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Dynamic Pricing of Information Goods under Demand Uncertainty Eric Cope The Sauder School of Business University of British Columbia Understanding demand response to price can be critical to effective pricing Retailer profits can be highly sensitive to price “For a company with average economics, … a 1% improvement in price, assuming no loss of volume, increases operating profit by 11%. Improvements in price typically have three to four times the effect on profitability as proportionate increases in volume.” (Marn and Rosiello, 1992) Customers’ price sensitivity is key to effective pricing The Internet makes it easier for retailers to assess customers’ price sensitivity Price sensitivity research has been difficult to conduct effectively Expensive Time-consuming Fear of alienating customers Difficult to assess customer base in advance Price tests can be performed in e-commerce channels Prices can be adjusted quickly and cheaply Price information can be carefully controlled Customer behavior can be tracked As we previously mentioned, since the prior is not conjugate to the sales data, it can be hard to compute posteriors. We introduce a set of exact and approximate methods. These methods are appropriate in situations where we have more or fewer customer arrivals per time period, i.e., more or fewer data. If only a few customers arrive per period, we’ve derived exact analytical formulas that can be applied. These formulas show that the posterior marginal demand distributions are mixtures of Dirichlet distributions. However, the mixture weights can be hard to compute for even moderate amounts of data. When the numbers of customers arriving per period number are moderate (numbering in the 100’s, say), it is possible to use a MCMC / Gibbs sampling method to approximate the posteriors. One such method was derived by Kuo and Smith in 1992. When the numbers of customers arriving per period number are large (numbering in the 1000’s, say), it bec
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