Complementarity and Substitution in the Theory of Capital

This article, reprinted from Economica and arranged in six sections with notes, is a compact statement of Lachmann’s plan-theoretic capital theory. It begins from the Hicks-Lange-Harrod debate but shifts complementarity and substitution away from demand analysis and into the structure of production. The central question is not how to measure capital as an aggregate, but how heterogeneous capital goods acquire economic order through plans and are reorganized when plans fail.

Complementarity, introduced into economic dynamics by Professor Hicks in 1939,¹ has since given rise to a host of bewildering and intricate problems.

Lachmann’s main thesis is that complementarity and substitution are not symmetrical static relations among factors. Complementarity describes the coherence of means within a production plan; substitution describes the response to disruption, error, or changed expectations. A locomotive may substitute for another locomotive, yet complement wagons, crews, tracks, and timetables in a particular transport plan. The relevant relation therefore depends on the plan within which goods are interpreted.

Complementarity is a property of means employed for the same end, or a group of consistent ends.

This distinction lets Lachmann reject the fiction of homogeneous capital without reducing capital theory to physical classification. Capital goods are artifacts made for purposes, and their economic character depends on the uses entrepreneurs expect to make of them. Technical specificity matters, but only as part of plan specificity. Substitution becomes important precisely when a plan must be revised and the actor seeks another way to pursue the same or a modified end.

The importance of substitutability lies in that it is usually possible to pursue the same end (output) with a different combination of factors.

The firm is thus a network of complementary capital combinations, but it survives by anticipating limited substitutions. Spare parts, standardization, reserve capacity, and inventories are not accidental frictions; they are devices for preserving a wider pattern of complementarity. Lachmann’s point is dynamic: a capital structure must be flexible enough to absorb small disturbances if it is not to be destroyed by large ones.

We have to provide for many minor changes in order to prevent a major one.

The article then extends the analysis from the firm to the economy. In equilibrium, production plans would be mutually consistent and capital goods would form one interlocking structure. In reality, plans are continually disappointed and revised. Disequilibrium destroys some complementarities while creating others, and a substituted input often requires further substitutions elsewhere. Capital gains and losses are therefore not peripheral accounting phenomena, but signs that earlier expectations about future complementarities were right or wrong.

Against aggregate capital theory, Lachmann treats the capital structure as a pattern of functional relations rather than a measurable stock. Accumulation does not simply add to a fund; it changes relative scarcities, alters coefficients, devalues some goods, and raises the value of others. His examples show new investment working through chain reactions: some existing goods become more useful as complements, while others are displaced as substitutes. For this reason, the effect of accumulation cannot be summarized by a single rate of profit or a smooth marginal productivity schedule.

The conclusion is methodological. Static equilibrium and aggregate magnitudes conceal the phenomena capital theory must explain: heterogeneous combinations, excess capacity, maladjustment, entrepreneurial revision, and the uneven spread of change across sectors. Lachmann’s article is therefore an argument for sequence analysis, attentive to how one disturbance sets off successive recombinations of capital goods. Its lasting importance lies in making capital theory a theory of plans, expectations, and structural change rather than of a single measurable quantity.