"Dimensions And Economics : Some Problems" By William Barnett II (An Economics Awakening : Disputing The Cobb–Douglas Function)Submitted by Cyril on Fri, 11/16/2012 - 01:37
From Wikipedia :
"In economics, the Cobb–Douglas functional form of production functions is widely used to represent the relationship of output and two inputs. The Cobb-Douglas form was developed and tested against statistical evidence by Charles Cobb and Paul Douglas during 1900–1947[...]
many modern authors have developed models which give Cobb–Douglas production function from the micro level; many New Keynesian models, for example. It is nevertheless a mathematical mistake to assume that just because the Cobb–Douglas function applies at the micro-level, it also always applies at the macro-level. Similarly, it is not necessarily the case that a macro Cobb–Douglas applies at the disaggregated level.[...]"
Dimensions And Economics : Some Problems
By William Barnett II
"The consistent and correct use of dimensions is essential to scientific work involving mathematics. Their very existence creates the potential for errors: omitting them when they should be included, misusing them when they are included, and others. However, their existence also makes possible dimensional analysis, which can be a significant factor in avoiding error. In the equation y = f(•), if y should have dimensions then so also should f, and they should be identical to those of y. If y should not have them then neither should f have them. Such an analysis of y = f(•) would determine: (1) which, if any, dimensions y and each element of f, and consequently f, itself, should have; and, (2) whether the dimensions of f and y are identical, which is a necessary, though not sufficient, condition for the equation to be correct. An error revealed by a correctly performed dimensional analysis indicates a fundamental problem. Therefore, the importance of dimensions for science can hardly be overstated.
The economics profession has attempted to achieve the degree of success in understanding, explaining, and predicting events in the social world that physicists and engineers have achieved in the natural world by emulating their methods; i.e., using mathematical and statistical analyses to model, understand, and explain, the relevant phenomena. However, in so doing, economists have failed to emulate physicists and engineers in one essential aspect of their work: the consistent and correct use of dimensions. This is an abuse of mathematical/scientific methods. Such abuse invalidates the results of mathematical and statistical methods applied to the development and application of economic theory.
This is not to say that there have not been advances in economic understanding by the neoclassicals, but rather to argue that mathematics is neither a necessary nor a sufficient means to such advances. Whether it even is, or can be, a valid means to such advances is a different issue. What is certain, however, is that mathematics cannot possibly be a valid means unless and until it is used properly. Among other things, that means that dimensions must be used consistently and correctly."