Result under these assumptions
Simulating…
- A bitcoin hoard holds its share at best.With fixed supply, money's real value grows with the economy, so a fortune kept in bitcoin grows about as fast as everyone else's. Any spending shrinks its share, unless demand for money keeps outgrowing GDP.
- Day one is a reshuffle.Households holding bitcoin at the switch gain many times over, and everyone else loses the premium on their house and savings. Whether that concentrates wealth depends on how unequally bitcoin is held compared with other wealth.
- Interest rates pull toward concentration.When holding money returns about real growth with no risk, lenders demand more than that. Mortgaged households pay it to people who hold bonds.
- The end of the inflation tax pulls the other way.Cash that holds its value, and no transfer to whoever gets new money first, helps the middle and bottom. Over 50 years it moves the top 1% by a few points, not tens.
Day one
The switch: premiums leave, bitcoin reprices
Each asset loses the share of its price you set as monetary premium. That value reappears as demand for bitcoin. Some goes to people who already held it, and the rest to people who rotate into it as their assets fall. Fiat cash and deposits are converted into bitcoin.
Share of all wealth, by today's wealth group
What happens to each group's wealth
Percent of each group's wealth before the switch. Debt relief is mortgage write-downs net of the losses they impose on lenders.
The next decades
Fiat and the bitcoin standard, same households, same luck
Both worlds start from the same people and get the same random shocks to wages and investments each year. Lines are the average of the runs; shaded bands show the range across them.
Table of values
Why the two worlds differ
From fiat to the bitcoin standard, one change at a time
The model starts from the fiat world and switches on each feature of the bitcoin standard in turn. Each bar is the change that step makes to the final result. The order matters a little, because steps interact.
The "keep their wealth forever" claim
Where a fortune goes, by what it is held in
Take one large fortune and follow it with no luck either way. Its share of all wealth changes each year by the gap between its own return, net of spending, and the growth of total wealth. Returns and wealth growth come from the runs above.
What history says
No clean experiment, several useful ones
There has never been a strictly fixed-supply world money. The classical gold standard is the closest case, but the gold stock grew by roughly 1.5 to 3% a year with mining, close to output growth. The record does not crown either side. Concentration peaked under gold, collapsed through wars, inflation and taxes, and has partly rebuilt under fiat.
Share of wealth held by the richest 10%
Anchor values reported in Piketty (2014), ch. 10. Europe is Britain, France and Sweden.
How to read the evidence
Each case below is tagged by which side it helps. Most are confounded. The gold-standard era had almost no income or estate tax, and the fiat era also brought globalisation and new technology. Treat the cases as ranges for the dials on the left, not as verdicts.
Methods
How to model this properly
No single statistical method answers the question. The usual approach chains three kinds of tool: accounting for the one-off repricing, a dynamic model of how wealth evolves, and history to pin down the parameters.
Inside this model
What a simulated year does
- Each household earns a wage (a fixed skill times GDP per head, with yearly noise) and a return on its capital: 5% real on average, with independent luck for each household. Cars, furniture and other durables earn nothing.
- Borrowers pay interest to lenders. Under fiat the real mortgage rate is set directly. Under bitcoin it is money's own real return plus a lending spread.
- Rent extraction moves a share of GDP from wage earners to owners of capital, in proportion to what each holds.
- Under fiat, cash earns a negative real return. That loss, plus any wage lag, goes to first recipients of new money, weighted by wealth to a power you set.
- Households save part of their wages and spend part of their wealth. Richer households spend a slightly smaller fraction of wealth, as observed in practice.
- Bitcoin's real price follows money demand, which grows with GDP plus any drift you set. Households rebalance toward a target money share.
- A household more than a year's wages underwater goes bankrupt, and its lenders absorb the loss.
Left out: births, deaths and inheritance, taxes, open-economy effects, and feedback from the economy to returns. Growth and the return on capital are inputs, not outputs. If a third of wealth sits in money rather than productive capital, real growth may suffer. The growth dial is where that belief goes.
Where the defaults come from
- Starting wealth shares: World Inequality Report 2022 (world: bottom half 2%, top 10% 76%, top 1% 38%). US: Federal Reserve Distributional Financial Accounts.
- Portfolio mix by wealth group: stylised from the Fed accounts. Housing is the main asset of the middle; stocks and business equity dominate at the top; the bottom half is heavily mortgaged.
- Scale: about $470T of household wealth against about $110T of world GDP. Bitcoin: about 20M coins mined, of which roughly 3.5M are presumed lost.
- Saving out of wages rises with earnings: 3%, 8%, 15% and 30% from bottom half to top 1%, in line with Saez and Zucman (2016).
- Return on capital: 5% real, below the roughly 7% Jordà et al. (2019) find for housing and equities before costs.
- Calibration: under the middle assumptions the fiat world's top 1% share ends a few points higher after 50 years, roughly the recent global trend. The bottom half's share rises for the first decade or so in both worlds as households settle into the model's behaviour.