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The amount that the government raises from the inflation rate tax is ΔM. (ΔM = change in money stock or the printing of more money or the change in the amount of money today from yesterday).
1. Write ΔM as a fraction of nominal GDP. Multiply and divide by the money stock (M) to obtain an expression for the inflation tax as a fraction to GDP. Interpret this equation.
2. Use now the quantity theory of money to replace the growth rate of money by a term that involves the inflation rate.
3. In the 1980's, M (measured as M1) as a fraction on nominal GDP was about 14% in the United States. How much revenue as a share of output did the inflation rate raise if it was about 5% per year and the growth rate in real output was 3% per year?
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Illustrate what should the Fed do in inflation continues to fall and eventually starts to become deflation.
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