A Reply to Aguilar
Robert P. Murphy
Part III: Conclusion
In this section Aguilar elaborates on his preferred DWCS instead of the clumsy and vague Hayekian triangles (or histograms) that pepper orthodox Austrian works. Again, I do not fully understand Aguilar’s proposal, since it is not fully elaborated in this Critique (though perhaps it is elsewhere). Even so, I see some serious difficulties with it, if it is to serve as the new foundation of Austrian capital theory.
First, as I have already discussed, the total (not average) period of production with the DWCS is infinite. Aguilar might respond that this is a harmless simplification, since the height of his graph goes to zero as we go out to infinity on the time axis. Even so, the “lengthening” of the capital structure in Aguilar’s framework would apparently mean simply a shifting of probability mass to the higher stages. This seems less intuitive to me than the (perhaps equally simplified) current Austrian approach of showing new stages being created at the highest end of the triangle.
Second, Aguilar has little flexibility because he has committed to the exponential function, in particular f(t) = Are-rt for 0 = t < 8. I do admit that this is quite “neat” in that he can take the derivative with respect to r in order to find the precise point on the time axis where the “fulcrum” pivots, and that he can also explicitly show how changes in the interest rate affect the distribution of wealth among the “stages” (which are here continuous). He can also set A equal to the total wealth so that the integral of this function over its domain sums to the total value of the capital stock. Very clever indeed.
However, what if we wish to depict an economy that does not have the smoothness inherent in this function? Surely there are differences between the capital structure of current America and Bangladesh, that cannot be attributed merely to different A and r. It is true that Hayek too made some simplifying assumptions, but that was merely in order to facilitate computations (which Aguilar scorned). It seems that once we want the DWCS to more accurately represent an actual capital structure, we would be forced to abandon the elegant mathematical construction and end up drawing a histogram.
Finally, I point out the grave defect that Aguilar’s suggested construction breaks down if the (real?) interest rate exceeds 100%. As Aguilar informs us, “So, as the interest rate advances from zero to 100%, we move along the PPF from a situation of all investment and no consumption to the other extreme of all consumption and no investment” (p. 38). But why should this be so? We can certainly imagine preferences such that the equilibrium interest rate is, say, 115%. The Austrians can handle such a case in their framework, but Aguilar would apparently need to use a different function or at least make an ad hoc adjustment to his current one.
In conclusion, I agree with some of Aguilar’s criticisms of the Austrians, in particular their sloppiness in exposition. However, his Critique alone would not have convinced me to abandon Austrian capital theory, and moreover his suggested improvements raise just as many problems as they solve.
