Money Supply in a Simple Economic Growth Model and Multiple Steady States Equilibria

We intend to examine a monetary economic growth model à la Sidrauski- Brock where money is introduced both in the utility function and the production function. We assume that utility is derived from the flow of services derived from real money holdings and that money is held by firms to facilitate production. We show that the level of equilibrium depends on the rate of discount. We give conditions to guarantee uniqueness of the equilibrium. We demonstrate that the unique equilibrium is either a classical « saddle point » or a « source point »; that the introduction of money in the utility and production function is sufficient to produce multiple stationary equilibria; and that the initial stock of money appears as an important economic control variable. Therefore, the initial amount of the monetary emission issued by the central bank becomes essential for the long run economic equilibrium properties.