Hayekian triangle

According to Renaud Fillieule, the origins of the Hayekian triangle lie in the numerical "schemes" Hayek used in a 1929 discussion of saving and production, before he converted them into a more compact visual form in Prices and Production.^[1] In that book, Hayek used the triangle to depict a multi-stage production process and to illustrate the effects of changes in saving, investment and credit on the temporal structure of production.^[2]

Hayek also noted that comparable triangular figures had been used earlier in the literature on capital, especially by William Stanley Jevons.^[2] In The Pure Theory of Capital (1941), Hayek returned to the device in revised form, distinguishing more explicitly between synchronic and diachronic readings of the production structure and experimenting with non-linear shapes rather than a simple linear triangle.^[5][1]

The Hayekian triangle is intended to visualize production as a time-consuming process: over time, goods move through successive stages of production (intermediate goods) before emerging as consumer goods (final output).^[2][3]

Roger Garrison emphasized that the triangle has two related interpretations. In one reading, it shows a single production process unfolding through time from its inception to the final consumer good. In another, it depicts the coexisting stages of many production processes in an equilibrium economy, with some goods at early stages and others near completion.^[3]

Within Austrian macroeconomics, the triangle has been used to illustrate how a rise in saving can lengthen the structure of production and how credit expansion can produce an unsustainable reallocation of resources across stages of production. In this respect, the diagram became one of the best-known visual devices associated with Austrian business-cycle analysis.^[1]

During the 1930s, Evan Durbin adapted Hayek's diagram in an attempt to incorporate fixed capital and profit more explicitly into the representation of production.^[6][1] Murray Rothbard used the triangle to incorporate interest more explicitly into capital-theoretic exposition, while Roger W. Garrison recast the device as part of a broader diagrammatic macroeconomics.^[1][3][4]

Garrison's version often replaced Hayek's continuous-input representation with a "point-input point-output" form, producing a trapezoidal figure rather than a right triangle. He integrated this structure-of-production diagram with other graphs, especially the market for present versus future goods, to show how interest-rate changes affect the pattern of production.^[3][4]

Mark Skousen used the triangle in a more explicitly pedagogical manner, presenting a simplified four-stage production structure and using it to contrast stage-by-stage production measures with standard national-income measures focused on final output.^[7]

From the 2000s onward, several authors formalized the Hayekian triangle mathematically. Renaud Fillieule developed a proportional goods-in-process model; Jörg Guido Hülsmann examined exponential structures of production; and Er'el Granot proposed a more general model encompassing both proportional and exponential cases.^[8][9][10]

This literature treated the Hayekian triangle as a family of related representations of intertemporal production, and also connected it to debates over the average period of production and the measurement of "roundaboutness" in capital theory.^[11][1]

The Hayekian triangle has been described as the Austrian School's counterpart to the circular-flow diagram, because it emphasizes the time structure of production and the role of intermediate stages rather than only the relationship between household income and consumption expenditure.^[1] It has remained a recurring teaching device in Austrian economics, but the underlying capital theory and its use in business-cycle analysis have been controversial both within and outside the Austrian tradition.^[11][1]

• Austrian business cycle theory