Final answer:
Laspeyre's price index measures average price changes using base year quantities, while Paasche's price index uses current year quantities. Given Fisher's ideal index is 250, Laspeyre's index number is calculated to be 105 and Paasche's is approximately 595.24 after performing the necessary calculations.
Step-by-step explanation:
Understanding Laspeyre's and Paasche's Index Numbers
In economics, Laspeyre's price index and Paasche's price index are used to measure the average change in prices or quantities over time. These price indices are calculated using current year prices and quantities as well as base year prices and quantities. Fisher's ideal index is a geometric mean of Laspeyre's and Paasche's indices and aims to provide a more accurate representation of price changes.
Given that Fisher's ideal index number is 250 and the current year's weighted index is 5% higher than the base year, we can use the relationship between Fisher's index, Laspeyre's index (L), and Paasche's index (P) to find L and P values Mathematically, Fisher's index (F) is the square root of the product of L and P. Hence, F = \(\sqrt{L \cdot P}\).
When deflating nominal figures to get real figures, we divide the nominal by the price index and adjust for the fact that price indices are published as integers after being multiplied by 100. Therefore, we also need to divide by 100 to make the math work.
Using the Fisher's index of 250 (which is actually 2.50 when not adjusted by the factor of 100), we can write the equation as \(2.50 = \sqrt{L \cdot P}\). Given that the weighted index is 5% higher, Laspeyre's index number can be calculated by increasing the base year index of 100 by 5%, leading to an index of 105, or 1.05 in decimal form. We can then solve for Paasche's index by rearranging the formula to \(P = (2.50^2) / 1.05\).
Therefore, to find Laspeyre’s price index number and Paasche’s price index number, we perform the following calculations:
Convert Fisher's index to decimal form: 250 / 100 = 2.50.
- Calculate Laspeyre’s index: Base year index (100) increased by 5% = 105 or 1.05 in decimal form.
- Calculate Paasche’s index: \(P = (2.50^2) / 1.05\) = \(6.25 / 1.05\) ≈ 5.9524 or 595.24 when multiplied by 100.
In conclusion, Laspeyre’s price index number is 105 and Paasche’s price index number is approximately 595.24.