This paper analyzes the persistency of the unequal exchange of labor (UE) in international trade. An intertemporal model of a world economy is defined with a leisure preference and no discount factor. Every incompletely specialized free trade equilibrium is characterized as having non-persistent UE, which verifies the convergence of economies without relying on economic growth or diminishing returns to scale. In particular, it characterizes a sub- class of equilibria in which the sequence of real interest rates does not converge to zero, but UE tends to disappear while equivalently the distribution of capital assets tends to be equalized in the long run.