For a country A, the real GDP growth rate is 8% and inflation is 4%. If the velocity of money remains constant, what is the required change in real money balances to keep inflation constant?

Question

For a country A, the real GDP growth rate is 8% and inflation is 4%. If the velocity of money remains constant, what is the required change in real money balances to keep inflation constant?

BlackTom AI · Accepted Answer

We start by restating the problem to anchor the analysis: With real GDP growth of 8% and inflation at 4%, and with velocity of money constant, what change in real money balances is needed to keep inflation unchanged?

Option a: 12%
- If we use the quantity equation in growth form: ΔM/M + ΔV/V = ΔP/P + ΔY/Y. With ΔV/V = 0 (velocity constant), this gives ΔM/M = ΔP/P + ΔY/Y = 4% + 8% = 12%. This calculates the growth rate of the money supply needed to keep inflation at 4% given real GDP growth. However, the question asks for the change in real money balances (M/P), not the nominal money stock M. So while 12% is the required growth rate of M, it does not directly represent the change in real money balances, which are M/P. Therefore, this option describes the nominal money growth, not the real money balances, making it incorrect as the requested measure.

Option b: 8%
- To get the change in real money balances, we look at the growth rate of M/P, which is (ΔM/M) − (ΔP/P). From above, ΔM/M = 12% and ΔP/P = 4%, so Δ(M/P)/(M/P) = 12% − 4% = 8%. This exactly matches the asked quantity—the required change in real money balances to keep inflation constant when velocity is fixed and output grows.

Option c: 4%
- This would imply that the real money balances grow at the same rate as inflation alone, ignoring the 8% real GDP growth. Since real GDP growth adds to the money balance needs to support higher real activity, allocating only 4% to real money balances would leave insufficient money to finance the higher output growth, leading to a mismatch and likely higher inflation, given the constant velocity assumption. Hence, 4% is too small and incorrect for the stated condition.

In summary, the key relationships are the quantity equation in growth form with velocity fixed, and the realization that real money balances grow at the difference between the nominal money growth and inflation. This yields 8% for the change in real money balances, not 12% or 4%.

For a country A, the real GDP growth rate is 8% and inflation is 4%. If the velocity of money remains constant, what is the required change in real money balances to keep inflation constant?单项选择题

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