On the Integrability of Money-Demand Functions by the Sidrauski and the Shopping-Time Models

This paper investigates which properties money-demand functions must satisfy so that they are consistent with Lucasís [Lucas, R.E., Jr., 2000. Inflation and welfare. Econometrica 68, 247-274] versions of the Sidrauski and the shopping-time models. We conclude that shopping-time-integrable money-demand functions are necessarily also Sidrauski-integrable, but that the converse is not necessarily true, unless a boundedness assumption on the nominal interest rate is made. Both the log-log with an interest-rate elasticity greater than or equal to one and the semi-log money demands may serve as counterexamples. All the models and results are also extended to the case in which there are several assets in the economy performing monetary functions