## [UPDATED] Division of labour and comparative advantage: what linearity hides in economics

*by* Carrie
*Sun Nov 13th, 2005 at 12:12:30 PM EST*

As a mathematical physicist I am bound to take a peculiar approach to economic issues, so I hope you will forgive me if this diary strikes you as, well, peculiar.

On the other hand, we have had a number of interesting comment threads about free trade and comparative advantage, *the* nontrivial true result of economic theory. A number of mathematically inclined types around here, including me, can't seem to let an economics discussion go by without taking a swipe at economists for mathematical naïveté or physics envy, and we keep hinting at parallels between economics and our own pet theories. It's about time we stuck our neck out. Maybe we'll get those promised diaries about economics and thermodynamics, economics and dynamical systems, or economics and Darwinian evolution.

So let me sum up the gist of my argument so you can jump directly to the comments after this if you wish. To make things easy to calculate, easy to visualize and easy to reason with, economic models are often formulated in terms of linear equations (if this is twice as big then that will be twice as big, too!). The problem is, to justify linearity one would have to impose a long list of implausible conditions on the economic system at hand. *Ceteris paribus* does look like a weak excuse. Comparative advantage is indeed a robust result which does not depend on all these extraneous hypotheses, but it is often presented (as it was originally by Ricardo) with the help of a linear model.

Thinking about this linear model I realized that *division of labour* can be described by a linear model without stretching reality too much, so I start from there. I imagine an economy consisting of just two people producing two goods. A simple linear diagram illustrates why specialization helps, and why it is possible that some tasks won't be carried out by those most capable of carrying them out. The result, though, is that the production line of more than one person is *not linear* but convex, and this is what makes division of labour possible.

I then look at comparative advantage, which is the generalization of division of labour from two people to two countries. Now, the discussion of division of labour makes it clear that a linear model is no longer adequate to describe the production of either economy, so I give a diagram full of nonlinear production curves.

A feature of both analyses is that, starting from a situation where both people (countries) share work (production) equally across all tasks (goods), a fairly large reassignment of tasks is needed to achieve a modest improvement in efficiency. If we take into account how reluctant people are to change careers, or how long it takes to convert an entire industry to another purpose, it is easy to see that the optimal solutions *on paper* will usually be implemented at a large human cost, if at all. This gives an explanation, *on paper* for the widespread resistance to liberalization.

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