### Abstract

When launching a new product, a firm has to set an initial price with incomplete information about demand. However, after observing the demand over a period of time, the firm might decide to mark down the price, especially when the Bayesian updated belief about demand is lower than originally anticipated. We consider the case in which the manufacturer makes three decisions: initial price, when to mark down the price, and the markdown price. Modeling the cumulative demand as a Brownian motion with an unknown drift, we compute the posterior probability distribution of the unknown drift. We then show that it is optimal to mark down the price when the posterior probability is below a computable threshold. This threshold policy enables us to determine the optimal (a) regular price, (b) markdown price, and (c) markdown time. Additionally, we examine the impact of demand volatility and evaluate the value of learning.

Original language | English (US) |
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Pages (from-to) | 77-104 |

Number of pages | 28 |

Journal | Probability in the Engineering and Informational Sciences |

Volume | 26 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2012 |

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Management Science and Operations Research
- Industrial and Manufacturing Engineering

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## Cite this

*Probability in the Engineering and Informational Sciences*,

*26*(1), 77-104. https://doi.org/10.1017/S0269964811000246