Trade, Efficiency and Redistribution
Published by Michael Greinecker on Wednesday, May 02, 2007 at 14:29Given all this talking about trade, it pays to get the theory right. Why is free trade modulo transfers better than autarky? The appropriate framework is general equilibrium theory. If we assume that all the technological possibilities available before trade are available afterwards, we can look for efficient international allocations, do the appropriate lump sum transfers required by the second welfare theorem and let markets do their job. There´s a problem: These transfers are usually international transfers, and domestic transfers are not sufficient.
What can we do when we restrict ourselves to domestic transfers? Grandmont and McFadden have a elegant solution. Take the autarkic equilibrium (equilibrium before trade) and use it as the endowment. Now open all international markets. The resulting equilibrium is efficient and since nobody accepts something worse than their endowment, nobody loses from trade. The problem reduces to a existence proof. This requires the transfers to happen before the opening of the borders.
We cannot always get Pareto improvements in comparison to autarchy, when we use only ex post transfers, that is transfers after the borders are open. Cordella and Ventura give two simple examples. One of their examples has a nice interpretation:
[I]t may well be the case that the possibility of alternative more profitable uses of resources may highly penalize the production of goods essential to some agents. [The 2nd example] might shed some light onto the case in which a poor country with some capitalists engages in free trade with a more developed country. Capitalists in the poor country will exploit the more profitable investment opportunities available in the richest country, whereby causing a decrease in the production of domestic industry output which might be what the rest of the population is interested in, e.g. food or services.
Ex post transfers are of course the kind of transfers most of the debate centers around. Wrongly.
References:
Cordella, T. and L. Ventura (1992), “A note on redistribution and gains
from trade,” Economics Letters, 39, 449 - 453.
Grandmont, J.- M. and D. McFadden (1972), “A technical note on classical
gains from trade,” Journal of International Economics, 2, 109 - 126.
I promise that I didn't read this before making the comment over at Gabriel's. And it's nice to know that McFadden and Grandmont showed that this applies to more than just an endowment economy (as I hedged my assertions), which thinking about it more, makes sense.
A quick search also yields this
http://www.econ.brown.edu/fac/H_Polemarchakis/trd.pdf
Also I'm having doubts again (need to read a the original McF and GM paper).
1. I'm not clear why you would need transfers at all, domestic or otherwise, before or after trade. Seems like this is about the First Theorem rather than the Second. You have First Theorem holding before trade so you got Pareto. Then you open up to trade which may change relative prices or whatever but so what. Everyone can stick to what they had before.
2. Suppose you're in a Hecksher-Ohlin world with capital and labor, capital mobile between sectors, constant returns, perfect competition, all that. Households own the capital and rent it to the firms. They use their incomes from labor and capital to consume a basket of produced goods. When you open up to trade the rental price of capital may change so some may loose. So the consumption bundle that was available before trade (the post-domestic trade "endowment") may not be available for some (basically the Stolper Samuelson effect). So in this case it seems like you'd still need transfers, though only domestic ones. The same kind of problem doesn't arise with labor if you stick consumption of leisure in there somewhere.
Huh... What I don't get is how an exogenous increase in the number of agents in the economy can cause inefficiency.
If two economies merge and form one big economy, in what circumstances can that violate the Pareto criterion (everyone at least as well off).
As far as I can see, only by taking the pre-free-trade/autarky equilibrium as endowment (my wage, before free trade, for example).
After liberalization, any equilibrium wage bellow my autarky wage will make me worse off, in this sense.
But, isn't that crazy? Why don't we take the previous equilibrium to be the endowment/baseline in all circumstances?
"Huh... What I don't get is how an exogenous increase in the number of agents in the economy can cause inefficiency."
It doesn't. The after trade equilibrium is always efficient (given standard assumptions).
"But, isn't that crazy? Why don't we take the previous equilibrium to be the endowment/baseline in all circumstances?"
ecause the people inside a country vote.
I will write more on this stuff later.
The Pareto criterion loses all its authority, the little or any it had, if we can flip-flop between what we consider the baseline against which we judge the worse off/better off valuations.
This is what I was trying to say with my too-clever-for-its-own-good post, before that stupid mistake on monopoly.
@Radek:
I actually read the Polemarchakis et al paper first, but I didn't think it´s message is that important.
On your points:
1. There is a closer connection between the first and second welfare theorem than is usually considered. I´ll post about it later today. The story with two stages of trading is a just a story. What we want to show is that free trade equilibria after redistribution of endowments can be at least as Pareto good as autarky equilibria. McF and G actually talk about income redistribution.
All firms maximizing profits is the same thing as profit maximizing over the aggregate production technology, given prices. So profit maximizing boils down to producing the most expensive aggregate net ouput. Now the autarky output at international prices can be at most as expensive as the aggregate production of a country at international prices. So one can give enough "real income" at international prices by domestic redistribution so that everyone can buy their autarky consumption bundle. The rest follows from a revealed preference argument.
2. Say there are two persons in a country. The first one (1) simply has some goods, the second one (2) can produce either a some medicine only (1) needs or cosmetics. Now at autarky 2 would trade medicine for some 1s endowment. But at international prices 2 would produce cosmetics and could sell them for more of what 1s entire endowment is worth. So there will be no ex post redistribution that allows 1 to get enough medicine, but ex ante 1 could have gotten a claim to the medicine that he could keep ex post.
@Gabriel:
There is a Pareto ordering which has Pareto efficient allocations as maximal elements. What we can show is that free trade with transfers can be made at least as Pareto good as autarky. Nothing oses it´s meaning here.
My point (and Radek's?) was that free trade, even without transfers, is at least as good off as autarky -- if you take "initial endowments" to be what we usually take to be the initial endowments.
And then you said something about voting, why it required an alternative "initial endowment" treatment, which you don't mention again in the newer post.
That doesn't work. Suppose you have a individual that has only apples and wants only oranges. If we "take "initial endowments" to be what we usually take to be the initial endowments", apples that is, then that persons welfare without transfers depends only on the relative price between apples and oranges. Now opening markets may well lead to oranges becoming relatively more expensive, so our individual in question loses from free trade.
I understand what you're saying but you're still comparing the equilibrium afters the borders open with the equilibrium of before they open. This is not what I have in mind. Let me try it this way:
He start off with (10 apples, 0 oranges).
With closed borders, he can get (0 apples, 10 oranges).
After the borders open, he can get (0 apples, 7 oranges).
Clearly, for him: (0, 10) prefered to (0, 7) prefered to (10, 0)
You say: He prefers (0, 10) to (0, 7) so he's worse off after the borders open. Compensate him.
I say: He prefers (0, 7) to (10, 0) so he's better off, compared with his initial endowment of (10, 0). No compensation for him!
And the point is? The question is wether international trade Pareto dominates autarky, not wether it Pareto dominates no trade and exchange whatsoever.
If that is the question then the answer is in every textbook.
But why should that be the question? And if that's the question, then why not apply it everywhere?
As it turned out in my entry, would you support compensating the monopoly?
"If that is the question then the answer is in every textbook."
Yes, but sadly without the details.
"But why should that be the question? And if that's the question, then why not apply it everywhere?"
Of course you can, it´s a general theorem.
"As it turned out in my entry, would you support compensating the monopoly?"
There´s not enough information there to answer that question.
I don't understand what you mean. :-(
Let's say I earn a large pure rent in equilibrium (for whatever reason) and that in this equilibrium there's considerable deadweight loss. Let's say that the government can trivially and without risk restore efficiency, but in a way that reduces my income.
What information do you need besides this to decide if I should or should not be compensated?
Maybe you didn't deserve the rent in the first place.
So what you're saying is that while the Pareto criterion might ask for a compensation, you'd only sanction it based on other criteria?
In which case, why bother about Pareto efficiency in the first place? What not have criteria about what people deserve and leave it at that?
Well, it´s all about the Pareto ordering. If A and B are allocations, we have the ordering ApB if and only if everyone is at least as well off in A as in B. What this post showed was that if B is the autarky allocation, then there is, after some transfers, a free trade allocation A such that ApB. Now pareto efficiency is something else. A allocation A is Pareto efficient if it is maximal in the Pareto ordering, that is if there is no allocation B such that BpA and not(ApB).
"In which case, why bother about Pareto efficiency in the first place? What not have criteria about what people deserve and leave it at that?"
That´s exactly my point of view. But I think that what is best according to these critera should also be Pareto efficient. No contradiction here.
Free trade efficiency is flawed. The only efficiency free trade brings is from raw resource movement. Food, steel, iron, and anything that a nation can't natural produce, which has to be imported. Anything that can be produced in a country, is only more efficient, because of tech advancement/information or an exceptional human being.
Human beings of a general population of a nation are going to have almost the same efficiency as any other general population of any other nation. Example, I can take 10,000 people from one nation and 10,000 people from another nation and teach them to produce something and they will have almost the same efficiency from this factor.
If tech advancement could be easily copied from one nation to another, than efficiency would be the same as with free trade. The only reason free trade is more efficient than a high tariff nation is from advance tech. If information was readily availible, free trade would lose all of its standing.