To calculate the Fisher price index for 2017 using 2010 as the base year, we will need to follow these steps:
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Calculate the value of the Fisher index which is the geometric mean of the Paasche and Laspeyres price indices.
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For Laspeyres Price Index, we use the formula: \[ Laspeyres = \frac{p1q0}{p0q0} \]
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For Paasche Price Index, we use the formula: \[ Paasche = \frac{p1q1}{p0q1} \]
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Finally, the Fisher Price Index is calculated as: \[ Fisher = \sqrt{Laspeyres \times Paasche} \]
Now, let’s fill in the missing values in your table and then perform the calculations.
Step 1: Fill in the Table
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For Product I
- \( p0q0 = 95 \times 90 = 8550 \)
- \( p1q0 = 75 \times 90 = 6750 \)
- \( p1q1 = 75 \times 100 = 7500 \)
- \( p0q1 = 95 \times 100 = 9500 \)
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For Product II
- \( p0q0 = 80 \times 70 = 5600 \)
- \( p1q0 = 65 \times 70 = 4550 \)
- \( p1q1 = 65 \times 80 = 5200 \)
- \( p0q1 = 80 \times 80 = 6400 \)
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For Product III
- \( p0q0 = 40 \times 80 = 3200 \)
- \( p1q0 = 45 \times 80 = 3600 \)
- \( p1q1 = 45 \times 50 = 2250 \)
- \( p0q1 = 40 \times 50 = 2000 \)
Step 2: Sum Up Values
Now sum up the respective values:
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Total \( p0q0 \) \[ = 8550 + 5600 + 3200 = 17350 \]
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Total \( p1q0 \) \[ = 6750 + 4550 + 3600 = 14900 \]
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Total \( p1q1 \) \[ = 7500 + 5200 + 2250 = 14950 \]
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Total \( p0q1 \) \[ = 9500 + 6400 + 2000 = 17900 \]
Step 3: Calculate Price Indices
Laspeyres Price Index: \[ Laspeyres = \frac{p1q0}{p0q0} = \frac{14900}{17350} \approx 0.8591 \]
Paasche Price Index: \[ Paasche = \frac{p1q1}{p0q1} = \frac{14950}{17900} \approx 0.8335 \]
Step 4: Calculate Fisher Price Index
\[ Fisher = \sqrt{Laspeyres \times Paasche} = \sqrt{0.8591 \times 0.8335} \approx \sqrt{0.7155} \approx 0.8462 \]
Conclusion
The Fisher price index for 2017 with 2010 as the base year is approximately 0.8462 or 84.62% of the base year's price level.