March 14, 2009

Mathematics and Economics

Having written Statistics and Economics a few days ago, I never intend to make this a series of Whatever and Economics articles. However it just happened that today I made a comparison again between economics and another subject.

I used to think that in mathematics, unlike economics, there are some facts that need not be substantiated by assumption, e.g. one plus one always equals two; while in economics, no basic fact exists. Even the very fundamental descriptions are essentially assumptions. When we say that, by receiving more dollars, Tom would buy extra ice creams, we have to assume ice cream is a normal good, i.e. the increase in income raises the consumption of ice cream for Tom. (He can actually choose to consume less if the substitution effect prevails, basing on some assumption.) Actually most economic questions require models on much more complicated and specific assumptions than this example.

Nevertheless, as I was trying to explain my opinion upon religious beliefs to a friend today, I used the example of one plus one equals two, and immediately I found that this is so not a fact. Instead, it is an assumption, one that is so widely used and applicable when explaining most, if not all, questions that require an answer to 1 + 1, that in most cases no alternative assumptions would be needed. That is to say, the behavior of consuming ice creams could be so possibly divergent when different individuals are faced with an increase in income or consumption budget, but possibly no phenomenon requires an answer to one plus one, other than two, to be sufficiently explained.

Therefore it seems that both mathematics and economics are based on assumptions that are unnecessary to be true, and probably the same to any theoretical studies.

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