Suppose the amount of output doesn’t change in an economy, but the consumer price index (CPI) increases. What happens to nominal gross domestic product (GDP) and real GDP?
Nominal GDP increases; real GDP doesn’t change.
Nominal GDP is a measure of how much is spent on output. An increase in the CPI indicates that inflation has occurred --- because prices have gone up, we know output must have cost more, and therefore nominal GDP has increased. An increase in inflation means that the prices used to calculate GDP have changed. However, the actual output hasn’t changed. Since real GDP is a measure of how much is produced, real GDP doesn’t change either.