What would it mean if an economy had real GDP increasing faster than nominal GDP?

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Real GDP is calculated using historical values. Using these values, we can more accurately measure and understand inflation, because these measurements have already been completed and we know how they trend. Nominal GDP is the opposite: it uses today's values to estimate GDP, and it can't properly account for inflation because we don't have all the data just yet. In a standard economy with typical inflation, the nominal GDP will increase faster than the real GDP, because inflation is pushing prices higher.

However, if the real GDP is growing faster, that means that the nominal GDP is experiencing deflation—the value of currency in the market is getting lower, and the historical values are higher than the current ones. If the prices in an economy were higher the previous year, then deflation is occurring.

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The definition of Real GDP is the value of economic output measured in "yesterday's" prices (or from a base year). Real GDP, calculated in this way, adjusts for price changes and measures the actual quantity of production changes—controlled, again, for inflation or deflation.

When we measure economic output using today's (current) prices, we are calculating Nominal GDP, which is not corrected for inflation or deflation, as Real GDP is. Nominal GDP calculates the change in quantities produced with current inflated or deflated prices.

If Real GDP (with a base year's prices) is increasing faster than nominal GDP (with today's current prices), this generally means that deflation is occurring in the economy. If a prior year's prices were higher than current prices, the economy is experiencing deflation.

Some key equations are the following:

Real GDP = (Nominal GDP) divided by (GDP deflator)

Nominal GDP = (GDP deflator) x (Real GDP)

From these equations, one can see that in order for Real GDP to be greater than Nominal GDP, the GDP deflator would have to be smaller than 1, or less than 100%. Only in cases of deflation would a GDP deflator be less than 100%.

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What this would mean is that the economy was experiencing deflation.

Deflation is when the price level for the economy as a whole drops.  If the price level is dropping, a small increase in production in the economy as a whole could still result in a decline in nominal GDP because the decline in price would offset the increase in production.

In such a case, real GDP would rise because production was rising but nominal GDP would drop because the price (in current dollars) of the goods and products made would be lower due to the deflation.

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