Ratio Orderings and Comparative Statics

Monotone ratio orderings are refinements of first order stochastic dominance that allow monotone comparative statics results in games of incomplete information. We develop analogous refinements for second order stochastic dominance based on the monotonicity of the cumulative probability ratio and the unimodality of the likelihood and probability ratios. We go on to investigate comparative statics in first price auctions, both private and common value, of the effects of more precise information in the sense of the new orderings. We find that almost all types bid more aggressively under the new distribution than they did under the old, but the highest types may bid less. This leads to higher expected revenue in a simple common value auction, but to an ambiguous result in the private value case.monotone likelihood ratio, monotone probability ratio, conditional stochastic dominance, generalized Lorenz order, comparative statics, first price auctions, common value auctions

Methods of Comparison in Games of Status

This paper considers the effects of changes in the income distribution in an economy where agents’ utility depends both on consumption and on their rank in the distribution of consumption of a positional good. We introduce a new methodology to compare the behavior of agents that occupy the same rank in the two different income distributions but typically have different levels of incomes, and analyze equilibrium choices and welfare of every member of the society for continuous distributions with arbitrary, even disjoint, ranges. If an income transformation raises incomes at the lower end of the income distribution, the poor will typically be better off. But because such an income transformation also increases the degree of social competition, the middle class will typically be worse off - even if they have higher incomes as well. An increase in incomes can make all better off, but only if it is accompanied by an increase in income dispersion. Our new techniques highlight the importance of density of social space as we demonstrate that one can have an increase both in income and relative position but still be worse off.Status, relative standing, income inequality, conspicuous consumption, consumption externalities, income inequality, social competitiveness, first price auctions, dispersive orderings.

Local Status and Prospect Theory

People are sometimes risk-averse in gains but risk-loving in losses. Such behavior and other anomalies underlying prospect theory arise from a model of local status maximization in which consumers compare their wealth with other consumers of similar wealth. This social explanation shares key features with the psychological explanation o.ered by Kahneman and Tversky.prospect theory, status, reference group, loss aversion, risk loving

Consumption, Status and Redistribution

This paper considers the effect of inequality when there are concerns for status. We analyse the effects of linear redistributive taxes in an economy where agents’ utility depends both on consumption and on their rank in the distribution of consumption of a positional good. This increase in equality increases the degree of social competition. The equilibrium level of expenditure on the positional good rises for most agents with the possible exception of some with above average income. Equilibrium utility falls for those with average and above income, while the utility of the poor may (or may not) rise.Status, relative standing, income inequality, consumption externalities.