Pareto Inferior Trade

The result is striking: with incomplete insurance markets, opening commodity trade between two otherwise competitive economies can make everyone worse off. The key insight is that goods prices themselves can provide insurance when explicit insurance markets are missing. Trade changes the price process, and can accidentally destroy that insurance.

Basic setup

There are two identical regions, $j=E,W$, each with farmers and consumers. Farmers allocate one unit of land between a risky crop, fraction $x$, and a safe crop, fraction $1-x$. Safe-crop yield is normalized to $1$. Risky-crop yield is

For the clean benchmark they assume perfectly negatively correlated weather:

Thus a bad harvest in East is exactly offset by a good harvest in West.

A farmer’s income is

where $p$ is the risky-good price and $q$ the safe-good price. Farmers are risk averse:

The first-order condition is

This marginal-utility weighting is the critical object.

Consumer demand

Newbery and Stiglitz deliberately choose unit-elastic demands. Their indirect utility can be written, for $\rho=1$, as

and more generally as CRRA over the price-adjusted income index. This produces

where $a$ and $b$ capture expenditure shares. Define consumer spending per farmer

This unit-elastic demand assumption gives the model its especially transparent insurance mechanism.

Autarky: prices insure farmers

Consider one country by itself. Supply of the risky crop is $nx\theta$, so market clearing implies

and therefore

That is the crucial equation. When output $\theta$ falls, price $p$ rises exactly proportionally, so revenue per acre from the risky crop does not depend on the weather. Likewise,

So although physical production is risky, the farmer’s income is not.

For an interior equilibrium, returns on the two crops are equal, $p\theta=q$. Therefore

giving

Farmer income becomes

so that

The commodity price system has created implicit harvest insurance.

Who bears the risk? Consumers. Since

consumer prices rise in a bad harvest. For logarithmic utility,

hence

So autarky transfers production risk from farmers to consumers through prices. The paper explicitly emphasizes that unit-elastic demand transfers the risk from producers to consumers.

Now open international trade

Because $\theta_E+\theta_W=2$, aggregate risky output is

It is nonstochastic. Consequently world prices are

Both prices are now constant. At first sight this looks wonderful: trade has diversified aggregate production risk. But look at the individual farmer. His income is now

and using equilibrium prices,

Thus $E[\pi_j^T]=(a+b)y$, exactly the same mean income as under autarky, but now

So:

For every strictly risk-averse farmer,

Farmers are unambiguously worse off from trade. This is the heart of Newbery and Stiglitz. Trade stabilizes prices, but those fluctuating prices were precisely what insured producers.

Farmers respond by reducing risky production

There is an additional general-equilibrium effect. Suppose initially we tried the autarky allocation $x=x^A=a/(a+b)$. Then $p^T=q^T\equiv c$, and the farmer’s first-order condition evaluated there is

Since income rises with $\theta$,

therefore $\operatorname{Cov}\left(U'(\pi),\theta\right)<0$, so

Thus the farmer wants less risky production: $x^T<x^A$. Newbery and Stiglitz derive, for small risks, approximately

where

is farmers’ relative risk aversion. So greater production risk or greater producer risk aversion causes a larger retreat from the risky activity. This is the real-efficiency effect of missing insurance markets: trade produces producer income risk, which produces less risky production.

What happens to consumers

This is where the Pareto-inferior result becomes surprising. Consumers get one obvious benefit. Under autarky $p^A\propto 1/\theta$; under free trade $p^T$ is constant. So consumers gain from international diversification.

But they suffer another effect, because farmers change production. Consumer deterministic welfare, suppressing constants, is

Its maximum occurs at

or

Hence the autarky production mix happens to be the allocation consumers would prefer. But trade causes $x^T<x^A$, and therefore $g(x^T)<g(x^A)$. Consumers face a trade-off: the change in consumer welfare is the gain from price stabilization minus the loss from distorted production.

For log utility this can be seen especially cleanly. We have

while

Thus

That one equation contains almost the entire argument.

When does trade become Pareto inferior?

Farmers are already worse off. For free trade to be Pareto inferior to autarky, consumers must also be worse off:

The left side gets large when farmers react strongly to risk. In particular, $x^A-x^T$ rises as $R$ rises. Hence sufficiently risk-averse producers move far enough out of the risky crop that the consumers’ production-composition loss overwhelms their benefit from stable prices.

Newbery and Stiglitz establish that, for given technological risk and demand parameters, there is a critical producer-risk-aversion level, depending positively on consumer risk aversion, above which

so that free trade is Pareto inferior to autarky.

They also show that some trade need not be bad — the welfare relationship can be non-monotonic. Indeed, their trade-policy analysis finds that starting from autarky, allowing a little trade can be Pareto improving, while starting from unrestricted free trade, a restriction can be Pareto improving under appropriate conditions.

Why doesn’t the First Welfare Theorem rule this out?

Because a hypothesis of the theorem is violated: markets are incomplete. There is no state-contingent contract $z(\theta)$ allowing the farmer to insure crop-yield risk. Under autarky, the goods market happens to synthesize one, since $p(\theta)\theta$ is constant. Opening another market — international trade — changes equilibrium prices,

and thereby destroys the implicit insurance contract.

Newbery and Stiglitz describe precisely this point: with incomplete markets, one market can perform several functions simultaneously, allocating commodities and allocating risk. Institutional change in one market can therefore remove an insurance service supplied indirectly by another. This gives the deepest way to state the paper: more markets do not imply better allocation when the original market structure is incomplete.

The mechanism in one diagram

Conceptually, under autarky,

whereas under trade,

So the paradox is that international trade diversifies aggregate quantity risk, but in doing so removes endogenous price insurance and can increase individual income risk. That distinction between aggregate stabilization and idiosyncratic income risk is exactly why this paper remains important. The result is not that diversification fails mechanically; it is that who bears the remaining risk is endogenous to equilibrium prices.

One important qualification: the model deliberately removes ordinary comparative-advantage gains — the two regions are identical except for their weather realizations — so the paper is a counterexample to a general theorem about free trade under incomplete markets, not an empirical claim that actual trade liberalization normally lowers welfare.