suppose that this year's money supply is $500b, nominal gdp is $10trillion, and real gdp is $5trillion, what is the price level and velocity of money? and if velocity is constant and the economy's output rises by 5% per year, what will happen to nominal gdp and the price level next year if the Fed keeps the money supply constant?

Question

suppose that this year's money supply is $500b, nominal gdp is $10trillion, and real gdp is $5trillion, what is the price level and velocity of money? and if velocity is constant and the economy's output rises by 5% per year, what will happen to nominal gdp and the price level next year if the Fed keeps the money supply constant?

Answer 1

To answer your questions, we need to use the quantity theory of money equation, which states that:

MV = PY

Where:
M = Money supply
V = Velocity of money (the average number of times a unit of money is spent in a given period)
P = Price level
Y = Real GDP (output or income)

Let's break down the information provided step by step:

1. Money supply (M) = $500 billion
2. Nominal GDP (PY) = $10 trillion
3. Real GDP (Y) = $5 trillion

Using the equation, we can find the velocity of money (V):

V = PY / M

Substituting the values:

V = $10 trillion / $500 billion
V = 20

So, the velocity of money is 20.

Next, we want to determine the price level (P). Rearranging the equation, we have:

P = (M * V) / Y

Plugging in the values:

P = ($500 billion * 20) / $5 trillion
P = 2

Therefore, the price level is 2.

Now, let's move on to the second part of your question. If velocity (V) is constant and the economy's output (Y) rises by 5%, we can determine the impact on nominal GDP (PY) and the price level (P).

Given that V and M remain constant:

PY = MV

Assuming the money supply (M) remains at $500 billion, if output (Y) increases by 5%, we can calculate the new nominal GDP (PY):

New Y = $5 trillion * (1 + 0.05)
New Y = $5.25 trillion

PY (next year) = $500 billion * 20 (constant velocity)
PY (next year) = $10 trillion

Hence, next year's nominal GDP will be $10 trillion.

To find the new price level (P) next year, we rearrange the equation:

P (next year) = (M * V) / Y (next year)

P (next year) = ($500 billion * 20) / $5.25 trillion
P (next year) ≈ 1.9048

Therefore, the price level next year will be approximately 1.9048.

In summary, if the Fed keeps the money supply constant and the economy's output rises by 5% per year, the nominal GDP will increase to $10 trillion, while the price level will decrease to approximately 1.9048.