Question

question 1 of 9
suppose a country has a money demand function ($\frac{m}{p}$)^d = ky, where k is a constant parameter. the money supply grows by 12 percent per year, and real income grows by 5 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?
v = k$\frac{py}{m}$: k times the ratio of nominal output to the money supply is related to velocity, i.e., the more money people hold, the larger velocity is, and vice versa.
there is no relationship between k and v, i.e., the amount of money people hold is not related to the velocity of money.
v = $\frac{1}{k}$: k is inversely related to velocity, i.e., the more money people hold for a given real income, the smaller velocity is, and vice versa.
v = k: k is directly related to velocity, i.e., the more money people hold for a given real income, the larger velocity is, and vice versa.
d. suppose that instead of a constant money demand function, the velocity of money in this economy was growing steadily due to financial innovation. assuming everything else was unchanged, how would that affect the inflation rate?
the inflation rate would remain unchanged.
the inflation rate would increase.
the inflation rate would fluctuate.
the inflation rate would decrease.

Explanation:

Step1: Recall the quantity - theory of money

The quantity - theory of money is given by $MV = PY$. The money - demand function is $(\frac{M}{P})^d=kY$, which can be rewritten as $M = kPY$. In growth - rate terms, the growth rate of the money supply $g_M$, the growth rate of velocity $g_V$, the inflation rate $\pi$ (growth rate of the price level $P$), and the growth rate of real income $g_Y$ are related by $g_M+g_V=\pi + g_Y$. Assuming velocity is constant ($g_V = 0$).

Step2: Calculate the inflation rate for part a

We know that $g_M = 12\%$ and $g_Y=5\%$. Since $g_V = 0$, from $g_M+g_V=\pi + g_Y$, we can solve for $\pi$. Substituting the values, we get $\pi=g_M - g_Y$. So, $\pi=12\% - 5\%=7\%$.

Step3: Analyze part b

From the equation $g_M+g_V=\pi + g_Y$, if $g_M$ and $g_V$ are constant, an increase in $g_Y$ would lead to a decrease in $\pi$. Because $\pi=g_M + g_V - g_Y$.

Step4: Analyze part c

From $MV = PY$ and $M = kPY$, we can rewrite $MV = PY$ as $kPYV=PY$. Canceling out $PY$ (assuming $PY
eq0$), we get $V=\frac{1}{k}$. So, $k$ is inversely related to velocity. The more money people hold for a given real income (higher $k$), the smaller the velocity is, and vice - versa.

Step5: Analyze part d

The quantity - theory of money in growth rates is $g_M+g_V=\pi + g_Y$. If $g_V$ is increasing (due to financial innovation) while $g_M$ and $g_Y$ are constant, then $\pi=g_M+g_V - g_Y$. So, an increase in $g_V$ will lead to an increase in $\pi$.

Answer:

a. 7
b. lower
c. $V = \frac{1}{k}$: $k$ is inversely related to velocity, i.e., the more money people hold for a given real income, the smaller velocity is, and vice versa.
d. The inflation rate would increase.