ABSTRACT: We present two arguments, one based on index theory, demonstrating that the multicountry Ricardo model has a unique competitive equilibrium if the aggregate demand functions exhibit gross substitutability. The result is somewhat surprising because the assumption of gross substitutability is sufficient for uniqueness in a model of exchange but not, in general, when production is included in the model.

It is well known that the competitive equilibrium is unique in a pure exchange economy when the market excess demand function satisfies the assumption of gross substitutability. However, if we introduce an arbitrary constant-returns-to-scale technology, a unique equilibrium is ensured only if the market excess demand function satisfies the weak axiom of revealed preference. Because gross substitutability does not imply the weak axiom, we can construct examples using an activity analysis model of production in which there are several equilibria even though the market demand functions display gross substitutability. The first such example can be found in Kehoe.

There are few results on how the assumption of the weak axiom may be relaxed, and uniqueness still prevail, as we impose conditions on the technology. One notable example is the case where there is only one primary factor of production and each productive activity produces a single good, using other produced goods as inputs in addition to the primary factor. In this case, the nonsubstitution theorem implies that the technology alone uniquely determines the equilibrium price.