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A controlled birth and death process model of optimal product pricing under stochastically changing demand

Published online by Cambridge University Press:  14 July 2016

S. D. Deshmukh  and
Wayne Winston
S. D. Deshmukh
Affiliation:
Northwestern University, Evanston, Illinois
Wayne Winston
Affiliation:
Indiana University
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Abstract

We consider the problem of product pricing when the firm's market share is changing stochastically according to a birth and death process. The current market share together with the price prevailing determine the current rate of profit made as well as the birth and death rates. The optimal pricing policy must balance the immediate advantage of setting a high price in terms of increased current profit against the disadvantage in terms of a possible erosion of the future market share. We formulate a continuous-time Markov decision model and analyse it using a recent technique developed by Lippman [6] for optimization of exponential queueing systems. The optimal pricing policy is characterized as having a sort of monotonicity property. We also analyse the dependence of the optimal policy on the problem parameters and indicate further extensions of the model.

Keywords

BIRTH AND DEATH PROCESSQUEUE CONTROLOPTIMAL PRICING STRATEGYDYNAMIC PROGRAMMING
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 328 - 339
Copyright
Copyright © Applied Probability Trust 1977 

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References

[1] Baron, D. P. (1971) Demand uncertainty in imperfect competition. Internat. Econom. Rev. 12, 196–208.CrossRefGoogle Scholar
[2] Deshmukh, S. D. and Chikte, S. D. (1976) Dynamic pricing with stochastic entry. Rev. Econom. Studies. 43, 91–97.Google Scholar
[3] Deshmukh, S. D. and Winston, W. (1976) Stochastic Control of Competition Through Prices. Discussion paper 205, Center for Mathematical Studies in Economics and Management Science, Northwestern University, Evanston, I11.Google Scholar
[4] Leland, H. E. (1972) Theory of firm facing uncertain demand. Amer. Econom. Rev. 62, 278–291.Google Scholar
[5] Lippman, S. A. (1973) Semi-Markov decision processes with unbounded rewards. Management Sci. 19, 717–730.CrossRefGoogle Scholar
[6] Lippman, S. A. (1975) Applying a new device in the optimization of exponential queueing systems. Opns. Res. 23, 687–710.CrossRefGoogle Scholar
[7] Lippman, S. A. (1976) Countable state continuous time dynamic programming with structure. Opns. Res. 24, 447–490.Google Scholar
[8] Nerlove, M. and Arrow, K. J. (1962) Optimal advertising policy under dynamic conditions. Economica 29, 129–142.CrossRefGoogle Scholar
[9] Sasieni, M. W. (1971) Optimal advertising expenditure. Management Sci. 18, P64–P72.Google Scholar
[10] Sengupta, S. S. (1967) Operations Research in Sellers' Competition: A Stochastic Microtheory. Wiley, New York.Google Scholar
[11] Sethi, S. P. (1973) Optimal control of the Vidale–Wolfe advertising model. Opns. Res. 21, 998–1013.Google Scholar
[12] Shapley, L. (1953) Stochastic games. Proc. Nat. Acad. Sci. U.S.A. 39, 1095–1100.Google Scholar
[13] Thomas, J. (1970) Price-production decisions with deterministic demand. Management Sci. 12, 747–750.Google Scholar
[14] Wagner, H. (1960) A postcript to ‘dynamic problems in the theory of the firm’. Naval Res. Logist. Quart. 7, 7–12.CrossRefGoogle Scholar
[15] Wagner, H. and Whitin, T. (1958) Dynamic problems in the theory of the firm. Naval Res. Logist. Quart. 5, 53–74.Google Scholar
[16] Wan, H. Y. (1966) Intertemporal optimization with systematically shifting cost and revenue functions. Internat. Econom. Rev. 7, 204–225.Google Scholar