Free trade doesn't always benefit everyone, but it's worth it

In the interests of blowing the dust off my attempt at communication, here's an essay my economics tutor liked. I'd apologise, internet, for not to talking to you, but my friends will tell you that I don't communicate with them enough either. Ignore the terrifying title, please.

Consider the 2x2 production model with constant returns to scale, where the two factors are immobile internationally and the two consumer goods are mobile internationally. Using this model, explain the statement “free trade does not benefit everyone”.

To explain why free trade between two countries might not benefit all involved, I shall first lay out the 2x2 production model, before describing how expanded markets for a particular good will reduce incomes for those whose factors of production are scarce in their country. I will then relax the assumption of factors' free movement between industries, and examine the potential short term effects of this. I shall finally briefly argue that the negative impact of free trade can be compensated for if lump sum redistributions are possible in the favour of those who would otherwise be losers from free trade.

The standard 2x2 production model includes two goods, which are produced by different ratios of two factors of production. For the purposes of this essay, these two factors of production will be called labour and capital, abbreviated to L and K respectively, while the goods will be called guns and butter, abbreviated to G and B respectively. Butter is a labour intensive good and guns is a capital intensive good, so for a given set of factor prices the ratio of labour to capital used in the production of butter will be higher than the ratio of labour to capital used in the production of guns. The 2x2 production model also includes two countries with competitive economies, which have different ratios of the factors of production. For the purposes of this essay, these countries will be called Australia and China. Australia is a capital abundant country and China is a labour abundant country, since China has a higher ratio of labour to capital than Australia.

Given that butter is a labour intensive good compared to guns, and China is labour abundant compared to Australia, the price ratio between butter and guns will be higher in Australia than in China, if trade is not free. Furthermore, when trade is not free, production of butter and consumption of butter must be equal within (but not between) each country, as must production and consumption of guns. Assuming that demand curves for each good are the same for each country, and the technology is the same, owners of scarce factors of production in each country will be relatively better off than owners of the same good overseas. Capital owners in China will get more purchasing power from each unit of capital than capital owners in Australia, because the ratio between returns to investment and wages will be higher in China.

When trade is free, however, only the value of production in each country will have to be equal to the value of consumption.

P_BxD_B + P_GxD_G = P_BxQ_B +P_GxQ_G

which can be rearranged to the following budget constraint:

D_G – Q_G = (P_B/P_G)x(Q_B – D_B)

Guns imports = Price ratio x Butter exports

Free trade between Australia and China will lead to a convergence of goods' prices, as free markets clear. In China, this will lead to a rise in the price of butter and therefore, since prices are relative, a reduction in the price of guns. In Australia the reverse will occur. Each country will export the good that it can make more efficiently than the other, leading to an equalisation of factor prices, despite the international immobility of the factors of production themselves. In China, owners of labour (workers) will have their purchasing power increased, because the rising price of butter will increase the price of the factor proportionately more used in its production; wages will increase. In Australia, for similar reasons, owners of capital will be better rewarded. However, as the relative price of butter rises in China, owners of capital in China will be made worse off as the relative price of guns falls. In Australia, owners of labour will be made worse off as the relative price of butter in the country falls. Therefore, in this situation, “free trade does not benefit everyone”.

By relaxing the assumption that factors of production can be freely moved between industries, 'specific factors' become possible. For example, a specialist in gun manufacture may not be as efficient at milking cows as she is at making guns. Factors of production, labour in this instance, can in the short term be paid different prices to make different goods. Only in the long run will earnings equalise, as factors of production gradually shift (by, for example, retraining). In 2x2 production model used above, a fall in the relative price of butter in Australia, though in the long term improving the purchasing power of owners of capital, may in the short run reduce the earnings of owners of capital whose capital is currently invested in herds producing butter, until they can reinvest their capital in gun factories.

Finally, I shall briefly note that according to the second fundamental theorem of welfare efficiency, lump sum redistribution of goods could potentially redistribute the gains from trade. A Hicksian compensating variation (the amount of money, and therefore value of goods, required to put a consumer back on their initial utility curve) would restore Australian workers (and/or Chinese capitalists) to their original welfare, allowing free trade to produce at least a weakly preferred allocation. If the gains from trade are greater than this, as they can potentially be because trade expands the consumption possibilities of an economy, then it is possible that everyone can strongly benefit from free trade.

In conclusion, because according to the 2x2 production model free trade causes the equalisation of factor prices, those who own factors whose relative price decreases will lose purchasing power, and (if standard assumptions are made about utility maximising consumers) will therefore be worse of after the trade. Some owners of the abundant factor of production may be worse off in the short term after free trade if they are specific factors. Despite these results, if lump sum transfers are possible, it should be at least potentially possible for everyone to gain from free trade.