The stock gathers more slowly than a wage arrives, but it can gather where a wage never goes. Earnings are received, spent and received again; a holding can remain, yield an income and be passed on with the unspent return attached. That difference gives wealth a memory. A year of high pay is one event in a worker's life, while a large portfolio can carry the consequences of many earlier years into the next one. Yet memory alone does not tell us whether ownership will spread or narrow. The question is how additions and losses fall across existing holdings, and what can interrupt the advantage of beginning with more.
Concentration concerns shares, so an increasing gap in dollars is only part of the account. Suppose two people own a hundred and nine hundred, and each retains a net five-percent return for a year. Their holdings become a hundred and five and nine hundred and forty-five. The gap widens from eight hundred to eight hundred and forty, but their shares remain one-tenth and nine-tenths. Repeating the same proportional increase preserves those shares however large the numbers become. If the rest of the economy grows more slowly, their combined wealth can rise relative to its annual income at the same time. A rising wealth-income ratio, a rising absolute gap and a rising concentration of ownership are distinct changes; the first two do not prove the third.
Different accumulation rates can move the shares. Let the smaller holding retain two percent and the larger six percent: a hundred and two now stands beside nine hundred and fifty-four, and the larger owner's share rises to about ninety and a third percent. The difference could reflect investment returns, spending, taxes or losses; the calculation does not identify its cause. Conversely, return to the common five-percent case and let the smaller owner add fifty from other income. Holdings become a hundred and fifty-five and nine hundred and forty-five, and the larger share falls to about eighty-six percent even though its owner's wealth has grown. The force that gathers fortunes must therefore be stated in terms of the additions people actually retain, not merely the fact that a return exists.
Saving from earnings gives one route by which the distribution of the flow reaches the distribution of the stock. People with the same income can save different amounts because their needs, ages, dependents and existing reserves differ. People with different incomes can face the same unavoidable expense and have very different amounts left. The ownership income yielded by a prior fortune can then provide resources for further saving without additional paid work. These mechanisms can reinforce one another, but none permits every difference in holdings to be read as a difference in virtue. The account must distinguish resources available to save from decisions about how much of those resources to retain.
Uncertain returns add another route to a highly unequal distribution. Some owners experience large gains, others losses, and a sequence of successes can carry a holding far from its starting point. Benhabib and Bisin survey models in which such accumulation combines with earnings, consumption and intergenerational turnover to produce a long upper tail. The mechanisms differ: a persistent saving advantage, variable returns and a fortune divided at death do different work. A distribution can remain highly concentrated even as particular people enter and leave its upper ranks. Conversely, a familiar name staying wealthy does not establish that the whole distribution has become more concentrated. Mobility of persons and inequality of positions must be examined separately.
The value attached to existing assets can also change the distribution without a new act of saving. Consider an owner with a house worth a hundred and a debt of eighty. Net wealth is twenty. If the house rises to a hundred and twenty while the debt stays fixed, net wealth becomes forty; a twenty-percent asset-price rise has doubled the owner's equity. If the house instead falls to eighty, the equity vanishes. The same percentage change in an unborrowed asset produces a much smaller percentage change in net worth. Leverage can magnify gains and losses, and different portfolios expose households to different revaluations. Observing who became richer is the beginning of an explanation, not proof that each received a higher reward for a new contribution.
The historical record establishes substantial concentration without establishing an uninterrupted law of increase. In the French series presented by Piketty and Zucman in 2015, the top tenth held roughly nine-tenths of wealth on the eve of the First World War, while its share near the end of their record was around three-fifths. The later figure still describes a sharply unequal distribution, and the authors warn about the difficulty of measuring large modern holdings. But the movement is enough to defeat the claim that concentration must rise in every period. Their comparison of European countries traces a large twentieth-century expansion of wealth held below the top tenth, especially in the middle of the distribution. History supplies changes to explain, not a single curve that ownership is bound to follow.
The categories used to describe that history matter. The chapter's wealth measure is market-valued, owned nonhuman assets less liabilities; it excludes household consumer durables and unfunded public pension promises. That is a coherent measure of transferable holdings. It does not inventory every protection a person has, every service the state supplies, or every advantage acquired through education. A society could change public retirement provision without producing an equal change in measured private wealth. That would not make its wealth account false. It would make the account incomplete as a description of security, which is the question The Buffer will take up next.
Measuring the largest holdings is especially consequential because a small number of cases can move a large share of the total. Surveys can miss or mismeasure them; tax records cover what the relevant rules require and what is declared. Estimating wealth from the income it yields requires a capitalization factor, and equal income does not imply equal wealth when returns differ. Estates reveal wealth at death rather than directly revealing the holdings of the living. Piketty and Zucman describe the adjustments needed to combine these sources. The resulting uncertainty is a reason to compare definitions and methods carefully, not a reason to treat every estimate as equally arbitrary or to ignore the broad inequality that different records disclose.
The rules of transmission and ownership help determine whether concentration reproduces itself. A fortune divided among several people can become several independent holdings, or remain pooled under a common arrangement that preserves effective control. A levy can reduce private holdings while financing assets or services available to others; an exemption can favor one form of wealth over another. Entry into a profitable activity can spread its return, while a protected position can preserve it for existing owners. Each mechanism changes a particular margin. There is no need to imagine that every institution acts in the same direction to recognize that the distribution is made within institutions rather than outside them.
The practical question is consequently which forces sustain the observed concentration and which proposed changes can reach them. A policy aimed at inheritance will not by itself explain a surge in the value of newly founded businesses. A policy aimed at asset-price gains will not by itself distribute the capacity to save from wages. Access to housing, the cost of debt, the ownership of pensions and the incidence of taxation each enter different people's accounts. Their effects can reinforce or offset one another. To call concentration natural conceals these choices; to promise that one lever must reverse it conceals their differences. The measure is useful when it directs attention to the mechanism rather than standing in for one.
Compounding enlarges a fortune; the distribution depends on who keeps the increase.
A large stock can make its own persistence easier, giving its holder more income, more resilience and more room to retain gains. That is a serious source of cumulative advantage. Its strength lies in specified relationships among returns, spending, entry and transmission, not in a theorem that every unequal beginning must converge on one owner. The spreading of fortunes and their gathering are historical outcomes to account for and institutional possibilities to judge. The next plate asks what those holdings let their owners withstand while the account is still being made. The argument remains open.