STEP-BY-STEP ANSWER:
Step 1: Start with the identity M * V = P * Y. Recognize that in the long run, both the velocity of money (V) and real output (Y) are relatively constant.
Step 2: With V and Y held constant, any change in the money supply (M) must result in a proportional change in the nominal aggregate spending (P * Y).
Step 3: Therefore, when M increases, P (the price level) must increase proportionally, leading to inflation.
Final Answer: In the long run, an increase in the money supply leads to a proportional increase in the price level.