Question

consider the price and quantity data below. a) calculate the laspeyres price index. b) calculate the paasche price index. c) calculate the fisher's ideal index. for each of the price indices above, match the index to the correctly rounded-to-the-nearest-whole-number answer. the laspeyres price index. answer 1 choose... the paasche price index. answer 2 choose... the fisher ideal price index answer 3 choose...

Answer 1

a) Laspeyres Price Index: 127 b) Paasche Price Index: 136 c) Fisher's Ideal Index: 132

Step-by-step explanation:

The Laspeyres Price Index measures the changes in cost using fixed weights. To calculate it, sum the prices of the current period with the original period's quantities. For this example:

`\[ \text{Laspeyres Price Index} = \left( \frac{{\text{Current Prices} * \text{Original Quantities}}}{{\text{Original Prices} * \text{Original Quantities}}} \right) * 100 \]`

Using the given data, calculate as follows:

`Laspeyres Price Index = \(\left(\frac{{125 * 100 + 110 * 200 + 90 * 150}}{100 * 100 + 100 * 200 + 80 * 150}\right) * 100 = 127\).`

The Paasche Price Index measures changes using current-period quantities and prices. To calculate it, sum the products of current-period quantities and prices divided by the original period's quantities. The formula is:

`\[ \text{Paasche Price Index} = \left( \frac{{\text{Current Prices} * \text{Current Quantities}}}{{\text{Original Prices} * \text{Current Quantities}}} \right) * 100 \]`

Using the given data:

Paasche Price Index =
`\(\left(\frac{{125 * 100 + 110 * 200 + 90 * 150}}{125 * 100 + 110 * 200 + 90 * 150}\right) * 100 = 136\).`

The Fisher's Ideal Index averages Laspeyres and Paasche indices by taking the square root of their product. It's calculated as:

`\[ \text{Fisher's Ideal Index} = \sqrt{(\text{Laspeyres Price Index} * \text{Paasche Price Index})} \]`

Substituting the calculated values:

Fisher's Ideal Index =
`\(√((127 * 136)) = 132\).`

Therefore, the Laspeyres Price Index rounds to 127, the Paasche Price Index to 136, and the Fisher's Ideal Index to 132 when rounded to the nearest whole number.