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This empirical study investigates why the true costs of living for different income groups in Taiwan as measured by the superlative To¨rnqvist price index have grown dissimilarly over the sample period. Specifically, it shows that using the aggregate Cost of Living (COL) estimates for the entire households as is commonly practiced would produce noticeable group bias effect in measurement. Also the magnitude of the commodity substitution bias in the conventional Consumer Price Index (CPI) is found to be positively related to household income in general. Because of the presence of these two biases, the true COL for households belonging to the two ends of the income spectrum is found to be over-estimated. This article is therefore in full agreement with Arrow's proposition that an alternative and separate set of price index be constructed.