In the equation of exchange, if the quantity of money (M) has doubled, while the price level (P) has increased by 50 percent and velocity (V) remains constant, then real output (Y) ________. (Hint: The quantity equation implies that Y = MV/P)

Question

In the equation of exchange, if the quantity of money (M) has doubled, while the price level (P) has increased by 50 percent and velocity (V) remains constant, then real output (Y) ________.    (Hint: The quantity equation implies that Y = MV/P)

BlackTom AI · Accepted Answer

Examining the prompt, we are told to use the quantity equation Y = MV/P and that M doubles, P rises by 50%, and V remains constant. This lets us compare the new output to the initial output.
Option 1: 'also doubles' — If P and V were unchanged and M doubled, Y would indeed double. However, in our scenario P increases, which dampens the effect of the doubled money supply. Since Y scales with M and inversely with P, the rise in P offsets part of the M increase, so Y does not simply double.
Option 2: 'decreases by 50 percent' — This would require a dramatic drop in Y despite M increasing, which contradicts the fact that M has risen. The positive effect of a higher M would counterbalance some of the change from P rising, not produce a substantial decrease.
Option 3: 'triples' — A tripling of Y would require a much larger net increase in the numerator relative to the denominator than what a doubling of M and a 50% increase in P provide. The math does not support a threefold increase when P grows by half.
Option 4: 'increases by 33 percent' — Start from Y0 = MV/P. After changes, Y1 = (2M V) / (1.5 P) = (2 / 1.5) * (MV/P) = (4/3) * Y0 ≈ 1.333... * Y0. This corresponds to an increase of 33.3% over the original Y0. The velocity term stays constant, so there are no additional effects altering this result.
In summary, evaluating each option against the relationship Y = MV/P with M → 2M, P → 1.5P, and V constant shows that only the statement about a 33 percent increase aligns with the mathematics of the quantity equation.

In the equation of exchange, if the quantity of money (M) has doubled, while the price level (P) has increased by 50 percent and velocity (V) remains constant, then real output (Y) ________. (Hint: The quantity equation implies that Y = MV/P)单项选择题

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