Lesson 2 of 8
The diagram, and its four limits
Hayek's triangle: what each axis is, what a change of shape represents, and the four things it cannot show. All four are Hayek's own qualifications.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- One axis is time: how far a stage sits from consumption. The other is value: what that stage's output is worth. The sloping edge traces the two together.
- A change in shape is the claim. Longer and narrower means more committed further from the shop, shorter and wider means the opposite.
- Hayek names four things it cannot show, in the lecture that introduces it, and every reader should learn them at the same time as the diagram.
The diagram is a right-angled triangle. Hayek introduced it in the second of four lectures given at the University of London and published in 1931, and noted that Jevons and Wicksell had drawn similar figures before him.
The stepped version of the same triangle
- Five periods out20 units
- Four periods out40 units
- Three periods out60 units
- Two periods out80 units
- One period out, the shop100 units
Reading the axes
The vertical dimension, measured in arbitrary periods from top to bottom, is time. The horizontal projection of the sloping edge is the value of the original means of production used. The base is the value of the current output of consumers' goods.
The area is the total of intermediate products that must exist at any moment to keep a continuous flow of consumers' goods coming out of the bottom.
Hayek also suggests reading the same picture as a picture of money, flowing the other way: paid first for consumers' goods at the bottom, moving upward through the stages, and paid out as wages and rent to the people who then buy consumers' goods.
What a change of shape means
A structure that lengthens gets taller and, at the base, narrower. More value sits in things that are not yet consumable, and less money is spent per period on the things that are.
A structure that shortens does the reverse. The base widens, the height falls, and value that had been committed further out is either brought forward or lost.
Those two sentences are the whole reason the diagram exists. The next two courses are about what makes them happen.
The four things it cannot show
Each of these is Hayek's own, in the same lecture.
It shows values, not physical quantities, so the extra output that the longer method yields is not represented anywhere in the figure. He says so directly.
It neglects interest. He states that he has intentionally left interest out of that lecture and will take it up in the next one.
It cannot handle durable goods properly. He explains that once the diagram is used to show intermediate products changing hands for money from stage to stage, durable goods cannot be treated the same way as goods in process, because the services embodied in a machine do not change hands as they mature.
And the straight sloping edge is an assumption, not a finding. He notes there is no reason to assume that the amount of original factors applied during successive stages is constant, which is what a straight edge means.
How to use it anyway
As a way of asking one question: where in the sequence did the commitment go. It is a heuristic, and Garrison, whose formal presentation is the seventh lesson of this course, calls it exactly that.
A reader who takes it as a measurement has already left the ground the theory can stand on. A reader who takes it as a way of keeping track of distance from consumption gets the benefit and none of the trouble.
Check yourself
What is the vertical dimension of the triangle?
- The quantity of goods produced
- Time, measured in arbitrary periods from the top down, showing how far a stage sits from consumption
- The interest rate
Show the answer
Answer: B.
The horizontal projection of the sloping edge is the value of the original means of production, and the base is the value of current consumers' goods output.Why is the extra output of a longer method absent from the figure?
- Because Hayek did not believe in it
- Because the figure represents values rather than physical production, and he says so in the same lecture
- Because it appears in the base only
Show the answer
Answer: B.
He states that the surplus return obtained by roundabout methods is not represented in the diagram, which is one of four limits he names himself.What is the problem with durable goods on this diagram?
- They have no value
- Their embodied services do not change hands stage by stage as they mature, so they cannot be treated like goods in process
- They belong at the base
Show the answer
Answer: B.
Hayek explains that this is why he abstracts from durable goods whenever the diagram is used to show intermediate products being exchanged against money at regular intervals.Sources
- Hayek, Prices and Production, first published 1931, second revised edition 1935, lecture II, section 6, for the construction of the triangle, the meaning of both axes and of the area, the note that Jevons and Wicksell used similar figures, the statement that the figure represents values so the surplus return is not shown, the deliberate neglect of interest in that lecture, the treatment of durable goods, and the observation that there is no reason to assume the sloping edge is linear.
- Hayek, Prices and Production, lecture II, section 7, for reading the same diagram as a flow of money in the opposite direction.
- Garrison, Time and Money: The Macroeconomics of Capital Structure, 2001, chapter 1, where the triangle is described as a heuristic device and as highly stylised, and is dated to the 1931 lectures and the second lecture in particular.
What this leaves out
- This is a heterodox tradition. The mainstream account of the same phenomenon differs, and nothing here is a forecast or a view on any security.
- The bars are invented round numbers from the previous lesson, chosen so the shape can be seen. They measure nothing.
- The stepped bar chart above is a discrete rendering of a continuous figure, which is a substitution Hayek himself makes for the same reason. A reader wanting the original should read the second lecture, where the triangle is drawn.
- Whether the shape of the production structure can be measured at all is contested, and the last lesson of this course is about that.