A person born a century from now cannot buy a place in today’s bond market. She cannot bid against an action that will damage her water, offer us a payment to preserve a forest or refuse the terms on which we leave her an atmosphere. Yet we must decide now about things that will affect her. The rate enters that decision as a device for comparing dates. It can look like a small technical input while determining how much of her future appears in our present account.
The force is visible in an imagined loss of one trillion dollars, expressed in constant purchasing power, two hundred years from now. At a constant annual discount rate of five percent, its present value is about fifty-seven million eight hundred thousand dollars. At one and a half percent it is about fifty billion nine hundred million. The lower-rate valuation is roughly eight hundred and eighty times the higher one. If preventing the loss costs one hundred million today and has no other effects, the two rates reverse the decision. Nothing about the stipulated future loss has changed. The rate has changed the weight assigned to it.
The earlier inquiry into discounting explained a private comparison. A person able to exchange money across dates at a specified rate can ask what present sum is equivalent to a later payment. The public question is larger. Which consumption does the project sacrifice today, whose benefit does it produce later, and what alternative investment could carry resources forward? A market rate can provide evidence about opportunities available under existing arrangements. It cannot by itself establish how people excluded from those arrangements should count. Using the rate from a traded promise silently imports the circumstances of that promise into a decision about people who never traded it.
Ramsey began his 1928 saving problem by refusing to discount later enjoyment merely because it came later. The ethical position was explicit, and so were the model’s exclusions: a continuing community, simplified production, no distributional differences within it and no disasters destroying the accumulated stock. His rejection of pure time preference did not say that every additional unit of future consumption must be valued equally with an additional unit now. If people will be better provided for, another unit can matter less to them. Equality between persons and equality between quantities are different commitments.
A small illustration makes the distinction concrete. Give present and future welfare equal weight, and let the value of consumption have a marginal utility of one divided by consumption. At consumption of one hundred, an additional unit has marginal value .01; at one hundred and two, it has value about .009804. The future unit then carries 100/102 of the present unit’s marginal weight. That is the same factor as discounting consumption at two percent for one period, although neither person’s welfare has been discounted for arriving later. If consumption is equal, this particular reason for discounting vanishes. If future consumption is lower, it points in the other direction.
The assumption of greater future abundance is therefore part of the argument. It cannot do its work merely by appearing in a spreadsheet. Nor does an increase in average consumption show that those exposed to a particular loss will be richer. A benefit protecting poor households from destruction can have a different welfare value from an equal monetary payment to already secure owners, whether the recipients live now or later. Ramsey set those distributional differences aside to solve his stated problem. A public decision that needs them must put them back, rather than allowing the convenience of an average to decide whose deprivation is tolerable.
Opportunity cost nonetheless remains. Resources devoted to protecting the future cannot simultaneously provide housing, care or other investments today. Some present investments may also make future people better able to withstand harm. Equal moral standing does not tell us that every distant benefit outweighs every immediate need, or that the most expensive protective measure must be chosen. It requires the comparison to preserve the claims on both sides. A low discount rate can expose a future cost that a higher rate nearly erases; it does not dispense with the need to establish the cost, the effectiveness of prevention and the alternatives forgone.
Uncertainty makes the arithmetic less accommodating than simply choosing a middle number. Imagine a small project delivering one hundred dollars of constant purchasing power in a century under either of two equally likely scenarios. In one, the applicable annual rate is one percent throughout; in the other, it is five percent throughout. Averaging the two present values gives about eighteen dollars and eighty-seven cents. Averaging the rates first and discounting at three percent gives only about five dollars and twenty cents. The operations are different. Lower-rate scenarios preserve more of a distant payment, so they carry more weight in its expected present value.
Weitzman’s result gives this observation a precise distant limit. In his model, rate paths converge, and scenarios with lower limiting rates increasingly dominate the surviving present-value weight. This does not instruct us to select the smallest number we can imagine for every project today. The scenario support and its probabilities are part of the setup; the time before the distant regime still discounts what follows. And the project must be treated differently if its payoff depends on the same conditions that determine the rate. A measure valuable precisely when future society is poor or damaged cannot be assessed by changing the discount rate while pretending its benefits are unrelated to those states.
The object being valued also resists compression. A monetary measure of future damage already contains judgments about what is lost, who bears it and what substitutes are possible. Applying a rate does not cure an incomplete measure. Nor can the possibility of a large investment return guarantee that a particular destroyed resource will be replaceable when replacement is needed. These are questions about production, exposure and institutions as well as preference. The discipline of discounting is useful when it makes the assumptions inspectable. It becomes a concealment when the resulting present value is presented as though it had arrived without them.
The future’s absence from the transaction is consequently a problem of representation. We can state the pure time preference separately from the expected consumption path; show who bears the cost and who receives the benefit; compare plausible rates and states; and identify the decisions whose ranking changes. None of these acts supplies a mechanical ethical answer. Together they prevent a single unexplained percentage from posing as one. A disagreement about posterity should appear where the disagreement lies, rather than being buried in the convention used to convert a date into a number.
A discount rate can measure an opportunity. It cannot, by itself, decide how much a person matters.
The volume began with the price of moving resources through time. It ends where some of the people affected cannot participate in setting that price. We owe them neither an effortless promise that every future loss will be prevented nor the convenience of treating distance as disappearance. We owe an account of the tradeoffs, with the assumptions exposed and their standing preserved inside the calculation. The rate helps make that account; it does not relieve us of making the judgment. The argument remains open.