Inverse demand function

Abstract: We consider a single product revenue management problem where, given an initial inventory, the objective is to dynamically adjust prices over a finite sales horizon to maximize expected revenues. Realized demand is observed over time, but the underlying functional relationship between price and mean demand rate that governs these observations (otherwise known as the demand function or demand curve), is not known. We consider two instances of this problem: i.) a setting where the demand function is assumed to belong to a known parametric family with unknown parameter values; and ii.) a setting where the demand function is assumed to belong to a broad class of functions that need not admit any parametric representation. In each case we develop policies that learn the demand function "on the fly," and optimize prices based on that. The performance of these algorithms is measured in terms of the regret: the revenue loss relative to the maximal revenues that can be extracted when the demand function is known prior to the start of the selling season. We derive lower bounds on the regret that hold for any admissible pricing policy, and then show that our proposed algorithms achieve a regret that is "close" to this lower bound. The magnitude of the regret can be interpreted as the economic value of prior knowledge on the demand function; manifested as the revenue loss due to model uncertainty.

Abstract: This paper provides a review of the theoretical basis and the assumptions required in order to use hedonic price equations derived from property value data to obtain measures of the prices and the inverse demand functions for environmental amenities such as air quality. It also includes a review and assessment of existing empirical applications of the technique to problems of air and water quality and urban noise.

Abstract: This paper presents a general analysis of the eects of monopolistic third- degree price discrimination on welfare and output when all markets are served Su¢ cient conditions -involving straightforward comparisons of the curvatures of the direct and inverse demand functions in the dierent mar- kets -are presented for discrimination to have negative or positive eects on

Abstract: In this study, we use a game-theory-based framework to model power in a supply chain with random and price-dependent demand and examine how power structure and demand models (expected demand and demand shock) affect supply chain members' performance. We demonstrate that whether a firm benefits from its power depends on the expected demand model but not on demand shock model. A firm benefits from its power only for linear but not for constant elasticity expected demand. The impact of power structure on supply chain efficiency depends on the models of both expected demand and demand shock. With additive shock, supply chain efficiency is highest (lowest) when neither firm dominates for linear (constant elasticity) expected demand. With multiplicative shock, the supply chain efficiency is highest with a power retailer (manufacturer) for linear (constant elasticity) expected demand. The manufacturer always benefits from a reduction in demand uncertainty. However, the retailer loses (benefits) from demand uncertainty reduction for linear (constant elasticity) expected demand. With a power retailer, the retail price is always on the higher end for linear expected demand, and the customer service level is the lowest for constant elasticity expected demand. Consequently, consumers do not necessarily benefit from a power retailer.