3. In lecture 10, we defined seigniorage and the inflation tax. The total amount of seigniorage raised by the government equals AM where M is the monetary base. We are going measure AM as the difference between the monetary base in the last period of a year and in the last period of the previous year. a) Use the quantity theory to show the steps in the derivation of the equation AM = M(TT + gy). Divide through by Y, so that you have an expression for seigniorage revenue as a share of GDP. Give an interpretation of the two parts of the right-hand side of this equation what does each represent? b) Suppose that gy rises from 1% to 2% and M/Y equals 0.25. There is no change in inflation. How much does government revenue rise? How much does the money supply growth rate change? What happens if gy remains equal to 1%, but inflation rises by 1%? = c) Use the FRED database to find the data you need to calculate M/Y. You should use the end of year monetary base for M and annual nominal GDP. For example, AM2019 = MDec 2019 Mdec 2018 and Mpec 2010 Calculate the revenue as a share of GDP Y Dec2019 for each of the two years below. Assume that the growth rate of real GDP was 2% for each year. i) the United States in 2019. ii) the United States in 2004. M Y 3. In lecture 10, we defined seigniorage and the inflation tax. The total amount of seigniorage raised by the government equals AM where M is the monetary base. We are going measure AM as the difference between the monetary base in the last period of a year and in the last period of the previous year. a) Use the quantity theory to show the steps in the derivation of the equation AM = M(TT + gy). Divide through by Y, so that you have an expression for seigniorage revenue as a share of GDP. Give an interpretation of the two parts of the right-hand side of this equation what does each represent? b) Suppose that gy rises from 1% to 2% and M/Y equals 0.25. There is no change in inflation. How much does government revenue rise? How much does the money supply growth rate change? What happens if gy remains equal to 1%, but inflation rises by 1%? = c) Use the FRED database to find the data you need to calculate M/Y. You should use the end of year monetary base for M and annual nominal GDP. For example, AM2019 = MDec 2019 Mdec 2018 and Mpec 2010 Calculate the revenue as a share of GDP Y Dec2019 for each of the two years below. Assume that the growth rate of real GDP was 2% for each year. i) the United States in 2019. ii) the United States in 2004. M Y