The money supply in Freedonia is $200 billion. Nominal GDP is $800 billion and real GDP is $400 billion. Assuming that velocity is stable, if real GDP grows by 10 percent this year, and if the money supply does not change this year, what is the change of price level?
what is the answer
To find the change in the price level, we can use the equation of exchange:
(1) GDP * Velocity = Money supply * Price level
We are given:
Nominal GDP = $800 billion
Real GDP = $400 billion
Money supply = $200 billion (assumed to be constant)
Velocity = assumed to be constant
We need to find the change in the price level when real GDP grows by 10 percent.
First, let's rearrange equation (1) to solve for the price level:
(2) Price level = (Nominal GDP * Velocity) / Money supply
Since we assume velocity and the money supply are constant, we can rewrite equation (2) as:
(3) Price level = (Nominal GDP) / Money supply
Now we can substitute the given values into equation (3):
Price level = ($800 billion) / ($200 billion)
Price level = 4
So, the initial price level is 4.
When real GDP grows by 10 percent, it becomes:
Real GDP = $400 billion + (10% * $400 billion)
Real GDP = $400 billion + $40 billion
Real GDP = $440 billion
Using equation (3) again:
Price level = ($800 billion) / ($200 billion)
Price level = 4
Therefore, the change in the price level is:
Change in price level = New price level - Initial price level
Change in price level = 4 - 4
Change in price level = 0
So, the change in the price level is 0, indicating that there is no change in the price level when real GDP grows by 10 percent and there is no change in the money supply.
To determine the change in the price level, we can use the equation of exchange, which relates the money supply (M), velocity (V), nominal GDP (NGDP), and price level (P):
M * V = P * NGDP
In this case, we are given the following information:
Money supply (M) = $200 billion
Nominal GDP (NGDP) = $800 billion (initial) + $400 billion (growth of 10%) = $1,200 billion
We also know that velocity (V) is stable, which means it does not change.
Now we can plug these values into the equation of exchange:
$200 billion * V = P * $1,200 billion
To solve for the change in the price level (P), we need to rearrange the equation:
P = ($200 billion * V) / $1,200 billion
Since the velocity (V) is stable, we can ignore it for now and focus on the changes in the money supply and nominal GDP.
Change in nominal GDP = $1,200 billion - $800 billion = $400 billion
Change in price level (ΔP) = ($200 billion * V) / ($400 billion)
Therefore, the change in the price level depends on the value of velocity (V), which we do not have in the given information. To calculate the exact change in the price level, we need the value of velocity or any additional information.