The Supply And Demand Of Status By Skill Levels

We determine how the supply and demand of hierarchically ranked agents within a status system affect its population and income inequalities. The supplies of high and low status agents are determined by parents who optimally choose investments in their children's human capital. The incentive of high status parents is to help their children maintain their own high status, while lower status parents are incentivized to help their children achieve higher status. Given that status is scarce and desireable, the parents naturally engage in a Nash-Cournot game. The solution of the supply problem yields a population complement-subtitute relationship between human capital investment and innate endowments; it requires either complementarity for one status type and substitution for the other status type as functions of the exogenous factors, never the same for both status types.The demand side under perfect insight is restricted to socio-economic systems in which differential skill levels determine status differentials (Acemoglu-Autor (2011). The solution of the combined supply and demand status model gives the main contribution of the present paper: a micro theory of skill-based status income inequality. Assuming high and low status agents are technological substitutes, the income of high status agents exceeds that of low status agents; and that inequality grows the larger is the relative relative population supply.The last section of the paper introduces uncertainty or "luck" due to statistical sampling by characterizing the relative population of status types as a Markov chain governed by a binomial distribution. It turns out that "luck" plays a larger role (compared to income inequality under perfect insight) in determining income inequality when two types of status agents are technolgical subtitutes than when they are technological complements