Suppose a country has a money demand function (M/P)^d = kY, where k is a constan

Question

Suppose a country has a money demand function (M/P)^d = kY, where k is a constant parameter. The money supply grows by 12 percent per year, and real income grows by 4 percent per year.

a.) What is the average inflation rate?

b.) How would inflation be different if real income growth were higher? Explain

c.) How do you interpret the parameter k? What is its relationship to the velocity of money?

d.) Suppose, instead of a constant money demand function, the velocity of money in the economy was growing steadily because of financial innovation. How would that affect the inflation rate? Explain

Explanation / Answer

Answer:
The money demand function is given as  (M/P)^d = kY

a. To find the average inflation rate the money demand function can be expressed interms of
growth rates:
% growth Md – % growth P = % growth Y.
The parameter k is a constant, so it can be ignored. The percentage change in nominal money
demand Md is the same as the growth in the money supply because nominal money demand
has to equal nominal money supply. If nominal money demand grows 12 percent and real
income (Y) grows 4 percent then the growth of the price level is 8 percent.
b. From the answer to part (a), it follows that an increase in real income growth will result in a
lower average inflation rate. For example, if real income grows at 6 percent and money supply
growth remains at 12 percent, then inflation falls to 6 percent. In this case, a larger money
supply is required to support a higher level of GDP, resulting in lower inflation.
c. The parameter k defines how much money people want to hold for every dollar of income.
The parameter k is inversely related to the velocity of money. All else the same, if people are
holding fewer dollars, then each dollar must be used more times to purchase the same quantity
of goods and services.
d. If velocity growth is positive, then all else the same inflation will be higher. From the
quantity equation we know that:
% growth M + % growth V = % growth P + % growth Y.
Suppose that the money supply grows by 12 percent and real income grows by 4 percent.
When velocity growth is zero, inflation is 8 percent. Suppose now that velocity grows 2
percent: this will cause prices to grow by 10 percent. Inflation increases because the same
quantity of money is being used more often to chase the same amount of goods. In this case,
the money supply should grow more slowly to compensate for the positive growth in velocity.   

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