Question

Suppose the money supply $M$has been growing at $10\%$per year, and nominal GDP, $PY$, has been growing at $20\%$per year. The data are as follows (in billions of dollars):

Calculate the velocity for each year. At what rate is the velocity growing?

Short answer

Velocities are equal to $10,11,12$in years $2018,2019,2020$respectively.

Velocity is growing at the rate of$10\%$.

Step-by-step solution

Step 1. Define velocity.

A velocity of an item is a function of frequency and is defined as the rate of growth of its location with respect to the criteria of reference.

Step 2. 

Use the formula: $V=\frac{PY}{M}$

For year $2018:$

width="74">V=1000100=10

For year width="42">2019:

$\begin{array}{rcl}V& =& \frac{1200}{110}\\ & \approx & 11\end{array}$

For year $2020:$

$\begin{array}{rcl}V& =& \frac{1440}{121}\\ & \approx & 12\end{array}$

Rate of change in velocity width="119">=11-1010×100

$=10\%$