Can Information Products Be Complements?

In "Marketing Information: A Competitive Analysis,'' Sarvary and Parker (1997) (S&P) [Marketing Science, 16(1): 24-38] argue that, a reduction in the price of one information product can lead to an increase in demand for another information product -- information products can be gross complements -- if they are sufficiently unreliable. We show that S&P obtain this surprising result by implicitly making the following internally inconsistent assumptions: (i) after purchasing information products, consumers update their beliefs using Bayesian updating rule and act as if they have a diffuse initial prior (i.e., their initial prior variance is infinity before receiving any information); (ii) but 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 and that utility of no purchase is "normalized" to zero). This internal inconsistency leads to the possibility that marginal utility can be 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, the marginal utility of information products must be diminishing. This implies that information products are always substitutes, regardless of their noisinesses/reliabilities, in a corrected S&P's framework