Optimal Pricing of Nondurables when Demand is Dynamic and Stochastic

Abstract This paper derives optimal pricing strategies for nondurables if demand is sluggish and stochastic. The puzzling result is that moving from a static demand to a dynamic relation alters the marketing strategy dramatically if the equilibrium demand is convex (in price): the profit maximizing price policy is to switch between a low and a high price depending on current demand while a continuous price policy is optimal for concave demand relations. However, the formal existence of such a price switching policy is restricted to the anyway more realistic stochastic version of the model. The clear cut implications of the model provide also a criterion to test empirically the characteristics and the optimality of actual price strategies.

[1]  D. Kahneman.  A Psychological Perspective on Economics , 2003 .

[2]  Barry Alan Pasternack,et al.  Optimal Pricing and Return Policies for Perishable Commodities , 2008, Mark. Sci..

[3]  M. Petit.  Dynamic optimization. The calculus of variations and optimal control in economics and management : by Morton I. Kamien and Nancy L. Schwartz. Second Edition. North-Holland (Advanced Textbooks in Economics), Amsterdam and New York, 1991. Pp. xvii+377. ISBN0-444- 01609-0 , 1994 .

[4]  M. Abramowitz,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[5]  Saroja Subrahmanyan,et al.  Developing optimal pricing and inventory policies for retailers who face uncertain demand , 1996 .

[6]  Mark J. Zbaracki,et al.  Managerial and Customer Costs of Price Adjustment: Direct Evidence from Industrial Markets , 2004 .

[7]  R. Hartl,et al.  Dynamic Optimal Control Models in Advertising: Recent Developments , 1994 .

[8]  Gopal Das Varma,et al.  Optimal dynamic pricing with inventories , 2001 .

[9]  H. Dai,et al.  Handbook of Mathematical Formulas and Integrals 4th edition , 2008 .

[10]  David F. Pyke,et al.  A Dynamic Pricing Model for Coordinated Sales and Operations , 2005 .

[11]  B. Dumas.  Super contact and related optimality conditions , 1991 .

[12]  Economics of (oil) price politics: Penalizing price changes , 1991 .

[13]  R. Vidal.  Dynamic optimization: The calculus of variations and optimal control in economics and management: Morton I. KAMIEN and Nancy L. SCHWARTZ Volume 4 in: Dynamic Economics: Theory and Applications, North-Holland, New York, 1981, xi + 331 pages, Dfl.90.00 , 1982 .

[14]  Matthias Koenig,et al.  List pricing versus dynamic pricing: Impact on the revenue risk , 2010, Eur. J. Oper. Res..

[15]  Eyal Biyalogorsky,et al.  Customer Referral Management: Optimal Reward Programs , 2000 .

[16]  A. Macdonald,et al.  Properties of the confluent hypergeometric function , 1949 .

[17]  Nicholas Economides,et al.  The Microsoft Antitrust Case , 2001 .

[18]  M. Spence,et al.  Learning Curve Spillovers and Market Performance , 1985 .

[19]  Franz Wirl.  Reversible stopping (“switching”) implies super contact , 2008, Comput. Manag. Sci..

[20]  D. Read,et al.  Predicting Hunger: The Effects of Appetite and Delay on Choice. , 1998, Organizational behavior and human decision processes.

[21]  Scott A. Neslin,et al.  The Determinants of Pre- and Postpromotion Dips in Sales of Frequently Purchased Goods , 2004 .

[22]  H. Huntington,et al.  Price and Income Responsiveness of World Oil Demand, by Product , 2007 .

[23]  R. Easterlin.  Income and Happiness: Towards a Unified Theory , 2001 .

[24]  G. Loewenstein,et al.  Projection Bias in Predicting Future Utility , 2000 .

[25]  R. Pindyck.  Gains to producers from the cartelization of exhaustible resources , 1978 .

[26]  Eduardo S. Schwartz,et al.  Investment Under Uncertainty. , 1994 .

[27]  Paul L. Fackler,et al.  Applied Computational Economics and Finance , 2002 .

[28]  M. Adelman.  The 1990 Oil Shock is Like the Others 1 , 1990 .

[29]  B. Bayus.  The Dynamic Pricing of Next Generation Consumer Durables , 1992 .

[30]  Daniel Gilbert,et al.  Stumbling on Happiness , 2015 .

[31]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[32]  Thomas J. Richardson,et al.  Monopolists and Viscous Demand , 2003, Games Econ. Behav..

[33]  S. Sethi,et al.  A survey of Stackelberg differential game models in supply and marketing channels , 2007 .

[34]  S. Kalish.  Monopolist Pricing with Dynamic Demand and Production Cost , 1983 .

[35]  Dominique M. Hanssens,et al.  The Long-Term Effects of Price Promotions on Category Incidence, Brand Choice, and Purchase Quantity , 2002 .

[36]  R. Pindyck.  The Structure of World Energy Demand , 1979 .

[37]  Dynamic demand and noncompetitive pricing strategies , 1991 .

[38]  K. Arrow.  The Economic Implications of Learning by Doing , 1962 .

[39]  Alan Jeffrey,et al.  Handbook of mathematical formulas and integrals , 1995 .