Income Effects, Wealth Effects, and Multiple Equilibria in Trade Models with Durable Goods

We examine the conditions for multiplicity of equilibrium in a dynamic, two‐country model of trade with a durable good of the type proposed by Shimomura (1993, 2004). If trade must balance in each period, we show that there will be a unique autarkic steady‐state equilibrium and that the principle of comparative advantage will hold if the nondurable good is not inferior. A necessary condition for the existence of multiple steady‐state equilibria with free trade is that the marginal propensity to consume a good be higher in the exporting country. We provide an example with three steady states where the “extreme” steady states are saddle points and the “middle” steady state will be either a source or a sink, depending on the intertemporal elasticity of substitution. If there is international lending, this example has the property that there is a range of initial endowments for which there are three distinct and Pareto‐optimal (saddle) paths that can be equilibria. We also show that there must be a unique saddle path from any endowment point with international capital markets when preferences are identical, homothetic, and have constant intertemporal elasticity of substitution.