Optimal Pricing and Introduction Timing of Improving Technologies

Abstract

Many technologies improve over time and technology providers can provide increasingly powerful service upgrades to their customers, but at a launching cost, and the expense of the sales of existing products. We propose a model of technology introduction in the context of subscription-based services and characterize the optimal pricing and timing of technology introductions for a service provider, in the face of customers who are averse to switching to improved offerings. Overall, we show that a simple policy of Myerson (i.e., myopic) pricing and periodic introductions is approximately optimal. We first show that under a linear pricing rule, which subsumes Myerson pricing, there is no loss of optimality with a periodic schedule of introductions, and that under periodic introductions, the potential additional revenue of any pricing policy over Myerson pricing decays to zero after sufficiently many introductions. We then argue that Myerson pricing is approximately optimal under arbitrary introduction times. To do so, we first characterize prices that achieve optimal revenue in a single period, given arbitrary fixed introduction times. We then establish that Myerson pricing achieves a bounded bicriteria approximation ratio to both revenue and cost, for the infinite-horizon problem. Third, we provide analytical bounds for the approximation ratio in terms of the customer type distribution. Our bounds show that Myerson pricing is approximately optimal when switching costs for the customers who upgrade are small or large. Following our analysis, we examine our analytical bounds for Myerson pricing with simulations and show that, after sufficiently many introductions, they are tight for all values of the switching cost, for several natural distributions for the customer type. Furthermore, when we numerically compute optimal prices for fixed introduction times, rather than using our analytical bounds, we find that Myerson pricing is often several orders of magnitude closer to optimal revenue than our analytical bounds suggest. Our conclusions on the quality of Myerson pricing can robustly be carried over to realistic settings for the switching costs, the customer lifetime, and the frequency of technology introductions.