Question

Suppose now that economists expect the velocity of money to increase by 50% as a result of the monetary stimulus. What will be the total increase in nominal GDP?

Short answer

The total increase of nominal GDP is $450.

Step-by-step solution

Equation for the Velocity of money

It is given that the Velocity of money was raised by 50%. Earlier velocity was 3. So, the latest velocity is estimated by

$3+(50\%\times 3)=3+\left(3\times \frac{50}{100}\right)$

Money Supply

Suppose previously nominal GDP was $X Billion and velocity is 3.

So money supply was, as written below:

Money Supply $=\frac{\text{Nominal GDP}}{\text{Velocity}}$

$=\frac{\$X}{3}$Billion

Nominal GDP

Now velocity has raised to 4.5. With the exact money supply, the Nominal GDP is calculated below:

Money Supply $\times$Velocity $=$Nominal GDP

Nominal GDP $=\frac{\$X}{3}\times 4.5$

$=\frac{\$3X}{2}$

Total increase of nominal GDP

The increase in Nominal GDP will be $\frac{\$3X}{2}-X=\frac{\$X}{2}$, which is 50% of the previous GDP

The total increase of nominal GDP due to $100 billion increase in money supply is given by:

$\$100$Billion$\times$localid="1645854955576" $4.5=$Billion

The total increase of nominal GDP is $450