  This paper examines the relationship between resource reallocation,
uniqueness of equilibrium and efficiency in economics. We explore the
implications of reallocation policies for stability, conflict, and
decision-making by analysing the existence of geodesic coordinate functions in
the equilibrium manifold. Our main result shows that in an economy with M = 2
consumers and L goods, if L coordinate functions, representing policies, are
geodesics on the equilibrium manifold (a property that we call the finite
geodesic property), then the equilibrium is globally unique. The presence of
geodesic variables indicates optimization and efficiency in the economy, while
non-geodesic variables add complexity. Finally, we establish a link between the
existing results on curvature, minimal entropy, geodesics and uniqueness in
smooth exchange economies. This study contributes to the understanding of the
geometric and economic properties of equilibria and offers potential
applications in policy considerations. Keywords: Uniqueness of equilibrium,
redistributive policies, geodesics, equilibrium manifold, equilibrium
selection, curvature, geodesics.
