In the models we have presented so far there is no role for money. In this chapter we allow for the role of money in the exogenous growth models we have analyzed. Money is a unit of account and a means of payments, which reduces transaction costs, and a liquid store of value (asset) which pays no interest. We first present a representative household model in which real money balances enter the utility function of households, and then analyze a corresponding model of overlapping generations.

In models with money, one can draw the distinction between real variables, as the ones we have analyzed so far, and nominal variables, such as the price level, inflation and nominal output, wages and interest rates. Nominal variables are expressed in terms of money, which has three functions. It is a unit of account, a means of payments and a store of value. By assuming that money enters the utility function of households, we derive a money demand function from microeconomic foundations, as a result of the solution of an inter-temporal optimization problem by households.

Based on this particular approach to money demand, we can show that the demand for real money balances is proportional to aggregate consumption, and depends negatively on the nominal interest rate, since money is an 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 which implies the neutrality of money. The stock of nominal money balances does not affect any real variables, but only the price level.

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

In the representative household model, the growth path of all real variables, with the exception of the stock of real money balances, is independent of the rate of growth of the money supply, which affects inflation and nominal interest rates. The demand for real money balances, which depends negatively on the nominal interest rate, is the only real variable that is affected by the rate of growth of the money supply. This is because the rate of growth of the money supply imposes an inflation tax on the real money balances held by households. The independence of the growth path of all other real variables from the rate of growth of the money supply is known as the super neutrality of money.

In overlapping generations models, the rate of growth of the money supply affects the growth path of all real variables, as it affects the aggregate savings rate, the accumulation of capital and the balanced growth path. The reason is that in overlapping generations models, holdings of real money balances differ among generations. Thus, when there is an increase in the rate of growth of the money supply, older generations, which hold higher real money balances, reduce their asset holdings and their consumption more than younger generations, since they pay a higher inflation tax. As a result, aggregate consumption falls, and aggregate savings rise. This leads to a higher accumulation of capital, which affects the growth path.

The differences in the effects of the rate of growth of the money supply between representative household and overlapping generations models arise for the same reason that government debt has no real effects in representative household models, while it has real effects in overlapping generations models. Ricardian equivalence and the super neutrality of money are closely linked, as the rate of growth of the money supply is essentially an inflation tax on real money balances, and has different effects on older and younger generations.

In the representative household model, neither government debt nor the growth rate of the money supply redistributes the tax burden among generations. In overlapping generations models, both result in a redistribution of the tax burden among generations, and thus affect the aggregate savings of current generations. An increase in public debt redistributes taxes from current to future generations, causing an increase in consumption by current generations, while an increase in the rate of growth of the money supply redistributes taxes from future to current generations, causing a reduction in consumption by current generations.

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