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My business offers a portfolio of 4 products which are substitutes for one another. Over the years, we have increased the prices of these products by varying amounts, such that we can estimate the change in demand for each product as we increase its price. However, we do not always increase price by the same amount for each product in the portfolio. Therefore the ratios of prices in the portfolio change. This impacts the demand for each product as well. Is there a simple way of isolating the cross-price elasticities in a pricing model for my portfolio of products? In my model, I'd want to handle:

  1. What is the change in demand for product X when I increase the price of X, holding the prices of all the other products constant?
  2. What is the change in demand for product X when I increase the price of Y, holding the price of X constant?

Looking for some sort of an analytical framework here. Is a regression my best/only option?

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