Equilibrium Welfare and Government Policy with Quasi-Geometric Discounting

We consider a representative-agent equilibrium model where the consumer has quasi-geometric discounting and cannot commit to future actions. With restricted attention to a parametric class for preferences and technology--logarithmic utility, Cobb-Douglas production, and full depreciaiton--we solve for time-consistent competitive equilibria globally and explicitly. For this class, we characterize the welfare properties of competitive equilibria and compare them to that of a planning problem. The planner is a consumer representative who, without commitment but in a time-consistent way, maximizes his present-value utility subject to resources constraints. The competitive equilibrium results in strictly higher welfare than does the planning problem whenever the discounting is not geometric. We also explicitly consider taxation in our environment. With a benevolent government that can tax income and capital, but cannot commit its future tax rates, time-consistent taxation leads to positive tax rates on capital. These tax rates reproduce the central planning solution, and thus imply a worse outcome in welfare terms when there is no government.