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The authors describe an approach to measuring self- and cross-price/demand relationships via conjoint analysis. The modeling “trick” is to characterize each brand as a separate price-related factor in which respondents are asked to indicate their subjective likelihood of buying a set of J brands, each priced at some experimental level. A first-order Markovian model is postulated to represent price-induced brand switching. The price-demand model is then fitted (by generalized least squares) to share of choices, estimated after T time periods. The model is illustrated empirically in the context of a consumer nondurable good.
Mahajan et al. (Sun,) studied this question.