Question

Suppose that velocity rises while the money supply stays the same. It follows that
a.

P x Y must rise.
b.

P x Y must fall.
c.

P x Y must be unchanged.
d.

the effects on P x Y are uncertain.

Answer 1

To answer the question, we can use the equation of exchange from the quantity theory of money, which states:

\[ M \times V = P \times Y \]

Where:
- \( M \) = Money supply
- \( V \) = Velocity of money
- \( P \) = Price level
- \( Y \) = Real output (real GDP)

In this scenario, we assume that the money supply (\( M \)) remains constant and that the velocity of money (\( V \)) rises. Therefore, if \( V \) increases and \( M \) is constant, the left side of the equation \( M \times V \) must increase.

Since the equation must hold true, if \( M \) is constant and \( V \) rises, the right side \( P \times Y \) must also rise to maintain equality. This indicates that either the price level (\( P \)) must rise, real output (\( Y \)) must rise, or some combination of both must occur.

Thus, it follows that:

**a. \( P \times Y \) must rise.**

So the correct answer is **a. \( P \times Y \) must rise.**