Grading Exams: 100, 99, ..., 1 or A, B, C? Incentives in Games of Status

We show that if students care primarily about their status (relative rank) in class, they are best motivated to work not by revealing their exact numerical exam scores (100,99,...,1), but instead by clumping them in broad categories (A,B,C). If their abilities are disparate, the optimal grading scheme awards fewer A's than there are alpha-quality students, creating small elites. If their abilities are common knowledge, then it is better to grade them on an absolute scale (100 to 90 is an A, etc.) rather than on a curve (top 15% is an A, etc.). We develop criteria for optimal grading schemes in terms of the stochastic dominance between student performances.Status, Incentives, Education, Grading, Wages

Inside and Outside Money, Gains to Trade, and IS-LM

We build a one-period general equilibrium model with money. Equilibrium exists, and fiat money has positive value, as long as the ratio of outside money to inside money is less than the gains to trade available at autarky. We show that the nominal effects of government fiscal and monetary policy can be completely described by a diagram identical in form to the IS-LM curves introduced by Hicks to describe Keynes' general theory. IS-LM analysis is thus not incompatible with full market clearing, multiple commodities, and heterogeneous households. We show that as the government deficit approaches a finite threshold, hyperinflation sets in (prices converge to infinity and real trade collapses). If the government surplus is too large, the economy enters a liquidity trap in which nominal GNP sinks and monetary policy is ineffectual.Central bank, gains to trade, inside money, IS-LM, outside money

Insurance Contracts Designed by Competitive Pooling

We build a model of competitive pooling and show how insurance contracts emerge in equilibrium, designed by the invisible hand of perfect competition. When pools are exclusive, we obtain a unique separating equilibrium. When pools are not exclusive but seniority is recognized, we obtain a different unique equilibrium: the pivotal primary-secondary equilibrium. Here reliable and unreliable households take out a common primary insurance up to its maximum limit, and then unreliable households take out further secondary insurance.Competitive pooling, insurance contracts, adverse selection, signalling, seniority, equilibrium refinement

Grading Exams: 100, 99, 98,...or A, B, C?

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 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 absolute 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 absolute 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.Status, Grading, Incentives, Education, Exams

Inside and Outside Money, Gains to Trade, and IS-LM

We build a one-period general equilibrium model with money. Equilibrium exists, and fiat money has positive value, as long as the ratio of outside money to inside money is less than the gains to trade available at autarky. We show that the nominal effects of government fiscal and monetary policy can be completely described by a diagram identical in form to the IS-LM curves introduced by Hicks to describe Keynes' general theory. IS-LM analysis is thus not incompatible with full market clearing, multiple commodities, and heterogeneous households. We show that as the government deficit approaches a finite threshold, hyperinflation sets in (prices converge to infinity and real trade collapses). If the government surplus is too large, the economy enters a liquidity trap in which nominal GNP sinks and monetary policy is ineffectual.Bank, gains to trade, inside money, IS-LM, outside money

From Nash to Walras via Shapley-Shubik

We derive the existence of a Walras equilibrium directly from Nash's theorem on noncooperative games. No price player is involved, nor are generalized games. Instead we use a variant of the Shapley-Shubik trading-post game.Nash equilibrium, Walras equilibrium, Shapley-Shubik trading-posts game, Money

Real Determinacy with Nominal Assets

We build a finite horizon model with inside and outside money, in which interest rates, price levels and commodity allocations are determinate, even though asset markets are incomplete and asset deliveries are purely nominal.Central bank, Inside money, Outside money, Incomplete assets, Monetary equilibrium, Real determinacy

Competitive Pooling: Rothschild-Stiglitz Reconsidered

We build a model of competitive pooling, which incorporates adverse selection and signalling into general equilibrium. Pools are characterized by their quantity limits on contributions. Households signal their reliability by choosing which pool to join. In equilibrium, pools with lower quantity limits sell for a higher price, even though each household's deliveries are the same at all pools. The Rothschild-Stiglitz model of insurance is included as a special case. We show that by recasting their hybrid oligopolistic-competitive story in our perfectly competitive framework, their separating equilibrium always exists (even when they say it doesn't) and is unique.competitive pooling, insurance, adverse selection, signalling, refined equilibrium, separating equilibrium