Hayek's Pure Theory of Capital

Not sure if this belongs here, as the Pure Theory of Capital is definately not for a beginner, but in the economics questions section there seem to be few questions regarding works. So given the foregoing I thought I’d err on the side of caution and post here.

I’m working on the introductory section of this book and Hayek’s description in the first chapter of the 2 magnitudes which make up the supply of capital has me puzzled. Any help would be appreciated.

Hayek says:

“..[T]here are at least two kinds of relevant magnitudes or rather proportions which must be taken into account if we want to understand the working of the price mechanism in this field; neither of them is a simple “quantity”, and neither of them stands in a unique relationship to the rate of interest except through its relation to the other. The first is the dimensions of the real structure of productive equipment, describing how it is organized for, or capable of, yielding various quantities of final output at different dates.”

Further down the page Hayek describes this first magnitude/ratio as describing “the proportions between the existing quantities of concrete resources in terms of their relative costs.”

So, these ‘dimensions of the real structure’ of equipment simply sounds like the existing placement of producer’s goods in the economy. However, his further description adds in their relative costs. Thus, it seems as though he has in mind not only the placement of producer’s goods A, B and C, but also their costs relative to each other. In other words, he has in mind a definite ordering of goods A, B and C in the economy, and at the same time a ratio of their costs: C(A) : C(B) and C(B) : C(C) and C(A) : C(C).

Regarding the second relevant proportion:

“The second is the proportional demands, or the relative prices, which are expected to rule for these different quantities of output at different dates.”

He goes on to say that this relationship “…describes the relative demand for the two kinds of resources.”

These ‘relative prices’ sound similar to the standard step-wise graph depicted in the production chapters of MES, showing the prices of output at different steps along the structure of production. The relative prices are the ratios of prices between each step, which in the ERE corresponds to the true rate of interest. So what of the first relationship that Hayek talks about?

“But only together do these two sets of quantitative relationships or proportions determine what is usually regarded as the supply of capital in value terms.

The treatment of the capital problem in terms of the demand for and supply of one single magnitude is only possible on the assumption that the proportions just described stand in a certain equilibrium relationship to one another.”

Ok, I understand that marginal costs determine supply. But now I think that my understanding of his first quantitative relationship is a bit off. Now I think that he is saying that producer’s goods A,B and C are ordered definitely according to their marginal costs. I.e., the reason that producer’s good A is used in step 1 and not 3 is because the marginal cost of using it in 3 is greater than 1. In other words the relative marginal costs of producer’s goods not only determine how much of the goods themselves are produced but also, and perhaps more importantly to Hayek’s point, their placement in the structure of production. Still not sure if I have it right. And how does this problem go away in equilibrium as Hayek asserts? How do these 2 magnitudes become 1 in equilibrium?

You might want to go ahead and re-post this on the Economics Questions page, might get more attention…?

forget the diagrams, they are unintelligible…

It sounds like you have a pretty good understanding of what Hayek’s saying. However, a lot of what you are asking is dealt with later on in the book

In particular, I am pretty sure that Hayek is talking about the difference between the input function and the output function here, which he introduces in Chapter 8. So in the paragraph you discuss above, he notes that there are two important “values,” that one will take into account when one is in intertemporal equilibrium (by “values” I mean relative values in terms of some product; often, Hayek discusses matter in “real” terms using a consumers’ good as the numeraire, meaning that all prices are in terms of quantities of consumers goods paid for said product; in turn, a value is just the relative price of some product, multiplied by the quantity of said product being traded or produced). The first is the value of the total quantity of input used in production during some period of time (" The first is the dimensions of the real structure of productive equipment, describing how it is organized for, or capable of, yielding various quantities of final output at different dates”). The second is the the value of outputs produced in production (“The second is the proportional demands, or the relative prices, which are expected to rule for these different quantities of output at different dates.”). Outputs here will include final output as well as intermediate output (i.e. intermediate products, higher order goods, or capital goods) Now these two values do not “become one” in equilibrium, but as Hayek notes, they “stand in a certain equilibrium relationship to one another.” All this means is that in equilibrium, the value of some number of inputs invested in a production process to produce outputs, must produce outputs at some future point in time that have a value equivalent to the value of the inputs invested PLUS accumulated interest, whatever that interest rate happens to be. If you want to skip ahead to p. 109, he has a simple graph that shows this equilibrium relatationship between the input function and the output function, or the value of input used at some stage of production, and the value of output produced at some stage of production.

Incidentally, I am pretty sure the graph on p. 109 is just a continuous time version of the graph you referenced from Man, Economy, and State, assuming I have the same graph in mind as you. So it sounds to me like you are very much on the right track.

Thanks for your help Sam. I sent you email.