Talk:Elasticity of a function

What is going on here? This is essentially the economics use. Elasticity in mathematics generally means the mathematical theory of elasticity.Billlion 05:51, 3 August 2007 (UTC)

The equation $$E (f \circ g)(x) = E f(g(x)) \cdot E g(x)$$ seems to be a misprint of $$E (f \circ g)(x) = E f(g(x)) \cdot D g(x)$$. Can anyone with reference material verify and correct this?

Merger proposal
Billlion is right that the most common use of elasticity in mathematics is the one from mechanics, not the one from economics. Besides, this article contains very little that isn't already said in that one, nor would that little extra be particularly out of place in its proposed new home.—PaulTanenbaum (talk) 05:59, 29 February 2008 (UTC)

They should remain separate, although they are both similar mathematically, people who search for price elasticity do not wish to see all the complex math. —Preceding unsigned comment added by 198.111.39.45 (talk) 21:16, 6 March 2008 (UTC)

Should be merge, no point in having an extra link to a essential related information. 60.51.48.205 (talk) 17:36, 1 May 2008 (UTC)

They should remain separate as although they contain similar information they are still separate topics. Those searching for economics related elasticity information do not require the detailed maths.

=> In response to this comment (and comment 6 March 2008): The mathematical article is no more detailed or complicated than the economics related article. Furthermore, as a practicing economist, I found the equivalence noted there useful. Both entries are very short and it would be easy enough to have a main article titled "Elasticity of a Function" and a sub-section with applications to economics and another with applications to mechanics if both are relevant. Concerns about the difficulty of the material could be alleviated with good writing and pictures. MountainGoat8 (talk) 17:07, 4 August 2008 (UTC)

I would keep them separate for ease of use. It is obvious they are related, but for quick reference it would be beneficial to maintain the separation.

They contain some of the same information, but they are still different, I would keep the separated, as users would typically search for either of the topics they each need information on.

I don't think there should be a merge. A google search for mathematical elasticity turns up some interesting stuff. Certainly there is pure math behind the elasticity concepts used in economics and physics, although I'm not familiar with it -- and it is likely more similar to the physics stuff than the economics. ImpIn | (t - c) 02:22, 10 June 2008 (UTC)


 * MERGE. We're dealing with some serious namespace pollution originating with the soft-science of economics.  Even if the only results of a search for "mathematical elasticity" referred to the math used by economists, that doesn't justify this article.  One would need to find a variety of other uses of the same math -- even if only in mathematics itself.  But the first result from google is Introduction to Mathematical Elasticity which is unrelated to the economics use of the term.  There are a few reasons to not grant this page to the neologism.  First, they didn't need to use the word "elasticity" for a neologism when that word already referred to a different concept, long in use in the hard sciences.  Second, it, unlike the physics definition, contradicts the folksonomy of the word "elasticity".  Third, just try parsing the phrase "price elasticity of demand" so it makes sense in terms of the intuitive definition of "elasticity".  Which is the noun phrase and which is the adjective?  Fourth, and finally, is this quote from a paper titled "Conspectus of Concepts of Elasticity":
 * ''Obviously, the response relations for an elastic body depend on the mathematical definition that we provide for them, which in turn depends on what we understand by a body being elastic. Different meanings and interpretations of the word ‘elasticity’ would of course lead to different mathematical models. Thus, it is imperative to recognize how the word has been used in the past, and to develop a precise understanding of what we would like the word to signify before we embark on the development of constitutive theories. Otherwise, a discussion amongst elasticians would be mere babel. In this context, it would be worthwhile to observe how the word has been used, not just by the experts in science, but also by others, for it might accord us the insight to understand why there are so many different interpretations of the term ‘elasticity’, even when used by scientists. Nowadays, we come across the terms ‘elasticity of demand’, ‘elasticity of supply’, ‘price elasticity’, ‘elasticity of thought’, ‘elasticity of mind’, etc. In fact, the word elasticity has been used in contexts that most practitioners of elasticity in the sciences could hardly dream of. For instance, consider the usage ‘elasticities in livestock production’ and ‘elasticity of signification’. The term elasticity has also been used to signify ‘buoyancy of mind or character’, ‘capacity for overcoming depression’, etc. Jane Austen [12] used the word in a letter that she wrote to her sister Cassandra dated 8 January 1880 in a manner that would hardly make much sense to an expert in mechanics:
 * The Prices are on not to have a house on Weyhill; for the present he has lodgings in Andover, and they are in view of a dwelling hereafter in Appleshaw, that village of wonderful Elasticity5, which stretches itself out for the reception of everybody who does not wish for a house on Speen Hill.
 * Our interest lies in how the term ‘elasticity’ has been used in the field of mechanics and we shall not concern ourselves with any of the meanings that are attached to the word ‘elasticity’ in fields such as economics, psychology, etc. We shall be primarily concerned with the use of the term as it pertains to a special classification of the response of bodies in the field of continuum6 mechanics.
 * Jim Bowery (talk) 19:59, 7 August 2021 (UTC)

They should merge. Luciuswiki (talk) 21:47, 5 September 2008 (UTC)

Price elasticity is a fundamental part of microeconomics, and it would be inappropriate not to have a page by itself. Beginning students of economics would want to see the economic concept of elasticity rather than the mathematical definition. If the pages merged the emphasis on the economics concept would be lost. Although the article is short at this point, there is much more that could be written; economists have written entire volumes on specific aspects of price elasticity. Larry (talk) 17:19, 21 September 2008 (UTC)

Dubious math
I have two problems with unsourced math assertions in the Rules section. First, it says


 * The chain rule is similar to the derivative


 * $$E (f \circ g)(x) = [ E(f(x)) \circ g(x) ] \cdot E(g(x))$$

I don't get the bracketed expression on the right side. In a composite function expression the argument of the first function is the output of the second function. But here the argument of the first function, f, is given as x, which is not the output of the second function, g(x). I'll put a clarification needed tag on this and delete it in a couple days if it doesn't get corrected.

Second, the same section says


 * For Homogeneous functions
 * $$E (f(ax )) = E(f(x)) \ $$

This seems just wrong. If f is homogeneous then $$ f(\alpha x) = \alpha^k f(x). $$ Then by the rule that the elasticity of the product equals the sum of the elasticities, we have $$E (f(ax )) = k + E(f(x)) \ $$ where k is the degree of homogeneity, which can't be zero except for trivial functions. So I'm removing this assertion. Duoduoduo (talk) 21:40, 16 November 2012 (UTC)

Percentage
The definition of semielasticity, with its mentions of percentages and "not percentage-wise", is difficult to understand. There are no percentages involved because there is no factor of 100. Is the definition not just the instantaneous change in f(x) relative to f(x)? &mdash; Paul G (talk) 05:02, 1 June 2019 (UTC)