The GDP that doesn't add up

Problem

Italy’s GDP in 2020 is $2100$ billion. In 2021 it falls by $10\%$, in 2022 it grows by $10\%$. How much is the GDP in 2022? Does it return to the 2020 value?

Solution

The two multiplicative factors are applied in sequence, one for the decrease and one for the increase:

• 2021: $2100\cdot\dfrac{90}{100} = 1890$
• 2022: $1890\cdot\dfrac{110}{100} = \boxed{2079}$

The GDP does not return to $2100$: the overall variation is $-21$ billion, that is, a decrease of $1\%$ compared with 2020. The reason is that the $10\%$ increase acts on a base ($1890$) smaller than the one on which the decrease had acted ($2100$): the two factors $0{,}9$ and $1{,}1$ give $0{,}99 < 1$.

Links

Topics: Percentages
Concepts: Percentage increase · Percentage decrease · Percentage variation
Skills: Calculating · Modelling
Exercise type: Word problem