Consider an economy where the quantity theory of money holds. Suppose the govern
ID: 1137288 • Letter: C
Question
Consider an economy where the quantity theory of money holds. Suppose the government
has the following budget constraint:
PtGt = Tt + B+ M
where PtGt is nominal government spending, Tt denotes nominal taxes, B is the change in government debt (i.e., government borrowing), and M is the change in money supply (i.e., government printing currency). Assume that government spending is always equal to 50% of GDP, the government's debt does not change through time, taxes are always equal to 30% of GDP, and the velocity of money is cocnstant and equal to one. Moreover, suppose real output is constant.
(a) How much must the money supply grow for the government to finance its spending?
(b) What is the effect of this on inflation?
Explanation / Answer
Part "A" answer
Government Nominal Spending, PtGt = Tt + B+ M
Tt denotes nominal taxes
B is the change in government debt
M is the change in money supply
Since the government debt does not change B = 0
Therefore, the equation reduces to - PtGt = Tt + M
Assuming that GDP = 100
Government spending, PtGt = 50 (government spending is always equal to 50% of GDP)
Since Tax is 30% of GDP, Tt = 30
PtGt = Tt + M
Or, 50 = 30 + M
M = 50 - 30 = 20
Therefore, money supply needs to grow by 20% in order to meet government spending requirements.
Part "B" answer
The important point here is that "real output is constant."
With output remaining constant, any increase in money supply will translate into higher inflation. As that's the only place to absorb an increase in money supply with output remaining constant.
Quantity theory of money can elaborate on the point.
%M + %V = %P + %Y
V is change in money velocity. In this case V = 0 since money velocity is always 1
Y is change in output. Since output remains constant Y = 0.
Therefore, %M = %P
Where %M is change in money supply and %P is change in price levels.