Suppose in an economy the nominal money supply is $ 1000, the general price level is 4 and the real output is at its full employment level of $4000.

a. what is the price level and velocity of money?
b. By assuming constant velocity of money, what would you expect to see the relationship between money supply and the price level from the quantity theory equation of money?
c. What would be the new price level if nominal money supply increases to $1800 and if nominal money supply decreases to $ 800?

To answer these questions, we can use the Quantity Theory of Money equation, which states:

MV = PQ

Where:
M = Nominal Money Supply
V = Velocity of Money
P = Price Level
Q = Real Output (or Quantity of Goods and Services)

a) To find the price level and velocity of money, we can rearrange the equation as follows:

P = (M * V) / Q

Given:
Nominal Money Supply (M) = $1000
Price Level (P) = 4
Real Output (Q) = $4000

Substituting these values into the equation, we can solve for V:
4 = (1000 * V) / 4000
16 = 1000 * V
Velocity of Money (V) = 16 / 1000 = 0.016

Now, substituting the known values into the equation, we can find the price level:
P = (1000 * 0.016) / 4000
P = 0.016

Therefore, the price level is 0.016 and the velocity of money is 0.016.

b) Assuming constant velocity of money, the quantity theory equation of money tells us that there is a direct relationship between the money supply (M) and the price level (P). This means that if the money supply increases, the price level is expected to increase proportionately, assuming other factors remain constant. Similarly, if the money supply decreases, the price level is expected to decrease.

c) Let's calculate the new price level in two scenarios:

Scenario 1: Nominal Money Supply increases to $1800
Given:
New Nominal Money Supply (M) = $1800

Substituting this value and the previous values into the equation, we can solve for the new price level (P):
P = (1800 * 0.016) / 4000
P = 0.0072

Therefore, if the nominal money supply increases to $1800, the new price level would be 0.0072.

Scenario 2: Nominal Money Supply decreases to $800
Given:
New Nominal Money Supply (M) = $800

Substituting this value and the previous values into the equation, we can solve for the new price level (P):
P = (800 * 0.016) / 4000
P = 0.0032

Therefore, if the nominal money supply decreases to $800, the new price level would be 0.0032.