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

The problem uses the quantity theory of money, with the relation: %ΔM + %ΔV = %ΔP + %ΔY. 
Since velocity growth is zero (V is constant), %ΔV = 0 and the equation simplifies to %ΔM = %ΔP + %ΔY.
Given: real GDP growth (%ΔY) = 8%, inflation (%ΔP) = 4%, and velocity is constant.
Plugging these in: %ΔM = 4% + 8% = 12%. This is the required growth rate of the nominal money supply.
Next, to assess the change in real money balances, consider real money balances M/P. Their growth rate is %Δ(M/P) = %ΔM − %ΔP (because P rises by %ΔP and money supply grows by %ΔM).
Using the numbers: %Δ(M/P) = 12% − 4% = 8%.
Now evaluate the answer options:
Option a: 12%. If the real money balances were to grow 12%, that would match the nominal money growth, but the real money balances would then change by 12% − 4% = 8% in line with the calculation, not 12% on a real basis. This option conflates nominal money growth with real money balances.
Option b: 8%. This aligns with the derived result that real money balances must grow by 8% to keep inflation at 4% while Y grows at 8% and V is constant.
Option c: 4%. A 4% increase in real money balances would correspond to %ΔM − %ΔP = 4%, which would imply %ΔM = 8% when combined with %ΔP = 4%, and would not satisfy the required nominal money growth given the 8% output expansion.
In terms of consistency, the logic hinges on separating nominal money growth from real money balance growth and on the given condition of a constant velocity. The correct relation shows that the real money balance growth should equal the inflation rate plus the real output growth, minus the inflation already present, yielding 8% here. The remaining options either double-count nominal effects or understate the adjustment, leading to inconsistencies with the stated conditions.

BU.220.610.51.FA25 M8 Final Comprehensive Exam - Multiple Choice Questions- Requires Respondus LockDown Browser

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?

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