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Sagot :
Let's calculate the Nominal GDP, Real GDP, and the GDP Deflator for the years 2020, 2021, and 2022 using 2020 as the base year.
### Year 2020
1. Nominal GDP 2020:
[tex]\[ \text{Nominal GDP} = (\text{Milk Price} \times \text{Milk Quantity}) + (\text{Honey Price} \times \text{Honey Quantity}) \][/tex]
[tex]\[ \text{Nominal GDP 2020} = (1 \times 150) + (2 \times 100) = 150 + 200 = 350 \text{ dollars} \][/tex]
2. Real GDP 2020:
[tex]\[ \text{Real GDP} = (\text{Base Year Milk Price} \times \text{Milk Quantity}) + (\text{Base Year Honey Price} \times \text{Honey Quantity}) \][/tex]
Since the base year is 2020, we use the same prices:
[tex]\[ \text{Real GDP 2020} = (1 \times 150) + (2 \times 100) = 150 + 200 = 350 \text{ dollars} \][/tex]
3. GDP Deflator 2020:
[tex]\[ \text{GDP Deflator} = \left( \frac{\text{Nominal GDP}}{\text{Real GDP}} \right) \times 100 \][/tex]
[tex]\[ \text{GDP Deflator 2020} = \left( \frac{350}{350} \right) \times 100 = 100\% \][/tex]
### Year 2021
1. Nominal GDP 2021:
[tex]\[ \text{Nominal GDP 2021} = (2 \times 150) + (4 \times 100) = 300 + 400 = 700 \text{ dollars} \][/tex]
2. Real GDP 2021:
Using 2020 base year prices:
[tex]\[ \text{Real GDP 2021} = (1 \times 150) + (2 \times 100) = 150 + 200 = 350 \text{ dollars} \][/tex]
3. GDP Deflator 2021:
[tex]\[ \text{GDP Deflator 2021} = \left( \frac{700}{350} \right) \times 100 = 200\% \][/tex]
### Year 2022
1. Nominal GDP 2022:
[tex]\[ \text{Nominal GDP 2022} = (2 \times 300) + (4 \times 200) = 600 + 800 = 1400 \text{ dollars} \][/tex]
2. Real GDP 2022:
Using 2020 base year prices:
[tex]\[ \text{Real GDP 2022} = (1 \times 300) + (2 \times 200) = 300 + 400 = 700 \text{ dollars} \][/tex]
3. GDP Deflator 2022:
[tex]\[ \text{GDP Deflator 2022} = \left( \frac{1400}{700} \right) \times 100 = 200\% \][/tex]
### Summary
- 2020
- Nominal GDP: [tex]\(350 \text{ dollars}\)[/tex]
- Real GDP: [tex]\(350 \text{ dollars}\)[/tex]
- GDP Deflator: [tex]\(100\%\)[/tex]
- 2021
- Nominal GDP: [tex]\(700 \text{ dollars}\)[/tex]
- Real GDP: [tex]\(350 \text{ dollars}\)[/tex]
- GDP Deflator: [tex]\(200\%\)[/tex]
- 2022
- Nominal GDP: [tex]\(1400 \text{ dollars}\)[/tex]
- Real GDP: [tex]\(700 \text{ dollars}\)[/tex]
- GDP Deflator: [tex]\(200\%\)[/tex]
Filling the table with these results, we get:
\begin{tabular}{cccc}
& \begin{tabular}{c}
Nominal GDP \\
(Dollars)
\end{tabular} & \begin{tabular}{c}
Real GDP \\
(Dollars)
\end{tabular} & GDP Deflator \\
\hline 2020 & 350 & 350 & 100\% \\
2021 & 700 & 350 & 200\% \\
2022 & 1400 & 700 & 200\% \\
& & &
\end{tabular}
### Year 2020
1. Nominal GDP 2020:
[tex]\[ \text{Nominal GDP} = (\text{Milk Price} \times \text{Milk Quantity}) + (\text{Honey Price} \times \text{Honey Quantity}) \][/tex]
[tex]\[ \text{Nominal GDP 2020} = (1 \times 150) + (2 \times 100) = 150 + 200 = 350 \text{ dollars} \][/tex]
2. Real GDP 2020:
[tex]\[ \text{Real GDP} = (\text{Base Year Milk Price} \times \text{Milk Quantity}) + (\text{Base Year Honey Price} \times \text{Honey Quantity}) \][/tex]
Since the base year is 2020, we use the same prices:
[tex]\[ \text{Real GDP 2020} = (1 \times 150) + (2 \times 100) = 150 + 200 = 350 \text{ dollars} \][/tex]
3. GDP Deflator 2020:
[tex]\[ \text{GDP Deflator} = \left( \frac{\text{Nominal GDP}}{\text{Real GDP}} \right) \times 100 \][/tex]
[tex]\[ \text{GDP Deflator 2020} = \left( \frac{350}{350} \right) \times 100 = 100\% \][/tex]
### Year 2021
1. Nominal GDP 2021:
[tex]\[ \text{Nominal GDP 2021} = (2 \times 150) + (4 \times 100) = 300 + 400 = 700 \text{ dollars} \][/tex]
2. Real GDP 2021:
Using 2020 base year prices:
[tex]\[ \text{Real GDP 2021} = (1 \times 150) + (2 \times 100) = 150 + 200 = 350 \text{ dollars} \][/tex]
3. GDP Deflator 2021:
[tex]\[ \text{GDP Deflator 2021} = \left( \frac{700}{350} \right) \times 100 = 200\% \][/tex]
### Year 2022
1. Nominal GDP 2022:
[tex]\[ \text{Nominal GDP 2022} = (2 \times 300) + (4 \times 200) = 600 + 800 = 1400 \text{ dollars} \][/tex]
2. Real GDP 2022:
Using 2020 base year prices:
[tex]\[ \text{Real GDP 2022} = (1 \times 300) + (2 \times 200) = 300 + 400 = 700 \text{ dollars} \][/tex]
3. GDP Deflator 2022:
[tex]\[ \text{GDP Deflator 2022} = \left( \frac{1400}{700} \right) \times 100 = 200\% \][/tex]
### Summary
- 2020
- Nominal GDP: [tex]\(350 \text{ dollars}\)[/tex]
- Real GDP: [tex]\(350 \text{ dollars}\)[/tex]
- GDP Deflator: [tex]\(100\%\)[/tex]
- 2021
- Nominal GDP: [tex]\(700 \text{ dollars}\)[/tex]
- Real GDP: [tex]\(350 \text{ dollars}\)[/tex]
- GDP Deflator: [tex]\(200\%\)[/tex]
- 2022
- Nominal GDP: [tex]\(1400 \text{ dollars}\)[/tex]
- Real GDP: [tex]\(700 \text{ dollars}\)[/tex]
- GDP Deflator: [tex]\(200\%\)[/tex]
Filling the table with these results, we get:
\begin{tabular}{cccc}
& \begin{tabular}{c}
Nominal GDP \\
(Dollars)
\end{tabular} & \begin{tabular}{c}
Real GDP \\
(Dollars)
\end{tabular} & GDP Deflator \\
\hline 2020 & 350 & 350 & 100\% \\
2021 & 700 & 350 & 200\% \\
2022 & 1400 & 700 & 200\% \\
& & &
\end{tabular}
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