4 Assume an economy has a real money demand function as disc

4. Assume an economy has a real money demand function as discussed in class thus far (see your book , pp. 108-109). You can assume V is constant. a. If this econom y\'s central bank grows the money supply (M) at 8% annually while the real GDP grows at 3.5% per year, what will be the inflation rate? b. How would your answer change above if real GDP growth were higher? Explain c. If the goal is price stability, what monetary policy should this central bank follow? d. Suppose the introduction of ATMs causes V to grow over time by 2%. How does this change your answer in part a? Explain.

Solution

a) according to quantity theory of money

MV = PY

Taking logs on both sides,

Log M + log V = log P + log Y

Now differentiate with respect to time, t

1/M.dM/dt + 0 = 1/P.dp/dt + 1/Y.dY/dt

Velocity is assumed to constant

Put the given information,

8 = 3.5% + 1/PdP/dt

1/P.dP/dt= 4.5%

Inflation rate= 4.5%

b) from the equation we can infer that there is a negative relationship between real GDP and inflation rate. Higher the inflation rate lower is the real GDP. So if real gdp were higher, inflation rate would have been lower.

c) central bank can pursue expansionary monetary policy that is increase money supply when price level is below target level and can pursue contractionary monetary policy that is decrease in money supply when price level is higher than the targeted level.

d) now if 1/V.dV/dt= 2%

We have the equation from a)

8+2= 3.5 + 1/P.dPdt

1/P.dPdt= 6.5%

Inflation rate is 6.5% which is higher that that in part a) becuase there is positive relationship between inflation rate and velocity.