People live in households, and a household can receive both a wage and a dividend. The functional distribution divides income between the factors that produced it; the personal distribution follows the income to its recipients. Ownership connects the two. Consider an illustrative economy with two households, each earning thirty-five, and thirty of capital income. If the first household owns all the capital, their incomes are sixty-five and thirty-five. If they own equal shares, both receive fifty. The national division remains seventy to labor and thirty to capital in either case. A change in that division therefore reaches persons through the distribution of earnings and ownership. The categories also cross within a life: the worker can hold a pension claim, the owner can draw a salary, and the highest wage can enter the same household as the largest dividend. The share requires a second map before it describes who receives what.1
The income that remains unspent carries this year's division into next year's stock. Wealth, in the account used by Piketty and Zucman, is the market value of owned nonhuman assets less liabilities: land, housing, businesses and financial claims, including funded pension claims. It records what a household owns at a date; an annual income records what arrives over an interval. Suppose a household begins with wealth of a hundred, earns twenty from work and receives five from its assets, and consumes twenty-two. With no taxes, transfers, depreciation or changes in asset prices, it finishes with a hundred and three. An additional rise of ten in the value of its existing assets would take it to a hundred and thirteen. The first addition is saving out of income; the second is a holding gain. Both change the balance sheet, through different routes.2
Saving makes the distribution of income consequential for the distribution of wealth without mechanically reproducing it. A person whose earnings barely meet expenditure has little to carry forward. Another can add to an existing portfolio, and the added assets can themselves generate income. Different consumption needs, risks, debts and opportunities enter this process; a shared annual income need not imply a shared capacity or decision to save. Returns can differ as well, and a large loss can undo years of accumulation. Benhabib and Bisin organize the theory around these separate mechanisms: earnings, saving behavior, returns and the transmission between generations. Their accumulation equation makes the discipline plain. What happens to wealth depends on what its owner receives and retains, together with the return on what was already held. The history of a fortune is a sequence of those decisions and events.3
The comparison between the return on wealth and the economy's growth rate concerns a different denominator from the concentration of ownership. Imagine two fortunes of eighty and twenty. If both earn and retain five percent, they become eighty-four and twenty-one; the first still represents eighty percent of their combined wealth. If national income grows by two percent, both fortunes have grown relative to income while their relative ownership remains unchanged. If both owners instead consume the entire return, neither fortune grows. The relation r > g can make inherited wealth easier to sustain relative to current income, but the return is available for consumption, taxation or reinvestment. A theory of increasing concentration must explain differences in the accumulation of fortunes, including entries, losses and divisions. A common percentage return, however large, leaves the proportions in this example exactly where they began.4
Inheritance carries a stock across persons as well as across time. A bequest of a hundred gives one heir a different starting position from a bequest of twenty-five to each of four heirs. In either case, ignoring taxes, costs and changes in value, the transfer leaves a hundred in existence. The identity and number of its holders change. Overlapping generations complicate the measurement further: this year's estates are a flow, while the wealth now held by heirs includes older transfers, gifts, their subsequent returns and the portion already consumed. Piketty and Zucman distinguish these measures and show why counting all past inheritances, or capitalizing all of them without regard to what recipients retained, answers different questions. The past reaches the present through a chain of transfers and uses. Its influence depends on how the chain divides, replenishes or spends the stock.5
The value assigned to existing assets gives the stock another way to change. A house or business can become more valuable because expected receipts rise or the rate used to discount them falls; a buyer then acquires a dearer claim on the future. Measured wealth can increase without a matching addition to buildings or equipment. In the simple long-run account examined by Piketty and Zucman, a stable saving rate divided by a stable growth rate determines the wealth–income ratio only under the specified accumulation and valuation assumptions. It does not supply the distribution of that wealth among households. Nor does a higher stock alone fix capital's income share: the income received per unit of that stock can change. Saving, valuation and ownership must remain visible separately if a rising national total is to tell us anything reliable about the fortunes inside it.
Wealth is the past's deposit in the present, with consequences for what its holder can refuse, undertake and survive. The household with a reserve can endure a lost wage, finance a move or wait for a better offer; the household living from one receipt to the next confronts the same market from another position. The yearly division of income helps to reproduce these differences when unequal receipts become unequal retained claims. Consumption, inheritance, asset prices and losses can reinforce or alter the pattern. The account therefore follows the wage into the saving, the saving into the asset, and the asset into the next recipient's alternatives. Those claims can also reach beyond the country in which their owners live. The final plate turns to that crossing: how a world market changes the product available for division, and the position from which people claim a share.