When does tiered wholesale pricing create an incentive to reduce retail prices?

Wholesale ‘ladder pricing’ involves setting the wholesale price retailers face as a nonlinear (generally increasing) function of price chosen by retailers. This form of wholesale pricing occurred recently in UK Telecoms, and the issue became extensively debated in the law courts. A major concern in deciding the merits of the case lay with the question of whether or not the introduction of tiered wholesale pricing created incentives for retailers to actually reduce their prices. This paper examines the incentive for the case where the wholesale tariff is a non-linear continuous differentiable function. It is shown that so long as the tariff is strictly increasing, convex, and positive only for retail prices greater than the maximum retailer marginal cost, then there is indeed an incentive to reduce price, whatever the actual gradient of the tariff schedule.