Question

Suppose the liquidity preference function is given by

$L\left(i,Y\right)=\frac{Y}{8}-1,000i$

Use the money demand equation, along with the following table of values, to calculate the velocity for each period.

Short answer

Velocities for periods $1,2,3,4,5,6,7$are$8.28,8.38,8.16,8.26,8.37,8.20,8.30$respectively.

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. Calculate velocity for various periods.

For period $1:$

$\begin{array}{rcl}V& =& \frac{Y}{L(i,Y)}\\ L(i,Y)& =& \frac{12000}{8}-1000X0.05\\ L(i,Y)& =& 1500-50\\ & =& 1450\\ V& =& \frac{12000}{1450}\\ & =& 8.28\end{array}$

For period $2:$

$\begin{array}{rcl}V& =& \frac{Y}{L(i,Y)}\\ L(i,Y)& =& \frac{12500}{8}-1000X0.07\\ L(i,Y)& =& 1562.5-70\\ & =& 1492.5\\ V& =& \frac{12500}{1492.5}\\ & =& 8.38\end{array}$

For period $3:$

$\begin{array}{rcl}V& =& \frac{Y}{L(i,Y)}\\ L(i,Y)& =& \frac{12250}{8}-1000X0.03\\ L(i,Y)& =& 1531.25-30\\ & =& 1501.25\\ V& =& \frac{12250}{1501.25}\\ & =& 8.16\end{array}$

For period $4:$

$\begin{array}{rcl}V& =& \frac{Y}{L(i,Y)}\\ L(i,Y)& =& \frac{12500}{8}-1000X0.05\\ L(i,Y)& =& 1562.5-50\\ & =& 1512.5\\ V& =& \frac{12500}{1512.5}\\ & =& 8.26\end{array}$

For period $5:$

$\begin{array}{rcl}V& =& \frac{Y}{L(i,Y)}\\ L(i,Y)& =& \frac{12800}{8}-1000X0.07\\ L(i,Y)& =& 1600-70\\ & =& 1530\\ V& =& \frac{12800}{1530}\\ & =& 8.37\end{array}$

For period $6:$

$\begin{array}{rcl}V& =& \frac{Y}{L(i,Y)}\\ L(i,Y)& =& \frac{13000}{8}-1000X0.04\\ L(i,Y)& =& 1625-40\\ & =& 1585\\ V& =& \frac{13000}{1585}\\ & =& 8.20\end{array}$

For period $7:$

$\begin{array}{rcl}V& =& \frac{Y}{L(i,Y)}\\ L(i,Y)& =& \frac{13200}{8}-1000X0.06\\ L(i,Y)& =& 1650-60\\ & =& 1590\\ V& =& \frac{13200}{1590}\\ & =& 8.30\end{array}$