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When we say about "the basket used for calculating the CPI is the same as the composition of GDP" What does it mean the "same basket"? Does it just mean the goods and service are the same but the weights of each good itself do not matter?(Basket of CPI and GDP are also included A and B but no matter weights) . Or it means the weights of each good in the basket are the also same? (Basket of CPI and GDP are included A and B, also the weights of A is 0.4 and B is 0.6 in both baskets)

I'm really confusing.

In additon, this is the original question though I think it would be useless for this question:

"Assume that the basket used for calculating the CPI is the same as the composition of GDP. Will CPI in a given year then equal the GDP deflator? If so why, if not why not?"

Thanks to all the people willing to help!!

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    $\begingroup$ Do we say "the basket used for calculating the CPI is the same as the composition of GDP"? It seems highly unlikely, except possibly for the consumer expenditure element of GDP. It does not make much sense for other components of GDP (expenditure basis) such as investment or government expenditure or trade; nor does it for other measures of GDP $\endgroup$ – Henry Sep 1 '19 at 22:06
  • $\begingroup$ Do you have a reference for somebody writing this? $\endgroup$ – Brian Romanchuk Oct 29 at 16:30
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Same basket means same goods and services at factor cost or market price. Weighting method could be different.

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Interesting question. I am not entirely sure of the answer below but here's an attempt:

"Assume that the basket used for calculating the CPI is the same as the composition of 
 GDP. Will CPI in a given year then equal the GDP deflator? If so why, if not why not?"

Answer should be NO.

So CPI comprises of basket that participants consume, and * private consumption* is only a part of GDP. From what I understand CPI basket being same as composition of GDP means is that in the consumption expenditure $(C)$ part of GDP $(Y)$ has same composition as the weights in CPI basket, i.e., if 30% of private consumption expenditure, say, comes from spending on food items then the weight of food in CPI basket will be exactly 30%.

So as such CPI can be used as a perfect deflator for deflating $C$ but not $Y$. The GDP deflator would have to additionally take account of private investment, and government consumption and investment which may or may not have same composition as that of CPI basket.

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