“Gains From Trade Without Lump-Sum Compensation,” A. Dixit & V. Norman (1986)

Let’s take a brief respite from the job market; I’ve noticed some foolish things said about free trade in the news recently. Yes, Ricardo showed that trade in two goods generates surplus for both countries under free trade. Samuelson later gave a more formal, general proof of the benefits of Ricardian trade for a nation, though his theorem with Stopler explains which individuals may be made worse off. Samuelson also showed that even when individuals are worse off, there is enough surplus that transfers can be made to the harmed individuals such that free trade is a Pareto improvement on autarky. Note that the last sentence is absolutely not implied by Ricardo, and how could it have been: he didn’t have the apparatus of ordinal utility nor the concept of Pareto improvement nor the idea of the Hicksian demand curve.

All of the above is true, but it does not justify the critique that, since we don’t always redistribute gains from trade to the losers, free trade may make us worse off under some social welfare functions. There turn out to be many ways, aside from direct income redistribution, to generate the Pareto improvement. Dixit and Norman, in a 1986 JIE, give a great example of one. Disallow transfers, but allow for arbitrary taxation of goods.

It is easy to show that free trade plus commodity taxes can leave everybody with exactly the same welfare as under autarky. Let consumers demand x0 under autarky. Under free trade, a new price vector for producers leads to equilibrium changes in production for Ricardian reasons. The government then sets a commodity tax such that consumers face the same prices they faced in autarky, with the government using the tax revenue to buy the excess supply of goods and then burning them. Everyone is exactly as well off as they were before. Now, rather than burning surplus, if there are any goods where some consumers are either all net sellers or all net buyers, then (using the case where all consumers are buyers) use the tax on that good to give it a price slightly below the autarky price. All the net buyers are better off, and those who were indifferent between buying and selling are also indirectly better off. In a non-exchange economy, we can always find at least one good where all the consumers are net on one side of the market.

Later work expanded this idea into a more general model; in particular, with limits on factor mobility, we don’t get a Pareto improvement, so direct payments to immobile factors (such as job market assistance to fired workers) may still be necessary. And of course, learning-by-doing and other forms of increasing returns to scale in production have all of the usual caveats that New Trade Theorists have mentioned. Nonetheless, as a policy perspective, if you are worried about the equity problems from increased openness to trade on the consumption side, taxing the goods that become cheaper as a result of trade is a simple fix. And, unlike direct redistribution, in a large economy it is more or less incentive compatible!

Final 1986 JIE copy (IDEAS version). As an aside, I remembered this old Dixit article when reading his recollections of the great Paul Samuelson in the newest Annual Rewiew of Economics. Dixit mentions a story I hadn’t come across before. In the late 70s, after the Cambridge Capital Controversy had died down, Samuelson joked in the faculty lounge that the whole debate had been nothing but a neoclassical conspiracy to keep far left-wing attackers so busy they don’t notice the rest of our schemes! (Joking aside, Dixit has a nicely pithy summation of the reswitching debate, which sums up well what you should know about it if you are a working economist: the rate of interest is not unique and is uninformative about many interesting phenomena, but turnpike theorems and other similar statements mean that a lot of the rest of growth and general equilibrium theory is still safe.)

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6 thoughts on ““Gains From Trade Without Lump-Sum Compensation,” A. Dixit & V. Norman (1986)

    • afinetheorem says:

      What can you do? There are only so many hours in a day, right? I am fully aware of how much I don’t know; nonetheless, it’s a bit rich of Vienneau to think that Avinash Dixit is somehow too ignorant and close-minded to understand the supposedly brilliant results of an obscure yet incredibly self-confident branch of heterodox capital theorists.

  1. Robert says:

    I am quite aware of who Avinash Dixit is. And I never described him as ignorant and close-minded.

    I believe you must have added that last paragraph. Anyway Dixit says something misdirected about the Cambridge Capital Controversy, both in his book The Theory of Economic Growth and in his 1977 paper, “The Accumulation of Capital Theory”.

    • afinetheorem says:

      Come on, man. I’ve never changed a word on this site, ever, without noting that the post has been updated. The entry you call “charlatanism” is literally just a writeup of Dixit’s article, and if anything, the Dixit article is correcting a Micro 101 misunderstanding.

      • Robert says:

        I do not know your policy about updates. (I silently update grammar flaws – I have many I have not got around to.) Anyways, you apparently did not click on the link in my second-to-last paragraph. And the first paragraph in your post is full of false claims, given the existence of capital goods and a positive rate of interest.

  2. Heckuva typo by the publisher in equation (1) of the Dixit and Norman article. “s” has become “2”.

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