Ian Little and James Mirrlees have argued that in an open economy the social opportunity cost or "shadow price' of a good is the "world price' at which it can be bought from or sold to foreigners. This proposition is valid in a wide range of circumstances, and these shadow prices can be used in cost benefit analyses. Difficulties arise when shadow prices must be found for goods which are not traded internationally, and for which there is no obvious "world price'. Several economists have discussed this problem and have proposed methods of calculating "foreign-exchange-equivalent factor shadow prices'. These derivations, however, have made the technical assumption that the number of traded goods does not exceed the number of non-traded inputs. Bertrand has argued that this assumption is not appropriate in many situations and that factor shadow prices cannot, in principle, be derived in such cases.
In Discussion Paper No. 42, CEPR Programme Director Alasdair Smith argues that Bertrand's conclusion is too pessimistic. He considers two plausible situations in which more goods will be produced than there are factors of production: a small open economy, in which diversification of production is itself an objective of government policy; and a large open or closed economy in which there is consumer demand for a wide range of goods. Input shadow prices can be calculated in the first case, provided that the government has applied its diversification policy consistently and that this policy is modelled explicitly in the analysis. In the second case, an explicit treatment of consumer demand makes possible the calculation of shadow prices.
In both cases the economist must model explicitly the causes of product diversification in order to calculate shadow prices. This is straightforward in the case of the small open economy in which there are no constraints on government policy other than a set of fixed market distortions. As we move away from such simple cases, the calculation of shadow prices for both goods and factors requires more detailed information about the structure of the economy. The issue, Smith argues, is not the existence of these shadow prices, but rather the practical problems involved in their calculation.

Factor Shadow Prices in Distorted Open Economies
Alasdair Smith

Discussion Paper No. 42, January 1985 (IT)