Trade

The following discussion is couched in terms of products and a single consumer utility function for each country.  Consequently, it does not address investments directly or the problem of aggregating individuals’ utility functions.  Nevertheless, the discussion provides useful insight that puts the pronouncements of most of the talking heads, media and politicians in perspective.

Advocates of free trade rightfully point out that it can lead to producing more of everything versus no trade, hence can make everyone better off.  What they gloss over or ignore is that actual trade is not the free trade presumed in their analysis and that not everyone ends up better off.

Background

Consider two countries, A and B, that each can produce several products.  Each country has a production possibility frontier (PPF) that represents the maximum possible output combinations of the products, i.e., where increased output of one product necessitates decreased output of one or more other products.  Equivalently, one person cannot be made better off unless another is made worse off.  This is called a Pareto optimum.  Each country’s PPF represents a Pareto optimum for itself.

If a country’s production combination plots inside its PPF, then production of one or more of products can be increased without decreasing production of any other product.  This implies that everyone can be made better off.  Therefore, maximum wellbeing requires that each country’s production schedule be on its PPF.

The PPF’s slope with respect to pairs of products is the ratio of how much more of one product can be produced per unit of the other product foregone.  It is called the marginal rate of transformation (MRT).

The discussion below presumes the following, unless otherwise stated.

·         Perfect competition, i.e., marginal revenue equal to price, no frictions due to government regulations, import or export taxes, subsidies, vampires etc.

·         Business decisions based on marginal analysis.

·         Marginal cost curves that slope upward.

·         A PPF that is convex outward for all countries (all MRTs are negative and decreasing, i.e., more and more of one product’s production must be given up to produce an additional unit of another product.)

In the absence of trade, the optimum point on a country’s PPF is determined by its PPF’s shape and its citizens’ product preferences.  At the optimum point, any increased production of one product produces a positive marginal utility (increased satisfaction) that is exactly offset by the negative marginal utility due to the necessary decreased production of other products.  This is true for each country.

Typically, the PPFs of different countries have different shapes and/or its citizens have different preferences.  If so, then, without trade, it is likely that each country’s production point on its PPF has MRTs for at least some pairs of products that differ from other countries’ MRTs for the same pairs of products. In this case, each country is said to have a comparative advantage for one or more products.  For such product pairs, trade makes possible increasing the aggregate production of one or both products without decreasing the production of other products.  This implies that trade makes it possible to produce more of everything and can make everyone better off if any country has a comparative advantage with respect to another.  Although each country may be at a Pareto optimum separately without trade, the countries cannot be at a Pareto optimum in aggregate without trade.

Example

Countries A and B are not trading and both are producing cars and oranges.  Due to differing circumstances, the MRT for Country A is currently 1 car for 1 ton of oranges and the MRT for Country B is currently 1 car for 2 tons of oranges.  Country A has a comparative advantage in cars and Country B has a comparative advantage in oranges.  The comparative advantages provide an incentive to trade.  It pays for Country A to ship cars to Country B, exchange them for oranges at 2:1 (rather than the domestic 1:1 tradeoff), and ship the oranges back to Country A.  Country A’s car production and Country B’s orange production increase.  Country A’s orange production and Country B’s car production decrease.  More of both cars and oranges are produced overall, and it is possible to make everyone in both countries better off.  This trading cycle works due to the countries’ comparative advantages, and regardless of the exchange rate.

Due to the PPF’s convexity, each country’s MRT changes as the trading builds.  The increased production of cars and decreased production of oranges in Country A results in raising the real relative price of cars and decreasing the real relative price of oranges in Country A.  In other words, 1 car becomes exchangeable for more than 1 ton of oranges in Country A.  In contrast, the decreased production of cars and increased production of oranges in Country B results in lowering the real relative price of cars and increasing the real relative price of oranges in Country B.  In other words, 1 car becomes exchangeable for less than 2 tons of oranges in Country B.  Trading continues until the MRTs and the real relative prices for cars and oranges is the same in both countries or until Country A produces only cars and Country B produces only oranges.

There is no incentive to trade if each country’s PPF shape and preferences results in equilibrium such that the countries’ MRTs are identical without trade.  This condition is unlikely, hence trade almost certainly provides a benefit.

Trade’s benefit.

Typically, as in the example:

·         Trade makes it possible to make everyone better off.

·         Trade ensures production across countries is at a Pareto optimum, i.e., making one person better off requires making another person worse off.

·         Each country will produce more of some products and less of others than they would without trade.

·         For products produced by more than one country, trade will equilibrate when each producing country is operating at a point on its PPF with the same MRTs for the products as the other producing countries.

·         For products produced by more than one country, every producing country’s real relative prices will be the same for the products produced in common.

An import tax

Suppose Country B applies an import tax on all imported products.

Start from the free trade, no-tax equilibrium, which is an aggregate Pareto optimum.  Then the MRTs for all pairs of products produced by more than one country are the same.  There is no incentive for further trading due to comparative advantages – because there are none.  Now impose the tax.  The real MRTs remain the same, hence there continue to be no real comparative advantages.  However, roughly, the countries’ effective MRTs, hence effective comparative advantages, are reduced by the amount of the tax. Trading at the current level is unprofitable, and it pays to reduce it until there are no effective comparative advantages.  Trading is reduced if the import tax is not too high or eliminated if it is too high.  Since the new equilibrium is no longer an aggregate Pareto optimum, at least one person is worse off and repealing the tax can make at least one person better off without making anyone worse.

Example

Consider the previous example with a T % import tax.  Adding the import tax is roughly equivalent to saying that for every 100 cars shipped from Country A to Country B, only (1-T)*100 cars arrive in Country B.  The result is a less profitable trading cycle, i.e., a lower effective comparative advantage.  Trading equilibrium will be reached prior to the countries’ real MRTs and relative prices being the same.  Either fewer car are produced or fewer oranges are produced or fewer of both are produced relative to no import tax.  With less aggregate production, at least some people are worse off.

An export tax

Suppose Country A applies an export tax on all exported products.

An export tax by Country A is roughly equivalent to an import tax by Country B, so the effect is the same.

A subsidy for exports

Suppose Country B subsidizes all exports.

Start from the free trade, no-tax equilibrium, which is an aggregate Pareto optimum.  The MRTs for all pairs of products produced by more than one country are the same.  There is no incentive for further trading due to comparative advantages – because there are none.  Now impose the subsidy.  The subsidy creates an incentive for Country A to export more of any of its products to Country B, sell it for Country B’s currency, buy Country B’s same product with the proceeds, ship it back to Country A, and use the subsidy to buy still more of Country B’s product with Country B’s currency and ship it home.  It is roughly equivalent to an increase in Country A’s productivity and a decrease in Country B’s productivity.

This trading cycle does not presume a change of production in either country and does not depend on the exchange rate, hence, other things equal, there is no reason for it to stop until the smaller country exports all its production and consumes only the other country’s products.  Country A is better off and Country B is worse off than before.  It is possible to make all of Country A’s citizens better off.  Country B’s citizens will be worse off, on average.

Unfortunately for Country A, other things are unlikely to remain equal.  Sooner or later, Country B may wise up – hmm - maybe not – the Export-Import Bank has a lot of adherents.

An import tax on some but not all imports

Suppose Country B applies an import tax on some, but not all imported products.

Start from the free trade, no-tax equilibrium, which is an aggregate Pareto optimum.  As before, the MRTs for all pairs of products produced by more than one country are the same and there is no incentive to trade.  Now impose the tax on some, but not all imports.  The real MRTs remain the same, hence there continue to be no real comparative advantages.  However, roughly, the countries’ effective MRTs, hence effective comparative advantages, are reduced by the amount of the tax for the taxed products. Trading at the current level is unprofitable for these products, and it pays to reduce it until there are no effective comparative advantages.  Trading in the taxed products is reduced if the import tax is not too high or eliminated if it is too high.  Since the new equilibrium is no longer an aggregate Pareto optimum, at least one person is worse off and repealing the tax can make at least one person better off without making anyone worse.

An export tax on some but not all exports

An export tax by Country A is roughly equivalent to an import tax by Country B, so the effect is the same.

A subsidy for some, but not all exports

Suppose Country B subsidizes some but not all exports.

Start from the free trade, no-tax equilibrium, which is an aggregate Pareto optimum.  The MRTs for all pairs of products produced by more than one country are the same.  There is no incentive for further trading due to comparative advantages – because there are none.  Now a subsidy on some but not all products.  The subsidy creates an incentive for Country A to export those of its products subsidized by Country B, sell them, buy Country B’s same product, ship it back to Country A, and use the subsidy to buy still more of Country B’s same products and ship them home.  This trading cycle does not presume a change in the production schedule of either country, hence does not necessarily change their real MRTs.  Aggregate production can continue to be at an aggregate Pareto optimum.  However, distribution has changed to favor Country A.

Other things equal, there is no reason for this process to stop until the smaller country exports all its production of the subsidized products and consumes only the other country’s subsidized products.  Country A is better off and Country B worse off than before.  It is possible to make all of Country A’s citizens better off.  Country B’s citizens will be worse off, on average.

Buy American

Suppose Country A decides to “Buy Country A”.  Then Country B will not have any of Country A’s currency with which to buy Country A’s products.  Nor will it be possible for Country B to trade its products for Country A’s products.  There will be no trade.  As discussed above, it will be possible to increase production of everything and make everyone in both countries better off by eliminating the Buy Country A policy.

Moving to a Pareto optimal production frontier does not imply that everyone is better off

Moving from no trade to Pareto optimal trading makes it possible to produce more of every product, hence makes it possible for everyone to be better off.  However, both countries will produce more of some products and less of others than before, hence both countries will gain some jobs and lose others.  Even if this does not lead to unemployment, there is no guarantee that a worker who was making a high marginal contribution on his old job can make as high a marginal contribution on his new job.  His knowledge, learning ability, physical characteristics, etc. may preclude it.  If so, free market equilibrium will make him worse off with trade than he was without trade.  Assuring that everyone is better off with trade requires an arrangement to redistribute the increased output that competitive free trade provides.  While there is an incentive for everyone to agree to such an arrangement to gain widespread acceptance of free trade, there is seldom a mechanism for establishing one.  Consequently, free trade is most likely to become a political issue with the strongest special interest groups that would be hurt winning at the expense of free trade.