Principles of Macroeconomics / Unit 12 MAC 1131 worked example, 60 to 90 seconds
Computing Velocity and Solving the Equation
The idea
Compute velocity from the data, then solve the equation for a missing term. The equation holds by definition, so it can be rearranged freely, but the units must survive the rearrangement. Real output is a quantity of goods, not a sum of money, and answers must be reported as such.
In practice
Take a money supply of 10,000 billion, a price level of 1.25 and real output of 16,000 billion in base-year terms. Nominal GDP is 1.25 times 16,000, which is 20,000 billion. Velocity is 20,000 divided by 10,000, which is 2: the money supply was spent twice. Now solve the other way. Hold velocity at 2 and the money supply at 10,000, and suppose the price level rises to 1.30. Then real output is 20,000 divided by 1.30, which is about 15,385 billion in base-year terms.
Where people slip
That last answer is a quantity of output measured in base-year dollars, not a sum of current money, and the difference from 16,000 is a fall in real output of about 615 billion in those terms. The anchor's own worked version solves for real output and then reports the change as plain dollars, which loses the distinction unit three spent a whole unit building.
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