How Prudence and Willingness-to-Pay Shape Price Trends in a Dynamic Pricing Model
Posted: 4 Nov 2012
Date Written: November 4, 2012
This paper studies a multi-stage dynamic pricing model, in which a state variable evolves as a stochastic process and affects customer demand at each stage. A firm has a limited amount of assets to sell and sets the price at each stage after observing the state variable. We find that besides the dynamics of customers' willingness-to-pay, the static form of the marginal revenue function plays an important role in influencing pricing behavior and price trends. Borrowing the concept of prudence from the precautionary saving literature, we show that a concave (convex, linear) marginal revenue function implies the firm's prudent (imprudent, prudent-neutral) pricing behavior and an upward (downward, flat) price trend. This new perspective connects revenue management with risk management. Logit and probit demand functions imply prudence, but iso-elastic and exponential demand functions imply prudence-neutrality. Gamma and Weibull distributions can imply either prudence or imprudence, depending on the shape parameter. The risk factor of prudence (imprudence) can be combined with the marketing factor of increasing (decreasing) customers' willingness-to-pay to produce an upward (downward) price trend over time.
Keywords: dynamic pricing, failure rates, martingales, prudence, risk management
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