We show that in almost every economy with separable externalities, every competitive equilibrium can be Pareto improved by a package of anonymous commodity taxes that causes prices to adjust and markets to reclear at different levels of individual consumption. This constrained suboptimality of competitive allocations might provide a rationale for economic policy in economies with externalities. It shows that policy makers should look for good tax packages that help everybody, rather than thinking taxes must inevitably be bad for some lobby that will oppose them.
The heated debate about how to reform Social Security has come to a standstill because the view of most Democrats (that Social Security must be a defined benefits plan similar in spirit to the current system) seems irreconcilable with the proposals supported by many Republicans (to create a defined contribution system of personal accounts holding marketed assets).
We describe a system of “progressive personal accounts” that preserves the core goals of both parties, and that is self-balancing on an ongoing basis. Progressive personal accounts have two critical features: (1) accruals into the personal accounts would be exclusively in a new kind of derivative security (which we call a PAAW for Personal Annuitized Average Wage security) that pays its owner one inflation-corrected dollar during every year of life after his statutory retirement date, multiplied by the economy wide average wage at the retirement date and (2) households would buy their new PAAWs each year with their social security contributions, augmented or reduced by a government match that would add to contributions from households with low lifetime incomes by taking from households with high lifetime incomes. PAAWS define benefits and achieve risk sharing across generations, as Democrats would like, yet can be held in personal accounts with market valuations, as Republicans propose.
The OLG model of Allais and Samuelson retains the methodological assumptions of agent optimization and market clearing from the Arrow-Debreu model, yet its equilibrium set has different properties: Pareto inefficiency, indeterminacy, positive valuation of money, and a golden rule equilibrium in which the rate of interest is equal to population growth (independent of impatience). These properties are shown to derive not from market incompleteness, but from lack of market clearing “at infinity;” they can be eliminated with land or uniform impatience. The OLG model is used to analyze bubbles, social security, demographic effects on stock returns, the foundations of monetary theory, Keynesian vs. real business cycle macromodels, and classical vs. neoclassical disputes.
We show that in almost every economy with separable externalities, every competitive equilibrium can be Pareto improved by a package of anonymous commodity taxes that cause prices to adjust and markets to reclear at different levels of individual consumption. The argument can be extended to economies with strategic interactions, incomplete asset markets or asymmetric information. This constrained suboptimality of competitive allocations might provide a rationale for economic policy in economies with externalities.
We show that in almost every economy with separable externalities, every competitive equilibrium can be Pareto improved by a package of anonymous commodity taxes that causes prices to adjust and markets to reclear at different levels of individual consumption. This constrained suboptimality of competitive allocations might provide a rationale for economic policy in economies with externalities. It shows that policy makers should look for good tax packages that help everybody, rather than thinking taxes must inevitably be bad for some lobby that will oppose them.
We prove the existence of monetary equilibrium in a finite horizon economy with production. We also show that if agents expect the monetary authority to significantly decrease the supply of bank money available for short term loans in the future, then the economy will fall into a liquidity trap today.
We introduce grading into games of status. Each player chooses effort, producing a stochastic output or score. Utilities depend on the ranking of all the scores. By clustering scores into grades, the ranking is coarsened, and the incentives to work are changed.
We first apply games of status to grading exams. Our main conclusion is that if students care primarily about their status (relative rank) in class, they are often best motivated to work not by revealing their exact numerical exam scores (100,99,…,1), but instead by clumping them into coarse categories (A,B,C).
When student abilities are disparate, the optimal grading scheme is always coarse. Furthermore, it awards fewer A’s than there are alpha-quality students, creating small elites. When students are homogeneous, we characterize optimal grading schemes in terms of the stochastic dominance between student performances (when they shirk or work) on subintervals of scores, showing again why coarse grading may be advantageous.
In both the disparate case and the homogeneous case, we prove that absolute grading is better than grading on a curve, provided student scores are independent.
We next bring games of money and status to bear on the optimal wage schedule: workers can be motivated not merely by the purchasing power of wages, but also by the status higher wages confer. How should the employer combine both incentive devices to generate an optimal pay schedule?
When workers’ abilities are disparate, the optimal wage schedule creates different grades than we found with status incentives alone. The very top type should be motivated solely by money, with enormous salaries going to a tiny elite. Furthermore, if the population of workers diminishes as we go up the ability ladder and their disutility for work does not fall as fast, then the optimal wage schedule exhibits increasing wage differentials, despite the linearity in production.
When workers are homogeneous, the same status grades are optimal as we found with status incentives alone. A bonus is paid only to scores in the top status grade.
We introduce grading into games of status. Each player chooses effort, producing a stochastic output or score. Utilities depend on the ranking of all the scores. By clustering scores into grades, the ranking is coarsened, and the incentives to work are changed.
We first apply games of status to grading exams. Our main conclusion is that if students care primarily about their status (relative rank) in class, they are often best motivated to work not by revealing their exact numerical exam scores (100,99,…,1), but instead by clumping them into coarse categories (A,B,C).
When student abilities are disparate, the optimal grading scheme is always coarse. Furthermore, it awards fewer A’s than there are alpha-quality students, creating small elites. When students are homogeneous, we characterize optimal grading schemes in terms of the stochastic dominance between student performances (when they shirk or work) on subintervals of scores, showing again why coarse grading may be advantageous.
In both the disparate case and the homogeneous case, we prove that absolute grading is better than grading on a curve, provided student scores are independent.
We next bring games of money and status to bear on the optimal wage schedule: workers can be motivated not merely by the purchasing power of wages, but also by the status higher wages confer. How should the employer combine both incentive devices to generate an optimal pay schedule?
When workers’ abilities are disparate, the optimal wage schedule creates different grades than we found with status incentives alone. The very top type should be motivated solely by money, with enormous salaries going to a tiny elite. Furthermore, if the population of workers diminishes as we go up the ability ladder and their disutility for work does not fall as fast, then the optimal wage schedule exhibits increasing wage differentials, despite the linearity in production.
When workers are homogeneous, the same status grades are optimal as we found with status incentives alone. A bonus is paid only to scores in the top status grade.
We show that if agents are risk neutral, prizes outperform wages when there is sufficient pride and envy relative to the noisiness of performance. If agents are risk averse, prizes are a necessary supplement to wages (as bonuses).