Notes on Equilibrium Financial Intermediation

These notes analyze the production of financial services in general equilibrium. 1 Real Economy 1.1 Households The finance industry provides credit as well as liquidity and payment services to households (and savers more generally). In addition, household debt has an important life-cycle component (i.e., mortgages). The model must therefore incorporate these features. To do so, I consider a setup with two types of households: some households are infinitely lived, the others belong to an overlapping generations structure. Households in the model do not lend directly to one another. Savers lend to intermediaries, and intermediaries lend to firms and households. Long-Lived Households Long-lived households (index l) own the capital stock and have no labor endowment. Liquidity services are modeled with money in the utility function (using a cash-in-advance framework gives similar results). The households choose consumption C and holdings of liquid assets M to maximize