Recent monetary models with explicit microfoundations are made tractable by assuming that agents have access to centralized markets after one round of decentralized trade. Given quasi-linear preferences, this makes the distribution of money degenerate — which keeps the models simple but precludes discussion of distributional effects of monetary policy. We generalize these models by assuming two rounds of trade before agents can readjust their money holdings to study a range of new distributional effects analytically. We show that unexpected, symmetric lump-sum money injections may increase short-run output and welfare, while asymmetric injections may increase long-run output and welfare.
Berentsen, A., G. Camera and C. Waller (2005). The distribution of money balances and the nonneutrality of money. International Economic Review 46(2), 465-487. doi: 10.1111/j.1468-2354.2005.00329.x