Competitive search with two-sided risk aversion

Abstract

We analyze a static competitive search model where risk-averse individuals with different wealth levels trade an indivisible good. The real estate market is a particularly relevant application. We show that the equilibrium is constrained efficient. Other properties of the equilibrium are derived, including the generalized version of the Hosios (1990) rule for this environment. Under risk aversion, buyers and sellers evaluate the trade-off between prices and trading probabilities differently as their wealth increases. As they become richer, buyers are relatively less concerned about paying higher prices and more concerned about increasing their trading probability. Conversely, richer sellers care less about increasing the probability of a sale than poorer sellers, and they care more about trading at a higher price. This results in positive sorting inequilibrium, that is, wealthier (poorer) buyers and sellers trading with each other. As transactions among wealthier agents involve higher prices, the equilibrium features frictional price dispersion. By contrast, with transferable utility, all individuals would trade at the same price, irrespectively of their wealth.