Before the water reaches the house, someone must make the channel. The labor spent cutting and hollowing wood produces no drink at the moment it is performed; it changes what later labor will have to do. Böhm-Bawerk begins his account of capital with such departures from the direct road to enjoyment. A bucket replaces repeated journeys to the spring, a channel replaces the bucket, and a sequence of earlier efforts makes a later abundance possible. The detour has a physical achievement which no argument about distribution can wish away. Yet the water arriving at the door does not announce the rate of interest. Between the useful work of an instrument and the percentage earned on its value stand the cost of making it, the timing and value of its services, and the price at which a claim to those services changes hands.
The capital in this account consists of intermediate products along the road to consumption. The axe helps make the channel; the channel delivers the water. In some cases an indirect method obtains more with the same labor; in others it makes possible a result that bare hands could never achieve at all. Böhm-Bawerk treats these gains as facts of technique, established by experience rather than deduced from the definition of capital. The detour recruits powers and arrangements which a direct effort cannot command. Its value lies in what that arrangement accomplishes. Spending twice as long on a useless apparatus does not double its contribution, and a method which saves time can be an advance over one which consumes more. Length alone is no warrant of fruitfulness.
The interval must nevertheless be provided for. Böhm-Bawerk's fisherman cannot spend a month making a boat and net if he must spend every day obtaining the food which keeps him alive. A supply of present food releases him to undertake a process whose product arrives later. In that sense, command over present consumption goods can enlarge the production methods available. A future promise which leaves the intervening hunger unanswered cannot perform the same service. This is the material strength of the argument: the time pattern of resources constrains the time pattern of production. It also shows why the advance may matter especially to someone without reserves. His exclusion from the better method can reflect the absence of a bridge across the interval, even when he knows perfectly well how to build the net.
The amount ultimately produced and the rate of return are different comparisons. Consider two invented, mutually exclusive projects, each using 100 units of a consumption good now. One yields 120 units after one year; the other yields 150 after three years, with no intervening receipts, further costs or residual value. The longer project yields more in total. Its annual compound return is about 14.47 per cent, against twenty per cent for the shorter one. At a five-per-cent discount rate their present values are 114.29 and 129.58 respectively, so the longer project has the larger net present value after the common initial cost. At twenty per cent the values are 100 and 86.81, and the shorter project ranks higher. More product at a later date does not settle which undertaking is worth making on the terms available.
Böhm-Bawerk himself placed the detour inside an account with three grounds for valuing the present. The first concerned differing provision for present and future wants; the second concerned the diminished force with which future wants could enter present judgment; the third concerned the productive opportunities opened by earlier command of resources. His theory therefore did not discard psychology in favor of machines. It attempted to show how technique gave present goods an advantage alongside the other grounds. He also resisted simply adding the three together: a resource consumed to meet an urgent present want cannot at the same time be employed in a distant productive process. The alternatives compete for it. Their relation has to be worked out before any premium can be assigned.
Fisher's objection concerned the step from productive possibility to an independently established premium. Starting a process earlier can bring its fruit earlier. How much more that earlier fruit is worth still depends on the value assigned to goods at the different dates. Fisher argued that Böhm-Bawerk's tables retained differences in future provision or valuation while claiming to establish a separate technical superiority in value. He did not conclude that production was irrelevant to interest. He recast its contribution as a choice among alternative income streams, comparing what must be given up at one date with what becomes available at another. That formulation allows technique to matter without pretending that the physical abundance of a later harvest already tells us its present worth.
A machine can produce more without telling us what the claim to its product should cost.
The valuation problem becomes plain when the productive object stays fixed and the rate changes. Imagine an asset yielding a certain net 100 units at the end of every year forever. The receipts already allow for every expense required to sustain them. At five per cent its capitalized value is 2,000; at ten per cent, 1,000. No additional machine has appeared in the first case, and no half of the machine has vanished in the second. Only the price of the stream has changed. Dividing the annual 100 by each of those values gives five or ten per cent, but it merely returns the rate used in the valuation. It cannot independently explain that rate. To call the resulting ratio the productivity of capital is to conceal the price inside what sounds like a physical measurement.
Adding unlike instruments by their prices carries that dependence into the total. A loom, a building and an inventory can each be described physically; their sum in money requires valuations. Changes in the rate can change those valuations while leaving the physical collection intact. A theory that takes the money total as an independently given quantity of productive stuff, then uses the return on that quantity to explain the rate, has asked its conclusion to help construct its starting point. This criticism leaves room for precise models with specified physical inputs, outputs and dates. It asks that their assumptions be stated, and that a value aggregate not silently be granted the independence of a quantity of grain.
Replacement costs give the productive object another connection to the world. If an equivalent instrument can be made more cheaply, a buyer has an alternative to paying the capitalized price demanded by its owner. Additional production can change the supply and value of its services, while wages, materials and time enter the cost of replacing it. Fisher considers this objection directly: the discount relation and the cost relation must be reconciled. A past expense does not ensure that an obsolete machine remains valuable, but a currently available substitute can constrain what a purchaser will pay. The useful inquiry therefore includes both the feasible processes and the prices at which their inputs and outputs are available. The dependence of value on the rate is a reason for more complete determination, rather than a license to ignore technique or cost.
A system can determine these quantities together without explaining any one of them by its own restatement. Fisher's productive opportunities, preferences over dated consumption, initial resources and market-clearing conditions supply distinct restrictions. Their joint solution can yield a rate and asset values, even though both enter the choices people make. The defect in the perpetuity explanation was narrower: the same discount relation was used once to produce the asset price and again, in reverse, to claim that the price explained the discount. Independent technological and behavioral restrictions add information; reversing an equation adds none. The challenge to a simple capital-productivity story is to show where that independent information enters, and how the institutional terms of finance allow the opportunities to be taken.
The productivity of the instrument leaves the division of its fruit to a further argument. The tool's maker, the worker who uses it, the person who advances provisions, and the owner of the claim may be different people. Each may contribute to the possibility of the final output; the yield does not print their shares upon itself. Böhm-Bawerk explicitly distinguishes production aided by capital goods from production conducted under the control of private capitalists. The technical detour is compatible with more than one arrangement of ownership. Recognizing that distinction preserves the real achievement of capital while refusing to let the machine itself adjudicate the rights of its holder. A useful instrument can justify efforts to provide it; the contractual reward still requires its own grounds.
The detour has therefore carried us to a distinction which the price of time needs. Production explains what an arrangement of resources can accomplish, with what costs and on what dates. Valuation explains the price of a claim upon those results under given terms of exchange. A theory of interest must connect them without treating the value it has calculated as an independent physical cause. The channel brings water; the net catches fish; the borrower may have good reason to obtain the means of making either. How much he must promise in return depends on more than their usefulness. The next plate, The Hoard, turns to the person who can keep command of money instead. Productive possibilities press upon the rate. The willingness to release the means of pursuing them remains part of the question.