The value of information for price dependent demand

Predicting demand and determining optimal pricing are essential components of operations management. It is often useful to think in terms of the price elasticity of demand when reasoning about the demand curve. Firms wishing to invest in demand prediction and information gathering should reason about the relationship between the expected value of perfect information (EVPI) on demand and demand elasticity. Should firms pay more/less for information on demand if elasticity is high/low? Furthermore, when considering different product prices, correlation may exist between demand at different prices. Should firms pay more/less for information if the correlation between demand at different prices is high or low? This paper derives analytic and numeric results to answer these questions. We start with the assumption that demand is uncertain and follows a uniformly distributed band around a deterministic demand curve where the upper and lower bounds of the demand distribution vary with price. This formulation enables a closed form expression for EVPI that provides a useful benchmark. We find nuanced behavior of EVPI that depends on both the elasticity and the initial price preference. The EVPI approaches zero as elasticity increases (decreases) for a firm that initially prefers the low (high) price. Numerical results using the truncated normal and beta distributions relax assumptions about the uniform distribution and show EVPI is similar when the distribution variances are similar. Finally, we relax the assumption of perfect information and show the expected value of imperfect information (EVOI) follows similar patterns as EVPI with respect to demand elasticity.