Question

Suppose that the real money demand function​ is:

L(Y,R + piᵉ) = (.01 x Y)/(r+piᵉ) where Y is real​ output, r is the real interest​ rate, and pi^e is the expected rate of inflation. Real output is constant over time at Y​ = 250. The real interest rate is fixed in the goods market at r​ = 10​% ​(0.10​) per year.

Suppose that the nominal money supply is growing at the rate of 12​% ​(0.12​) per year and that this growth rate is expected to persist forever.​ Currently, the nominal money supply is M​ = 200.

What is the value of the real money​ supply? __

Answer 1

The real money supply is calculated by adjusting the nominal money supply for the rate of inflation. In this case, since the nominal money supply and the expected rate of inflation are both 12%, the real money supply equals the nominal money supply divided by 1.12, which is approximately 178.57.

Step-by-step explanation:

The real money supply is calculated by adjusting the nominal money supply for the rate of inflation. If we have a nominal money supply (M) of 200 growing at 12% annually, and the expected rate of inflation (π^e) is also 12%, then the real money supply will be equal to the nominal money supply because the inflation rate cancels out the nominal growth in money supply. To calculate the real money supply, we divide the nominal money supply by 1 plus the expected inflation rate (since inflation is the same as the growth rate of money supply, it effectively becomes 1 and does not change the money supply).

Real Money Supply (M/P) = Nominal Money Supply (M) / (1 + π^e)
Therefore, Real Money Supply = 200 / (1 + 0.12) = 200 / 1.12 = 178.57 (approximately).