The HO theory is a development of the Ricardo’s trade theory along the neo-classical lines. Where as for Ricardo, the transformation curves where straight and trade arised because of different technologies available in different countries, for HO model, the transformation curves are not straight, technologies are the same in each country, and trade arises due to different endowments in different countries. This will make the productivities of different countries different.
The concave transformation curve means that the production of wheat requires inputs depending on the amount of wheat produced. For Ricardo, it was always along the lines of wheat=2L+3C etc. The transformation curve(TC) is a curve similar to production possibility frontier, depicting how much of the other good must be given up to produce the first good, in a two good economy. Non-linear TC-s arise because of diminishing marginal returns. Although the economy is assumed to have constant returns to scale, some factors are better suited for the production of one good, and they will become scarce.
The following diagram can depict the economy under HO:
Now a new concept of isoquant must bee introduced to analyse the equilibrium. It will depict the amounts of labour and capital needed to produce some fixed number of units of the good. In the above diagram, wheat production is more labour intensive. Under some restrictive assumptions of uniform preference, technology being constant, perfect competition and no factor intensity reversals (all isoquants cross only once) a single equilibrium occurs in autocracy. When the assumptions are extended to include free trade, homogeneous tastes across countries, different factor endowments across countries and no complete specialisation, then a unique equilibrium will also occur in trading economies. But let me first look at the single economy. There must be a set of prices for the factors of production, that maximise the utility of the nation. One needs mathematical programming to calculate the solution for more than two goods, however, for two goods all inputs will be used and conventional techniques can be applied. I will try to tackle the problem mathematically at the end, for now I just assume that the prices of factors and their endowments will produce the budget line AB above. Now, there is an isoquant for every amount of goods produced. Maximum production can be obtained when isoquants are tangent to budget line and the equilibrium will occur. The two isoquants are drawn so that in equilibrium all resources are in use. I have no idea however, how it is achieved in practice. Anyway, comparatively it is clear that when the relative price of factors changes, possible due to the increase in one of them, the equilibrium quantities produced will change. Furthermore, one will produce relatively more of the good that requires more of the factor that is now cheaper.
When the trade is opened up according to HOS the country has a comparative advantage in the good that makes relatively intense use of the country’s abundant factor. In a two good/two country world when original endowments differ, trade will occur. However, the specialisation will not be complete, because as one country produces more of the good she has the comparative advatage in, its price will rise. From this there will arise a number of other theorems. The Rybczynski theorem states that at constant prices, an increase in one factor endowment will increase absolutely the output of the good intensive in that factor and will reduce absolutely the output of the other. However, as there is perfect competition and factors are paid according to their marginal revenue product, then the Stolper-Samuelson theorem applies, that says a decrease in the relative price of the labour-intensive good will decrease the wage rate relative to both commodity prices and increase the rent. The international trade will equate the prices of two goods, it will thus equate the rents and wages as well. Changes in the factor endowment will change the relative price of that factor in both countries, the remuneration it is paid and will change the output according to the factor intensity of different goods.
One should be able to use envelopes theorem and implicit functions to solve this mathematically. We need to express wages, rents and outputs in terms of prices of factors in equilibrium and input constants. Then by partially differentiating with respect to factor endowment, one should be able to answer the question directly. however, this is way too difficult to do, because of the nonlinear isoquants. Furthermore, it will not generalise without the help of linear programming. That is probably why it was not attempted in the references.
As HO theory is not verified empirically, it does have many criticisms and enhancements. The classical empirical criticism is that of Leontief. He predicted that USA will have more capital and thus should import goods that are labour intensive. In fact, it did the opposite. This can be accounted by the inclusion of human capital and the exclusion of goods that use natural resources. However, it might also be that the factor intensities reverse over some product range. And the HO model does not give accurate results with trade deficit. However, the HO theory gives better results for the trade between two very different countries, thus there is some rationale in analysing the trade with LDC-s by using HO models.
This question is a much debated one. Common logic supports the idea, very simple theory as well. However, most empirical results reject it. So is the link between wages and imports one that is though up by economists due to spurious correlation, or is the link expressed in a more complicated form than most studies assume?
H) model is the theory behind the claim. If correct, then after the trade liberation the LDC-s will specialise on products requiring more unskilled labour, and western countries will specialise on more skilled work. As the pay in LDC-s is very low, and with international trade the pay will equalise, then the pay of unskilled workers in the west must fall.
This has indeed happened wide scale in USA. However, Europe with its labour market protections has avoided the erosion of low-skilled workers, but its unemployment rates have gone up significantly.
Meanwhile the manufacturing imports from LDC-s (though of as the tradable good, that employs most unskilled workers) have more than doubled. There are two further extensions. Firstly, when the pay of unskilled in manufacturing falls, then the pay of non-tradable sectors labour will fall as well, because the manufacturing workers can shift easily. Secondly, no actual import needs to occur, the mere threat of an import will serve as an incentive for domestic producers to cut costs. And indeed, evidence shows that the productivity in manufacturing has risen significantly, and the amount domestically produced had fallen with an increasing rate after 1970-s.
But there were two types of studies done in 1980-s that rejected the idea of imports being the main cause for wage reduction. Firstly, writers looked at the input coefficients of different industries, and the coefficients of imports, to find out what would be the price in domestic industries when no import would be allowed to occur. They concluded, that with the increased price, only about 10% of the unemployment/wage reduction can be accounted for. Secondly people looked at cross country data – whether the countries with more imports have experienced higher increase in equality or not. They found no supportive evidence, especially because the import penetration to Europe is not significantly larger than the import penetration to USA, despite the fact that wages have remained high in Europe. More lately, Richardson has used the general equilibrium framework to extend HO theory and discuss when will trade really lead to wage changes. Only in two cases out of five, according to him.
However, Wood has argued that the input coefficients used by other writers are biased downwards. This happens because firms in USA will adopt labour saving techniques as a response to LDC competition. One would get a proper picture of the world without LDC-s if the LDC weights are used. This will magnify the effect by 10x and now about 50% of the increase in inequality has been caused by LDC-s. Taking the other 50% to mean that the wage diffuses to non-tradable sector as well, Wood concludes that the trade has caused the inequality.
Obviously Wood has been criticised for the study, as it is the only one predicting that LDC-s will have influence. Mainly other writers think that USA being as capital intensive as it is would have adopted some of the labour saving techniques anyway.
Completely another branch studies the same problem by using price data instead of quantity data. They as well find no support for LDC-s determining the wage. However, the price data is subject to severe errors arising from exchange rates, menu costs of adjustment etc.
Although writers do not agree on the cause of inequality, none of them supports tariffs. Instead, the skilled that are now richer, because Chinese want their products as well, could compensate to the unskilled by means of welfare system. Also, because Chinese people are getting richer, because their unskilled workers pay will increase, they will demand successively more of USA-s output. The increased demand, falling on skilled workers, will have a trickle down effect as well. It will take time, as will the transformation of unskilled workers to skilled ones. However, the final outcome is very attractive indeed.