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# Inflation Rate = Growth Rate of Money Supply

Using this fact and rearranging the equation, we discover that the long-run inflation rate depends on the difference between how rapidly the money supply grows and how rapidly output grows: inflation rate = growth rate of money supply − growth rate of output. The long-run growth rate of output does not depend on the growth rate of the money supply or the inflation rate. We know this because long-run output growth depends on the accumulation of capital, labor, and technology. From our discussion of labor and credit markets, equilibrium in these markets is described by real variables. Equilibrium in the labor market depends on the real wage and not on any nominal variables. Likewise, equilibrium in the credit market tells us that the level of investment does not depend on nominal variables. Since the capital stock in any period is just the accumulation of past investment, we know that the stock of capital is also independent of nominal variables. Therefore there is a direct link between the money supply growth rate and the inflation rate. The classical dichotomy teaches us that changes in the money supply do not affect the velocity of money or the level of output. It follows that any changes in the growth rate of the money supply will show up one-for-one as changes in the inflation rate. We say more about monetary policy later, but notice that there are immediate implications for the conduct of monetary policy:

 In a growing economy, there are more transactions taking place, so there is typically a need for more money to facilitate those transactions. Thus some growth of the money supply is probably desirable to match the increased income.

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 If the monetary authorities want a stable price level—zero inflation—in the long run, then they should try to set the growth rate of the money supply equal to the (long-run) growth rate of output.

 If the monetary authorities want a low level of inflation in the long run, then they should aim to have the money supply grow just a little bit faster than the growth rate of output.

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