The auction hears the bid and not the silence behind it. One person would give a hundred dollars for an improvement, another ten; the hundred wins, and the result arrives wearing the authority of a comparison. Yet a bid has two parents. It descends from the wish for the thing and from the means that can be surrendered to obtain it. The richer voice may speak a weaker wish more loudly. To count the voices in dollars is to measure something real, but it is not yet to measure whose need is greater.
Willingness to pay asks a disciplined question: what is the most this person could give up for a change and remain at least as well off with it? The answer is conditional on what else can be bought, what income and assets are available, whether borrowing is possible, and what commitments already press upon the household. A dollar surrendered is not simply a token removed from a pile. It is something else forgone — food, time, a reserve against an emergency, or another luxury. The same number of dollars can therefore represent very different sacrifices. Nor is a person's entire fortune the sum he is willing to spend on everything he likes. Taste still matters; alternatives still matter; money in reserve has uses of its own. Ability to pay shapes the answer without being identical to it.
An invented example separates the two parents of the bid. Suppose two households face the same unchanged prices for everything else, receive the same personal benefit from access to a small garden, and would each sacrifice precisely one tenth of their available consumption budget to obtain it. One has a hundred dollars; the other a thousand. Their maximum payments are ten and a hundred. At those payments each gives up the same fraction of the rest of its consumption. Nothing in the example has made the richer household's enjoyment of the garden ten times as great. It has only given that household ten times as many dollars with which to express the stipulated preference. An appraisal adding the bids will nevertheless hear a hundred and ten dollars, ninety-one percent of it coming from the richer household.
Give the example a little more structure and the distinction becomes exact. Let each household's preferences be represented by the logarithm of its remaining consumption money, plus a fixed addition for garden access; choose that addition so that access exactly offsets a ten-percent reduction in consumption. This is an assumption for the illustration, not a measurement of anyone's mind. It generates the two bids just described. If four hundred and fifty dollars were transferred from the richer household to the poorer before the decision, each would have five hundred and fifty and each would bid fifty-five. The physical garden has not changed. The assumed preference rule has not changed. The purchasing power through which those preferences are expressed has changed, and so has the weight of each voice in the money total.
This is why the distribution of resources cannot always be postponed until after the efficient arrangement has been found. The demand against which costs are compared already embodies that distribution. A different division of purchasing power can change which uses command resources, which projects show the larger surplus, and which products are worth supplying. The garden example leaves the total bid unchanged because of its deliberately simple proportional rule; it changes who contributes to the valuation. With different preferences, different income responses, or different projects benefiting different people, even the ranking of projects can change. There is no general law that the rich always want an improvement more, or that every transfer raises its money value. There is a more consequential fact: the ranking is conditional on circumstances that the ranking itself cannot vindicate.
Marshall did not overlook this difficulty. In the very chapter that constructs consumer's surplus, he distinguishes comparisons involving similar mixtures of rich and poor from comparisons involving different classes of purchaser. A sum that looks comparable on the page can cease to be so when one side is chiefly a necessity of the poor and the other a luxury of the rich. The qualification is not a modern objection pasted onto an innocent diagram. It belongs to the measure's own account of what it means. The triangle can faithfully count dollars and still fail to tell us how the gains in those dollars should be valued across people. Better observation of the curve repairs a measurement problem; it cannot, by itself, settle a distributive judgment.
The distinction also survives the more exact money measures discussed in The Triangle. Ask what payment after a change would restore a person to the position she previously preferred, or what payment in place of the change would leave her as well off as the change itself. These questions can improve on a rough area under an ordinary demand curve. They still ask what money does for a particular person in a particular situation. A precise money equivalent of her gain is not a precise comparison between her welfare and her neighbor's. And a sum someone would accept to relinquish an entitlement is not simply interchangeable with the sum that person could afford to pay to acquire it. The starting rights and the available budget help determine which question is being answered.
The strongest defense of the unweighted dollar is therefore practical rather than mystical. Common money units make costs and gains comparable for a limited purpose; they can reveal an opportunity large enough to leave everyone better off if the necessary transfers are feasible and made. A calculation can also be more transparent than a discretion that calls every favored project priceless. These are serious virtues. But they support reporting the number together with its incidence and its assumptions. They do not convert the sum into a complete account of advantage. If a proposal's merit depends on giving greater social weight to a dollar received by someone with little, that weight should be defended openly. If it depends on making a transfer later, the transfer should become part of the proposal.
There is a further reason not to let a low bid settle the matter. Deprivation can alter the desires people learn to express, as well as the means by which they express them. A person who has adjusted to restricted opportunities may ask for little without thereby needing little. Nor does equal cash establish equal opportunity when illness, disability, distance, or care responsibilities change what it takes to use that cash. Sen's widening of the information relevant to welfare helps identify the missing questions: what can a person actually do, what deprivation remains, and which opportunities the arrangement opens or closes. These are matters to investigate, not sensations that can be read directly from a price. Their difficulty is a reason to describe them honestly, not a reason to assign them the value zero.
A bid tells us what someone can afford to surrender for a want. It does not, on its own, tell us what the want deserves.
Whose wants does efficiency serve? When the criterion is an unweighted money surplus, it serves the wants as they appear through the purchasing power and entitlements already in place. That is a conditional answer, not an accusation that every rich person's preference is frivolous or every poor person's is wise. It is a demand that the condition be kept visible. The next plate takes the most persuasive promise made on behalf of the total — that the winners could repay the losers — and asks what remains of the promise when the payment is never made. The dollar has told us what could be afforded. It has not yet told us who will receive it.