This post raises a question. Supposedly, the classical concept of prices of production with non-uniform rates of profits can be recast as a theory of foreign trade. I do not see how wages can properly be treated in such recasting.
D'Agata (2018) and Zambelli (2018) are two recent papers that argue prices of production can be formulated with non-uniform rates of profits. They argue that this introduces a certain indeterminateness into prices, as in some of my examples of foreign trade. Both D'Agata and Zambelli cite Adam Smith and David Ricardo to justify their models as of classical inspiration. If somebody is to draw on this research for a theory of foreign trade, I hope they cite this passage from Adam Smith:
… every individual … endeavors as much as he can both to employ his capital in the support of domestic industry, and so to direct that its produce may be of the greatest value; every individual necessarily labours to render the of the society as great as he can. He generally, indeed, intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he only intends his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in so many other cases, led by an invisible hand to promote an end which was no part of his intention.
I suspect many propertarians are not aware that Smith was arguing that a lack of foreign direct investment is desirable, that enough barriers exist against entrepreneurs investing in other countries that no need exist for certain protectionist laws to be passed by government.
D'Agata models non-uniform rates of profits as arising due to both "objective and idiosyncratic factors affecting producers' investment decisions". Objective factors are modeled by different groups of producers having access to different techniques of production for producing the same commodities. For example, firms in England and Portugal might have access to different techniques for producing corn and wine, as in Ricardo's Principles. I guess countries having different endowments of land and labor, thereby limiting the scale at which some processes can be operated, is also an objective factor important to the theory of foreign trade.
Idiosyncratic factors are formalized by different producers having different valuation functions, where a valuation function is a continuous, strictly increasing function of the rate of profits obtained in a given industry. In terms of the theory of foreign trade, one might model entrepreneurs in England all having identical valuation functions, while entrepreneurs in Portugal have another valuation function, common among the Portuguese. Each valuation function might be assumed not to vary among industries. For example, English entrepreneurs value the rate of profits made in making corn the same as the rate of profits made in making wine.
From these considerations, one can obtain a theory of foreign trade in which:
(I do not claim such a theory is complete, since it does not consider Keynesian effective demand, paths with unbalanced trade, fluctuations in exchange rates, and so on.)
When I have tried to develop such a theory of foreign trade, I have created examples in which the wage also varies across countries. This is easy to justify based on an assumption of a lack of a free movement of people across national borders. But how is this idea formalized in D'Agata's approach?References