"There's no secret about success. Did you ever know a successful man who didn't tell you about it?" - Kin Hubbard
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Via MFM:
Comments on “The Calculus of Prostitution”:
"[(δU/δL) / (δU/δC) | Sp=0] ≤ w - [(δU/δr) / (δU/δC) | S = 0]
An individual will start to sell prostitution if the price for selling the first amount of prostitution, minus the costs of a worsened reputation for doing so, exceeds the shadow price of leisure evaluated at zero prostitution sold."
[Ed: A wonderful example of useless maths.]
hueoblue: I’m declared in a BSc(it’s doubtful whether there should actually be such a thing) Econ program and I wish that someone would make it clear to economists that our use of mathematics outside of statistics is almost always illegitamate. I am pretty sure that the poor use of mathematics and the subsequent hand waving is a manifestation of our latent physics envy.
Fermi-Walker Public Transport: Agreed, this does look like an illegitame use of mathematics. For a start, it is assumed that the functions can be differentiated. There is no reason for this assumption, let alone whether there may be other relevent variables, differentiable or not.
hueoblue: Actually, we do assume that it is continuosly differentiable for all positive real numbers, although we treat the numbers as ordinal. All kinds of assumptions are made to ensure differntiability as well as convexity of the function. None of these assumptions are justified by observation and are made because it makes the math manageable. A terrible reason to make an assumption.
Isaac: Economists use math differently than physicists. Physicists use it to generate quantifiable predictions; economists use it to generate qualitative predictions.
The relevant comparison of the math in economics is not with physics but with the prose in social theory: the math is often a much clearer way to communicate a complex social process than words. Additionally, it forces an internal consistency that social theorists often lack.
Economists make assumptions to make the model tractable so that others can see the core of the idea about how something in the world is supposed to work and not because these assumptions hold in all their strictness. A lot of yeoman’s work is done seeing if the resuts of a model hold when assumptions are relaxed in order to see how robust the idea is.
Sacha: This is a bit harsh on economists! I doubt that the equation is taken to be literally true, but moreso an idealisation.
It’s probably just about succintly communicating an idea.
Ike: Most economics is all idealization, zero realization.
Jyotirmoy: This seems to be a problem with a lot of economics–what are essentially parables are presented as if they were testable quantitative theories. But this does not mean that the parables themselves are worthless. For example I think this story about prostitution which takes social stigma into account [Ed: Which didn't need all that maths in the first place] is more interesting that another story (which has also been told in economic journals) of the earnings of female prostitutes being explained by their reduced chances of marriage.
Jonathan Vos Post: So, you folks are commenting what might be summarized as:
“this math sucks!”
dave tweed: If you’re going after areas where economics really has a disconnet with reality, I’d say it’s in the sentence “when a prostitute finds it worthwhile to sell (typically) her services” (which to be fair might be a quick blog phrasing rather than intentional). What that really ought to say (and economists have been slowly cottoning on to) is “when a prostitute ought to find it worthwhile to sell (typically) her services”. Economics in the past often seemed termined to figure out what “perfectly analysing” (obviously wrt a given value system) individuals would do, ignoring the fact that in large swathes of their behaviour people aren’t and are swayed by inbuilt prejudices, etc. It’d be like physicists coming up with ever more precisely stated and proved theorems in classical mechanics, completely ignoring the fact physics (appears) inherently quantum. The best mathematics can’t be useful when your modelling assumptions are wrong.
Chris Tunnell: Talk about nit-picky.
1) This is a fitted model
2) Determining a good model to fit involves understanding symmetries of the problem
3) Extrapolating predictions from the model yields something interesting
The thoroughness of a model only becomes important when faced with wrong or boring predictions from the model. Unless you’re in maths, hand-waving is fine until your wrong or boring.
Maybe I’m missing something…