I have put a copy of this paper in the library for ease of reference as it is referred to in Jill Leyland's paper on an uprating index.

I have some comments on that part of the paper which deals with maximisation of entropy and which equates to use of the Jevons formula (geometric mean).

In particular I refer to the last paragraph of section 6 of the paper.

This shows that the same considerations imply a Cobb-Douglas utility function to represent consumer preferences. In turn this is equivalent to assuming elasticities of substitution of exactly unity for all products in all time periods.

There is therefore quite a lot of information available to test these hypotheses which are all effectively equivalent.

In particular I refer to ONS' paper CPAC(12)15 + Annex A which was lodged in the library of this website on 7th June 2012. This is an empirical study of data on the alcohol sector.

It shows that elasticities of substitution vary considerably. Some are approximately unity while others are significantly higher or lower. Moreover there is no guarantee that those near unity would remain so over time. This effectively shows that the Cobb-Douglas utility function and assumptions equivalent to it are not valid.

ONS' paper also compares the performance of different elementary formulae relative to a target index using several different loss functions.

Under this analysis, both the Carli and Dutot formulae outperform the Jevons formula under all loss functions. Given that consumer substitution clearly takes place in the alcohol sector and that the Carli and Dutot formulae make no allowance for it, this is a remarkable finding. It implies that the form of consumer substitution implied by the Jevons formula is so far from reality that formulae representing no substitution do better in representing reality.

This point is confirmed by a paper of my own entitled "Implausibility of the Geometric Mean ......." lodged in the library on 9th March 2012. This shows that the Jevons formula does not represent substitution towards cheaper products but towards products whose rate of price rise is lower (even if the products are more expensive).

I think these papers effectively refute the Jevons formula, the Cobb-Douglas utility function and the maximisation of entropy.

GJ