Asset Prices, Liquidity, and Monetary Policy in an Exchange Economy

I formulate a search-based asset-pricing model where equity shares and fiat money can be used as means of payment. I characterize a family of optimal stochastic monetary policies. Every policy in this family implements Friedman’s prescription of zero nominal interest rates. Under an optimal policy, equity prices and returns are independent of monetary considerations. I also study a perturbation of the family of optimal policies that targets a constant but nonzero nominal interest rate. Under such policies, the average real return on equity is negatively correlated with the average inflation rate.