Assume the money supply is equal to $40b, the velocity of money is constant at 6, and nominal GDP equals $240b. According to the Quantity Theory of Money, by how much will a $10b increase in the money supply change nominal GDP?

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To tackle this, I start by noting the given quantities and the relationship from the Quantity Theory of Money, MV = PY, where P is the price level and Y is real GDP. Here, M = $40b, V = 6, and nominal GDP PY = $240b, which is consistent since 40 × 6 = 240.

Now consider an increase in the money supply by $10b while V remains constant at 6. The new money stock is M' = $50b. Using MV = PY with the same velocity, the new nominal GDP becomes PY' = M' × V = 50 × 6 = $300b.

The change in nominal GDP is PY' − PY = 300 − 240 = $60b.

Option-by-option analysis:
- a. $60b: This matches the calculated change from 240b to 300b using the unchanged velocity, so it is consistent with the Quantity Theory of Money given the new money supply. 
- b. $300b: This would imply the entire $300b is the change, which misinterprets the baseline; the actual change is the difference between post- and pre-change nominal GDP, not the final level alone.
- c. $250b: This would require a final nominal GDP of 490b or a miscalculation of the baseline, which contradicts the given numbers and the formula.
- d. $10b: This would reflect simply the size of the money supply increase without accounting for the multiplier effect of velocity on nominal GDP.
- e. $50b: This suggests the change equaled the increase in M alone, ignoring the velocity of money; the product MV shows that the impact on PY is greater than the raw change in M when V is constant.

In summary, applying the equation with the new money supply and unchanged velocity yields a $60b rise in nominal GDP, which aligns with option a and contradicts the other options through straightforward arithmetic and the core idea of the money–income channel in the Quantity Theory.

NFLS2024ECON11 Textbook HW 6. Macroeconomic Theories and Long-Run Economic Growth - Modules 5.3, 5.6, 5.7

Assume the money supply is equal to $40b, the velocity of money is constant at 6, and nominal GDP equals $240b. According to the Quantity Theory of Money, by how much will a $10b increase in the money supply change nominal GDP?

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