Question

Suppose a country has a money demand function (??)?=?? 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. If real income growth were higher, inflation would be

c. What is the relationship between the parameter k and the velocity of money?

There is no relationship between k and V because the amount of money people hold is not related to the velocity of money.

?=1?V=1k: k is inversely related to velocity because the more money people hold for a given real income, the smaller velocity is, and vice versa.

?=????V=kPYM: k times the ratio of nominal output to the money supply is related to velocity because the more money people hold, the larger velocity is, and vice versa.

?=?V=k: k is directly related to velocity because the more money people hold for a givne real income, the larger velocity is, and vice versa.

d. Suppose, instead of a constant money demand function, the velocity of money in this economy was growing steadily because of financial innovation. Assuming everything else was unchanged, how would that affect the inflation rate?

Answer 1

Sol::-

a) Money demand function is given as :

The above demand function in terms of growth rate will be :

Percentage Growth Md – Percentage Growth of Price = Percentage Growth Y

Since, parameter k is a constant, so it can be ignored. The percentage change in nominal money demand i.e 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% and real income i.e. Y grows 4% then,

12% - Percentage growth of Price = 4%

Percentage growth of Price level = 12% - 4% = 8%

Therefore, the inflation rate is 8 percent

b) If real income growth were higher let say, 5% then, percentage growth of price level will be:

Percentage Growth Md – Percentage Growth of Price = Percentage Growth Y

12% - Percentage Growth of Price = 5%

Percentage Growth of Price = 12% - 5% = 7%

It shows that an increase in real income growth will result in a lower average inflation rate. In this case, it is clearly shown that if economy wants low inflation then, it requires higher level of gdp with larger money supply

c) The parameter k defines how much money people wants to hold in every dollar of their income. The parameter k is negatively related to the velocity of money since, if people are holding fewer dollars of their income then, each dollar must be circulated many times to purchase the same quantity of goods and services by different people.

d) If velocity growth is positive, then all remaining else the same inflation will be higher. Quantity theory of money states that : MV = PY

This implies : Percentage Growth M + Percentage Growth V = Percentage Growth P + Percentage Growth Y

If money supply grows by 12%, real income grows by 4% and velocity growth is zero then, inflation is 8 percent as shown in part (a). But now suppose that velocity grows 3%, this will cause

12% + 3% = Percentage Growth P + 4%

15% - 4% = Percentage growth of P

Percentage growth of P = 11%

This shows inflation increases because the same quantity of money is used to purchase the same amount of goods.

D. In this case, an increase in money would cause the inflation rate to increase. If we think about the past and events such as hyperinflation, look at what the cause was. Governments were printing money to pay debts, which in turn was decreasing the value of their currency. In this case, people would get paid and run to the store to spend their money because their dollars today may only be worth 50 cents tomorrow or in some cases, the next hour. Therefore, our answer is if the velocity of money keeps growing, inflation will keep growing as well. These two variables are pro cyclical with each other meaning they move together.