A geometric view of welfare gains with noninstantaneous adjustment

A geometric approach which defines distance between equilibrium states has proved useful in the physical sciences. The notion is applicable to any system which exhibits optimizing behavior and which does not adjust its states instantaneously to exogenous shocks. In this paper this geometry is used to analyze an economic system perturbed out of equilibrium by discrete or continuous shocks in order to establish in-principle limits to welfare gains generated by adjustments. The geometry is defined by the second derivative of the utility function which is used as the metric matrix. The minimum net gain in utility due to adjustment is proportional to the square of the distance traversed as measured in this geometry. An integrated welfare loss measuring the welfare losses due to the non-instantaneous response is defined. Finally, the geometry of the Cobb-Douglas utility function is explored. Key words: Geometric economics; welfare gains; adjustment. I