Complementarity of Information Products

In “Marketing Information: A Competitive Analysis,” Sarvary, M., and P. M. Parker. 1997. “Marketing Information: A Competitive Analysis.” Marketing Science 16 (1): 24–38 (S&P) argue that in part of the parameter space that they considered, a reduction in the price of one information product can lead to an increase in demand for another information product, i.e. information products can be gross complements. This result is surprising and has potentially important marketing implications. We show that S&P obtain this complementarity result by implicitly making the following internally inconsistent assumptions: (i) after purchasing information products, consumers update their beliefs using a Bayesian updating rule that assumes they have a diffuse initial prior (i.e. their initial prior variance is ∞ before receiving any information); (ii) if consumers choose not to purchase any information product, it is assumed that their initial prior variance is 1 (implied by the utility function specification). This internal inconsistency leads to the possibility that when information products are uncorrelated and their variances are close to 1, marginal utility is increasing in the number of products purchased, and hence information products can be complements in their model. We show that if we remove this internal inconsistency, in the parameter space considered by S&P, information products cannot be complements because the marginal utility of information products will be diminishing. We also show that, in parts of the parameter space not considered by S&P, it is possible that information products are complements; this space of parameters requires consumer’s initial prior to be relatively precise and information products to be highly correlated (either positively or negatively).