Mergers with interfirm bundling: a case of pharmaceutical cocktails

Abstract

Pharmaceutical cocktails often consist of two or more drugs produced by competing firms. The component drugs are often also sold as stand‐alone products. We analyze the effects of a merger between two pharmaceutical firms selling complements for colorectal cancer treatment. In this setting there are two merger effects: the standard upward pricing pressure due to firms internalizing the substitution between the stand‐alone products, and an additional effect where the firms internalize the impact of selling complements and reduce the price of the cocktail product. The net impact of a merger is a modest price increase, or even a price decrease.

An Empirical Model of Quantity Discounts with Large Choice Sets

“…An essential factor behind the practical advantages of the proposed C2SLS estimator is the use of individual-level purchases in the aggregate form of bundle-level purchase probabilities. Bundle-level purchase probabilities are not typically directly observed (with the exception of a few industries, see Crawford and Yurukoglu, 2012;Song et al, 2017) but rather computed from samples of individual-level purchases (Ershov et al, 2021) and thus subject to sampling error. When the number of bundles is large relative to the sample of individual-level purchases, sampling error in the bundle-level purchase probabilities can be pronounced and lead to estimation bias (Gentzkow et al, 2019), for example because of the large number of observed "zeros" (Gandhi et al, 2020).…”

“…9 The MNL implies that the unobserved preferences of any two bundles are independent. The NL instead requires every bundle to belong uniquely to one nest, so that either all bundles have equally correlated preferences (a unique nest) or some of the bundles with overlapping components end up with uncorrelated preferences (more than one nest, Song et al, 2017). We return to this point below.…”

“…In general, the NL model cannot accommodate this intuitive requirement for all products and bundles: because bundle (1, 2) can only be allocated to either N i or N ii , its unobserved preferences will either have correlation 1 − λ 2 i with those of {1, (1, 1)} or 1 − λ 2 ii with those of {2, (2, 2)}, but will not correlate with both. 14 Any nesting structure in the NL must partition C, ruling out correlation among at least some of the bundles with overlapping components (Song et al, 2017).…”

“…As a practical alternative, we propose the PONL model in which there is a nest for each product and every bundle belongs to as many nests as the different products it includes. In a standard nested logit model where each bundle only belongs to one nest, either all bundles have equally correlated preferences (a unique nest) or some of the bundles with overlapping products have uncorrelated preferences (more than one nest, Song et al, 2017). Differently, the PONL model allows for correlation in the unobserved preferences to depend on the degree of overlap in the composition of products between any two bundles.…”