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

$\text{The change in nominal GDP is}\$450\text{billion.}$

Step-by-step solution

Concept Introduction 

Money supply: Monetary resource is that the total stock of cash within the economy at some extent of your time.

GDP (Gross Domestic Product): GDP of a rustic is that the value of all finished (final) goods and services produced in an economy during a specific year. It represents the economic well-being of a rustic because it is that the aggregate income of that economy.

Velocity of cash:It's the pace of circulation of money within the economy.

Explanation of Solution

The velocity of cash is pace of circulation of cash within the economy. The formula for calculating velocity of cash is given below.

$\text{velocityof money}=\frac{\text{Nominal GDP}}{\text{MoneySupply}}$

$v=\frac{Y}{M^s}$

Given information

$\text{Change in Money supply,}{\mathrm{M}}^{\mathrm{S}}=\$100\text{billion}$

$\text{Initial velocity of money,}v=3\text{.}$

Calculation

The velocity of money is initially equal to 3 . WE calculate the new velocity of money, v' after a 50% increase as follows:

$\Rightarrow v^{\text{'}}=3+50\%\text{of}3$

$\Rightarrow v^{\text{'}}=4.5$

With new velocity of money $(v\text{'})$and change in money supply, we calculate the change in nominal GDP as follows:

$v=\frac{Y}{M^S}$

$\Rightarrow Y=v{M}^S$

$\Rightarrow \Delta Y=v\Delta M^S$

$\Rightarrow \Delta Y=4.5\times \$100\text{billion}$

$\Rightarrow \Delta Y=\$450\text{billion}$

$\text{Hence, the change in nominal GDP is}\$450\text{billion.}$