything above uses the mean, which exchanges and whales dominate. The multi-chain page repeats the test with the daily median: the median Bitcoin transaction was worth about $63 in 2011 and about $68 in 2026, peaking near $800 in 2021, across a 23,000x price move, with an elasticity of median coins per transaction to price of about -0.8. The gauge is usable if it is the median, and it is distorted mainly when fees price small payments off chain.

Two caveats on the data itself. Only the mean transaction size is available for free; the median would be far less dominated by exchange and whale transfers and is worth buying or computing from a full node. And "estimated transaction volume" is a heuristic for removing change outputs, so the absolute levels are approximate even though the trends are robust.

7. Reproduce

git clone https://github.com/pastacoin/pastacoin && cd pastacoin
python -m venv .venv && .venv/Scripts/pip install -e ".[dev,report]"
.venv/Scripts/python -m pasta.analysis.bitcoin_report --figures figures        # uses the committed data/bitcoin-daily.csv
.venv/Scripts/python -m pasta.analysis.bitcoin_report --fetch --figures figures  # refresh from blockchain.com first