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This paper presents a revealed preference method for calculating a lower bound on the virtual price of new goods and suggests a way to improve these bounds by using non-parametric expansion paths. This allows the calculation of cost-of-living and price indices when the number of goods changes between periods.

The calculation of cost-of-living or price indices is complicated by changes in the number of goods available between periods. This is because the full set of prices is not observable in every period. When, for example, a new good is introduced, it is necessary to impute its virtual price for the period before it existed.

The usual approach is to set this virtual price at the level which would just have driven demand for the new good to zero in that period. In other words the rationed model (in which some goods are not available in all periods) is rewritten as an unrationed model with virtual prices. This allows revealed preference conditions to be applied to data in which the number of goods changes over time.

We show that revealed preference restrictions can be used to calculate the lower bound on the virtual price of a new good which is consistent with the maintained hypothesis that the data were generated by the maximisation of any well-behaved utility function.

We show how this bound can be improved through use of non-parametric expansion paths if circumstances allow for their estimation.

We argue that this approach has two principal merits compared to parametric estimation of virtual prices. Firstly, it does not require a maintained assumption regarding the form of the utility function. Secondly, it is computationally simple.