Question: A formula for the inflation tax (hard): As in exercise 13, the amount of money the government raises from the inflation tax is ?M.

(a) Write this amount as a ratio to nominal GDP. Multiply and divide by M to get an expression for the ratio of revenue from the inflation tax to GDP. Your answer should take the form of the product of a growth rate and a different ratio. Interpret this equation.

(b) Use the quantity theory to replace the growth rate of money in this product with a term that involves the inflation rate.

(c) How much revenue, as a share of GDP, would the inflation tax raise in the following episodes? Assume the growth rate of real GDP is 2% in these calculations:

i. The United States in 1981. (Use the tables from the Economic Report of the President to compute the answer. How does this compare with your answer to exercise 13?)

ii. The United States in 2005.

(d) Suppose there is a hyperinflation where the inflation rate rises to 2,000%. For a given value of M / Y, the formula you derived in (b) suggests that the inflation tax could raise more than 100% of GDP in revenue. Clearly this could not actually happen. Why not?

Exercise: Revenue from the inflation tax: The amount of money the government raises from the inflation tax is ?M. Consult the statistical tables at the back of the Economic Report of the President (available online) to answer the following questions:

(a) How much currency was in circulation in 1981? What was the size of the monetary base in 1981?

(b) If the monetary base is the measure of M, how much revenue was raised from the inflation tax between 1980 and 1981, in dollars? What fraction was this of 1981 GDP?

(c) Why does this exercise ask you to do these calculations for the year 1981 instead of some other year?