History-Based Versus Uniform Pricing in Growing and Declining Markets

Business Analytics using Dynamic Pricing based on Customer Entry-Exit Rates Tradeoff

“…The firms produce homogeneous services (or goods). Consumers gain utilityū from consumption, which means thatū is the maximum amount that they are willing to pay for the service [10]. The following rates are defined: (a) Consumers enter the market at a rate β ≥ 0 (entry rate).…”

“…This means that, in a period of length dt, new consumers buy βN (t)dt units (since there are βN (t)dt entering consumers during dt) and existing consumers buy N (t)dt units, whereas consumers who exit the market do not buy during the time interval dt. Thus, the proportion of products purchased by new consumers is [10]:…”

“…To ensure that the market is fully covered, we assume that the utility rateū is sufficiently high such that all consumers subscribe to the offered service (buy the offered goods). A sufficient condition for the market to be covered under the two pricing regimes to be analyzed (history based pricing and uniform pricing) [10]. Note that, we consider the rate of willingness to pay is bounded from below.…”

“…to their existing (locked-in) customers, and p N (σ L i ) to new customers. With history-based pricing, the unique model is given by (Shy, 2016):…”

“…An increased entry rate of consumers (higher β ) implies a reduced average price, meaning that an increased entry rate makes the investment effect stronger. On the other hand, a reduced β implies a higher average price as it makes the harvesting affect stronger [10].…”