Indexing Question

[Little_Louis]

Here is a question from a test I sat recently at work. Please could you provide information on how I might solve it rather than the answer itself? I'll then attempt it and come back for comments if that's ok. Thank you very much in advance.

Question: A price index is calculated for a basket of 500 items with weights for the individual items fixed in the base year. Over the next year some items increase in price by up to 5% and others fall by up to 10%. If the weightings remain the same, which one of the following options is correct.

1. The index will fall by around 2.5%
2. The index will fall but it is not possible to say by how much
3. If items with a combined weight of 40% all fall in price by 10% then the index will fall
4. The index will rise or fall according to the price movement of the item with the largest weight.

 

[Cubist]

Please could you provide information on how I might solve it rather than the answer itself?

Read the question statement before looking at the options (perhaps several times until you understand it)

Then reply to this post with your thoughts about each option
- write whether you think it's correct or incorrect
- justify your answer
...and don't worry if you think that more than one is correct. Just write what you're thinking.

Then we'll be able to offer advice based on your actual thoughts (rather than us trying to guess why you're struggling)

 

[Little_Louis]

Hello @Cubist, well I've thought about this question and this is my working out...

A price index is calculated for a basket of 500 items with weights for the individual items fixed in the base year. Over the next year some items increase in price by up to 5% and others fall by up to 10%. If the weightings remain the same, which one of the following options is correct.

1. There are 500 items in a basket, some go up and some go down - so if 50% go up and 50% go down then...
2. 250 items increase by 5% = 250 x 1.05 = 262.50
3. 250 items decrease by 10% = 250 x 0.9 = 225
4 262.50 + 225 = 487.50
5. Percentage decrease = ((500 - 487.50)/(500) x 100 = 2.5% decrease

So from the list, I think it might be option 1? Is this correct?

1. The index will fall by around 2.5%
2. The index will fall but it is not possible to say by how much
3. If items with a combined weight of 40% all fall in price by 10% then the index will fall
4. The index will rise or fall according to the price movement of the item with the largest weight.

 

[blamocur]

Hint: it is impossible to answer without knowing the weights; but of the four answers only two mention weights.

 

[JeffM]

Hello @Cubist, well I've thought about this question and this is my working out...

A price index is calculated for a basket of 500 items with weights for the individual items fixed in the base year. Over the next year some items increase in price by up to 5% and others fall by up to 10%. If the weightings remain the same, which one of the following options is correct.

1. There are 500 items in a basket, some go up and some go down - so if 50% go up and 50% go down then...
2. 250 items increase by 5% = 250 x 1.05 = 262.50
3. 250 items decrease by 10% = 250 x 0.9 = 225
4 262.50 + 225 = 487.50
5. Percentage decrease = ((500 - 487.50)/(500) x 100 = 2.5% decrease

So from the list, I think it might be option 1? Is this correct?

1. The index will fall by around 2.5%
2. The index will fall but it is not possible to say by how much
3. If items with a combined weight of 40% all fall in price by 10% then the index will fall
4. The index will rise or fall according to the price movement of the item with the largest weight.

Suppose each of the items that go up in price does so by 5% and each of the items that go down does so by 10%. Further suppose that the items that go up do represent 50% of the items in the basket and have an aggregate weight of 80 and that the items that go down also represent 50% of the items but have an aggregate weight of just 20. What would the change in the index be?

The point that blamocur is making is that weights matter. You effectively made two assumptions, one about the proportion of items that had increased prices and another that all weights are equal. Neither assumption is warranted.