Shadow prices for a small open economy under uncertainty
Which expected values are valid
This paper re-examines the validity of using expected values to evaluate the social profitability of public investments under uncertainty. Departing from the usual assumption of an aggregate good, the setting is a small open economy that faces stochastic world prices for tradable goods and productivity levels in domestic production. It is shown that the so-called ‘border price rule’—the vector of the shadow prices of traded goods is a scalar multiple of their world price vector—is, in general, invalid when the vector of mean world prices is used.
The rule in that form is valid when the coefficient of risk aversion is 1. The error involved is small, however, even for values of that coefficient far from 1, including risk neutrality, when public expenditures are financed by lump-sum taxes. It is also small when preferences over goods are Cobb-Douglas and revenues are raised by taxing commodities. In contrast, using expected values to derive the shadow wage rate results in quite substantial errors when risk aversion is strong.