Retail Price Optimization from Sparse Demand Data

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It will be shown how the retailer can use economic theory to exploit the sparse information available to him to set the price of each item he is selling close to its profit-maximizing level. The variability of the maximum price acceptable to each customer is modeled using a probability density for demand, which provides an alternative to the conventional demand curve often employed. This alternative way of interpreting retail demand data provides insights into the optimal price as a central measure of a demand distribution. Modeling individuals’ variability in their maximum acceptable price using a near-exhaustive set of “demand densities”, it will be established that the optimal price will be close both to the mean of the underlying demand density and to the mean of the Rectangular distribution fitted to the underlying distribution. An algorithm will then be derived that produces a near-optimal price, whatever the market conditions prevailing, monopoly, oligopoly, monopolistic competition or, in the limiting case, perfect competition, based on the minimum of market testing. The algorithm given for optimizing the retail price, even when demand data are sparse, is shown in worked examples to be accurate and thus of practical use to retail businesses.

References

[1] R. G. Lipsey and K. A. Chrystal, An Introduction to Positive Economics,” 8th Edition, Oxford University Press, Oxford, 1995.

[2] D. Begg, S. Fischer and R. Dornbusch, “Economics,” 3rd Edition, McGraw-Hill, London, 1991.

[3] G. F. Stanlake, “Introductory Economics,” 5th Edition, Longman, Harlow, Essex, 1989.

[4] Institute of Fiscal Studies (IFS), 2010.
http://www.ifs.org.uk/wheredoyoufitin/

[5] A. A. Cournot, “Recherches sur les Principes Mathématiques de la Richesse,” Chez L. Hachette, Paris, 1838.
http://books.google.co.uk/books?id=K2VHAAAAYAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&

[6] J. Bertrand, “Review of ‘Théorie Mathématique de la Richesse Sociale’ and ‘Recherches sur les Principes Mathématiques de la Richesse’,” Journal des Savants, 1883, pp. 499-508.

[7] R. L. Hall and C. J. Hitch, “Price Theory and Business Behaviour,” Oxford Economic Papers, No. 2, 1939, pp. 12-45.

[8] P. M. Sweezy, “Demand under Conditions of Oligopoly,” Journal of Political Economy, Vol. 47, No. 4, 1939, pp. 568-573. doi:10.1086/255420

[9] G. Stigler, “Kinky Oligopoly Demand and Rigid Prices,” Journal of Political Economy, Vol. 55, No. 5, 1947, pp. 432-449. doi:10.1086/256581