Anticipated inflation and rates of return in a search-theoretic monetary model

How does anticipated inflation of fiat money affect the real return of a near money-an asset with real value used to mediate trades? This essay studies a search model in which decentralized trade takes place under a fixed bargaining rule. The essay analytically studies the comparative statics of a near money's real return as it varies with inflation. The effects diverge markedly over the parameter space. There exist parameters for which higher inflation lowers the real asset return, as suggested by asset substitution theories. There also exist parameters for which inflation has the opposite effect.