I want to model a economy where consumers have a Cobb Douglas utility function and where X1 = goods that pay a value added TAX (VAT), and X2 = goods that are exempt from this tax.
I am working with data collected on expenditures on X1 and X2, however, I am in doubt about how to aggregate the quantities of all goods that fall into X1 and X2, given that different goods have different measurement units (e.g., apples are in grams and houses are in squared meters).
One approach that came to my mind was to take the mean/median price of a good and to calculate the rest of quantities relative to that price. For example, if the mean price of an apple is $1, then a house that costs 1 million dollars would be equivalent to buying 1 million apples. Therefore, my unit of measurement becomes apples.
My problem with this apparent solution is that it would imply that, if I set the reference price at 1, then it implies that all the goods in the economy have a price of 1. That is not very intuitive to me, but I can't find the conceptual problem.
What do you think? Is it okay or should I use another approach? Do you recommend an alternative solution?
