A student asks…
How do we calculate chained-dollar real GDP when the base year is the later year?
What is chained-dollar real GDP?
Chained-dollar real GDP measures the value of real GDP in each year in base-year dollars.
How do we calculate chained-dollar real GDP when the reference base year is the later year?
The steps for calculating chained-dollar real GDP when the base year is the later year are the same as the steps when the base year is the earlier year:
- (a) Value production in the prices of adjacent years.
- (b) Find the average of two percentage changes.
- (c) Chain to the reference base year.
The only difference is in the last step. When the base year is the earlier year, the chained-dollar real GDP in the later year is real GDP in the earlier year increased by the growth rate. But when the base year is the later year, the chained-dollar real GDP in the earlier year is real GDP in the later year decreased by the growth rate.
Can we see an example?
Of course!
Problem: The economy of Coffeeland produces only americanos and lattes. The table gives the quantities produced and the prices.
Calculate the chained-dollar real GDP in 2023 expressed in 2024 dollars.
Solution: Value production in both years using 2023 prices and calculate the percentage change.
Nominal GDP in 2023 (i.e., 2023 production at 2023 prices) is:
2024 production at 2023 prices is:
The percentage change in production at 2023 prices is:
Now, value production in both years using 2024 prices and calculate the percentage change.
2023 production at 2024 prices is:
Nominal GDP in 2024 (i.e., 2024 production at 2024 prices) is:
The percentage change in production using 2024 prices is:
The average percentage change in the value of production is:
We are asked to express the answer in 2024 dollars, so the base year is 2024. In 2024, the growth rate is 60.0 percent and nominal GDP is $1,140. Let g be the growth rate. The chained-dollar real GDP in 2023 expressed in 2024 dollars is:
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