Question

question 2 of 9 (\\(\frac{m}{p}\\))^d = l(i, y)=\frac{y}{5i} where i is the nominal interest rate, and y is the real output (income). a. if output grows at a rate of g, and the nominal interest rate is constant, the demand for real balances will grow at a rate of. b. what is the velocity of money in this economy? 0 5i \\(\frac{y(5i)}{y}\\) \\(\frac{5i}{y}\\) c. if inflation and nominal interest rates are constant, at what rate, if any, will velocity grow? d. how will a permanent (once - and - for - all) increase in the level of interest rates affect the level and growth rate of velocity? a one - time increase in the nominal interest rate will cause a one - time increase in velocity, and the growth rate of velocity will now be positive. a one - time increase in the nominal interest rate will cause a one - time increase in velocity, and the growth rate of velocity will now be negative.

Explanation:

Step1: Find growth - rate of real - balance demand

The demand for real balances is given by $(\frac{M}{P})^d=\frac{Y}{5i}$. Since $i$ is constant and $Y$ grows at rate $g$, the growth rate of $(\frac{M}{P})^d$ is the same as the growth rate of $Y$. So the demand for real balances will grow at a rate of $g$.

Step2: Calculate the velocity of money

The quantity equation is $MV = PY$, or $V=\frac{PY}{M}$. From $(\frac{M}{P})^d=\frac{Y}{5i}$, we can rewrite it as $M^d=\frac{PY}{5i}$. In equilibrium $M = M^d$. Then $V = 5i$.

Step3: Analyze the growth rate of velocity when inflation and nominal interest rates are constant

Since $V = 5i$ and $i$ is constant, the growth rate of velocity is $0$.

Step4: Analyze the effect of a permanent increase in interest rates on velocity

Since $V = 5i$, a one - time increase in $i$ will cause a one - time increase in $V$. And since $i$ then remains constant, the growth rate of $V$ is $0$.

Answer:

a. $g$
b. $5i$
c. $0$
d. A one - time increase in the nominal interest rate will cause a one - time increase in velocity, and the growth rate of velocity will now be $0$.