Understanding Cost Pass-Through when Prices are Dispersed

There is limited theoretical understanding of cost pass-through within markets where prices are dispersed. Under a general demand function, we analyse the effects of cost changes in a seminal model of price dispersion, where some consumers are captive to particular sellers while others are not (Varian, 1980). To study pass-through in this mixed-strategy context, we employ a novel approach that links well to the pass-through literature in pure-strategy settings. Following an industry-wide cost increase, we show how the magnitudes of price rises faced by different consumer types, as well as the wider effects on price dispersion, depend upon whether demand is log-concave or log-convex. Furthermore, we examine whether the burden of the cost increase is expected to fall more heavily on captive or non-captive consumers. Finally, we show how our results vary with the level of competition and analyse the relationship between pass-through and demand shocks under price dispersion.