« Is There a Hauser’s Law for Canada Too? | Main | An upward-sloping IS curve »


Feed You can follow this conversation by subscribing to the comment feed for this post.

economics should keep it's dogma out of the natural sciences.

Good question. Do you put information asymmetry in the category of transaction cost? Cause that seems like a pretty good reason not to trade.

Since I'm the one who asked for Nick's perspective as an economist on 'biological market models', I feel like I'd better comment (and not just to thank Nick for going from zero to substantive blog post in the space of a few hours!)

The implicit assumption of two perfectly complementary goods is, in the biological case considered in the paper Nick links to, entirely reasonable. All organisms need (say) carbon and phosphorus, and neither of those resources can substitute for the other (you can't stick C atoms in your DNA where P atoms are supposed to go, for instance). The assumption of fixed preferences is also empirically reasonable for many organisms (though actually not for plants). Many species have quite homeostatic chemical composition, and so require different, perfectly complementary resources in fixed ratios. So some aspects of biological market models that look unusual to economists are unusual for good biological reasons. But I'm suspicious that some other aspects of current biological market models may be economically unusual for less-good reasons. Hence my curiosity (which Nick satisfied insanely fast!) as to how an economist would react to these models.

In addition to the points Nick raised here, I'm also chewing on the issues raised in his previous post, to do with what happens (in a biological context) when future expectations of market players aren't satisfied, perhaps because it's impossible for them all to be satisfied...

Anyway, thanks again to Nick for taking the time to offer his thoughts and make an economically-ignorant ecologist a little less economically-ignorant.

Nathan: It's far too late for that, I'm afraid. If you add Thomas Malthus and Adam Smith together, and apply it to biology (OK and do a lot of thinking and observation) you get Charles Darwin!

K: yes. Asymmetric Information underlies a lot of transactions costs, in one way or another.

Jeremy: "The implicit assumption of two perfectly complementary goods is, in the biological case considered in the paper Nick links to, entirely reasonable."

Aha! I really did wonder about that. I assumed (uncharitably) that it was just because they weren't comfortable with more general preferences, and drawing indifference curves. If critters really do consume in fixed proportions, regardless of relative prices, then that is a much simpler way of drawing preferences.

Let me recommend Michael Ghiselin's _The Economy of Nature and the Evolution of Sex_ to anyone interest in the economics opand biology of the division of labor, among other economic / biological topics.

Wonderful stuff. Better then Richard Dawkins.

OK. Is this a genuine "proof" that there are always gains from trade under increasing returns to scale (PPFs convex to the origin)?

At autarky, either MRTi=MRTj or not. Lets take each in turn.

1. If MRTi is not = MRTj then it is clear that total output of both goods will increase if both agents make a small move in opposite directions towards specialising in that good in which they have a (local) comparative advantage.

2. Draw a straight line between the 2 agents' autarky points. The mid-point of that line represents average production per agent. Double it, and we get total production. If MRTi=MRTj, then let both agents make a medium-sized move in opposite directions away from autarky. The mid-point of the straight line drawn between the two production points must move North-East as they move away from the autarky points. So we get more of both goods produced.

Thus, there are always gains from trade with increasing returns to scale.

Well, wasted a good chunk of morning thinking about this, but I think you can prove it more generally than that[1]:

Assume 2 goods, X and Y, and two individuals, A and B. The PPF's for A and B are, respectively[2], Y_A = F(X_A) and Y_B = G(X_B). Assume both F and G have negative first derivatives. [X_A*, F(X_A*)] is the autarky point for A, and [X_B*, G(X_B*)] is for B.

To get gains from trade (when goods are perfect complements), we have to find a new combo, X_A, X_B, where X_A + X_B >= X_A* + X_B* and F(X_A) + G(X_B)>= F(X_A*)+G(X_B*). To simplify, I'll hold the sum of X's constant, and look at small changes along the ppf's: X_A = X_A+n, X_B = X_b-n.

The change in the sum of Y's is:
delta_Y = Y_A + Y_B - Y_A* -Y_B* = F(X_A*+n) + G(X_B*-n) - F(X_A*) - G(X_B*)

After Taylor expanding and simplifying:
delta_Y = n*F'(X_A*) - n*G'(X_B*) + n^2/2*F''(X_A*) + n^2/2*G''(X_B*) + ...

If F' != G', we can ignore the higher order terms (since they vanish for small n). In that case, either F' > G', so n>0 leads to delta_y > 0, or F' < G', so n<0 leads to delta_y >0.

If F' == G', you still get gains from trade if F'' & G'' >0, (both convex) or if F'' or G'' > 0, and F'' + G'' > 0.

I think that covers all the bases. These are, though, only sufficient, not necessary conditions to get gains from trade.

[1]I'm absolutely positive this proof, or its equivalent, isn't new, but I don't have any trade textbooks handy to pull it from.

[2] God, I wish latex worked in Typepad comments.

Well done Eric! A morning well-wasted!

There was one case I missed: what if one agent has a convex and the other a concave PPF?

God, I wish latex worked in Typepad comments.


If the first derivatives aren't equal at their respective autarky points, the convexity/concavity of the ppf's don't matter. If they are equal, their'll still be gains from trade if the second derivative of the ppf of the agent with a convex ppf is greater in magnitude than the second derivative of the agent with a concave function.


If A'' (convex) > 0 > B'' (concave), then, to have gains:

A'' > 0 > B'' > -A''.

Eric: that makes sense, intuitively.

The bottom line to all this: given the assumptions (especially both agents consume both goods in autarky), there really are almost always gains from trade. If two critters don't exhibit mutualism, it must almost certainly be because of transactions costs (one critter would eat the other critter if both appeared in the marketplace).

Nathan: It's far too late for that, I'm afraid. If you add Thomas Malthus and Adam Smith together, and apply it to biology (OK and do a lot of thinking and observation) you get Charles Darwin!

i should have been more clear. Modern Economics should keep it's dogma out of the social sciences. i have much more respect for classical economics then i do for neoclassical economics

If there is no gain to be had from the trade, why are the parties trading?

Adam: If there are no gains from trade, they won't trade. If there are gains from trade, they will trade, unless the transactions costs exceed the gains from trade.

The comments to this entry are closed.

Search this site

  • Google

Blog powered by Typepad