Answer Happy

Now, consider the government budget constraint as shown on slide
30 of Chapter 8 slides (or Chapter 8.5 in the textbook). In that
part of the class, we argued that issuing money can be used to
finance government spending. The (nominal) amount of revenue the
government raises from the inflation tax is ∆M. In this and
following points, you will analyze how large the revenue from this
inflation tax is, relative to the size of the economy (nominal
GDP): ∆M . Since the change in money supply (∆M) is difficult to
work with, we should PY express the revenue as a function of the
growth rate of money supply ( ∆M ≡ gM ). Use this definition of the
M growth rate of money supply to calculate the revenue from the
inflation tax as a share of GDP ( ∆M ) as a PY function of gM and
other parameters of the economy. You answer should be something
like: ∆M = gM · x. PY What is x? Can you give an interpretation of
it?
Look at slide 17 in Chapter 8 slides. Take your answer to part
c) of this question and use the quantity theory of money to replace
the growth rate of money supply (gM ) with a term that includes the
inflation rate (and other terms, like the growth rate of
output).
How much revenue is raised from inflation tax as a share of GDP?
Suppose that M = 10%, and use the PY equations from part c) and
numbers from part a) of this question. Based on your answer, do you
think inflation tax is an important source of revenue for the
government?