In the long-run growth models we have presented so far, there is no role for money.

Yet money performs very important functions in an economy. Money is a unit of account, in terms of which prices are defined; a means of payments, which reduces transaction costs; and the most liquid store of value.

In this chapter, we allow for the role of money in the growth models analyzed so far. We first consider a representative household model, in which real money balances enter the utility function of households. Then we analyze a corresponding OLG model.¹

In models with money, one can draw the distinction between real variables (such as the ones we have analyzed so far) and nominal variables (such as the stock of money, the price level, inflation, nominal output, nominal wages, and nominal interest rates). Whereas real variables are measured in physical or money-free terms, all nominal variables are expressed in terms of money.

By assuming that money enters the utility function of households, we can derive a money demand function from microeconomic foundations, as a result of the solution of an intertemporal optimization problem by households.

Based on this particular approach to money demand, we will see that the demand for real money balances is proportional to aggregate consumption and depends negatively on the nominal interest rate. Because money is a nominal asset that pays no interest, the nominal interest rate measures the opportunity cost of holding real money balances. The demand for nominal money balances is proportional to the price level, a property that implies the neutrality of money. The stock of nominal money balances does not affect any real variables in these models, only the price level.

We also analyze the determination of inflation, the nominal interest rate and other nominal variables, and the intertemporal effects of the growth rate of the money supply on the path of economic growth.

Monetary conditions in modern economies are determined by central banks. The central bank may affect both interest rates and the money supply through a variety of policy instruments at its disposal. The money supply consists of the quantity of bank notes (and coins) in circulation and the stock of deposits in commercial banks. Thus, central banks can affect the money supply both directly and indirectly. In this chapter, we concentrate on the dynamic effects of the growth rate of the money supply, assuming that the money supply is fully controlled by the central bank. More general and more detailed treatments of the money market and the role of central banks is postponed until chapters 12 and 20.

In the representative household model, the dynamic path of all real variables (with the exception of the stock of real money balances) turns out to be independent of either the level or the rate of growth of the money supply. These chiefly affect nominal variables, such as the level of prices, inflation, and nominal interest rates. The level of the money supply affects no real variables, only the level of prices. This property is known as the neutrality of money. The rate of growth of the money supply only affects inflation and nominal interest rates. The demand for real money balances, which depends negatively on the nominal interest rate, is thus the only real variable that is affected by the growth rate of the money supply. This is because this growth rate affects the opportunity cost of holding real money balances. To put it differently, the growth rate of the money supply imposes an inflation tax on the real money balances held by households. The independence of the path of all real variables—apart from the path of real money balances—from the growth rate of the money supply is known as the superneutrality of money.

In OLG models, the growth rate of the money supply affects the path of all real variables, because in OLG models, holdings of real money balances differ among generations.

The differences in the effects of the growth rate of the money supply between representative household and OLG models arise for the same reason that government debt has no real effects in representative household models, whereas it has real effects in OLG models. Ricardian equivalence and the superneutrality of money are closely linked, as the growth rate of the money supply is essentially an inflation tax on real money balances.

In OLG models, this inflation tax and government debt have different effects on current and future generations, and thus they affect aggregate savings. An increase in government debt redistributes taxes from current to future generations, causing an increase in the consumption of current generations, whereas an increase in the growth rate of the money supply redistributes taxes from future to current generations, causing a reduction in the consumption of current generations. This redistribution among generations and its effects on aggregate savings are thus the reason for the nonexistence of Ricardian equivalence and the superneutrality of money in OLG models.

7.1