IDEAS home Printed from https://ideas.repec.org/p/sce/scecf4/100.html
   My bibliography  Save this paper

Optimal marketing decisions in a micro-level framework

Author

Listed:
  • Luigi De Cesare
  • Andrea Di Liddo

Abstract

A number of continuous models to explain the influence of some parameters (e.g. advertising) on the diffusion of an innovation have been proposed since the seminal paper by Bass (1969). Only some recent papers deal with both spatial and temporal features as, i.e., De Cesare et al. (2003). There the dynamic of the adopters is described by a nonlinear partial integro-differential equation. In this paper a different approach is performed. A micro-level stochastic model is built up to follow the individual paths of the potential and actual adopters. At first the influence of the information about the innovation given by local interactions is suitably treated. This leads to a Markov process describing the dynamic of adopters. Some convergence results to the continuous related models are proved. The way how marketing mix variables (advertising, prices, ...) affect the diffusion process is investigated by incorporating related parameters. Furthermore some optimal control problems are stated in order to compute the optimal marketing decision variables for a monopolistic firm's maximization profits. Here the expected value of the adopters represents the state variable whose dynamics is given through the Markov process introduced above. Due to the nonconvexity of the objective functional, random search algorithms are more appropriate because they impose few restrictions. Special attention is paid to compare the performances of simulated annealing scheme and genetic algorithms

Suggested Citation

  • Luigi De Cesare & Andrea Di Liddo, 2004. "Optimal marketing decisions in a micro-level framework," Computing in Economics and Finance 2004 100, Society for Computational Economics.
  • Handle: RePEc:sce:scecf4:100
    as

    Download full text from publisher

    File URL: http://web.tiscali.it/decesare/De_Cesare-Di_Liddo.pdf
    File Function: main text
    Download Restriction: no

    References listed on IDEAS

    as
    1. Evans, George W. & Honkapohja, Seppo, 1996. "Least squares learning with heterogeneous expectations," Economics Letters, Elsevier, vol. 53(2), pages 197-201, November.
    2. Bennett T. McCallum, 2002. "Consistent Expectations, Rational Expectations, Multiple-Solution Indeterminacies, and Least-Squares Learnability," NBER Working Papers 9218, National Bureau of Economic Research, Inc.
    3. Thomas J. Sargent, 1973. "Rational Expectations, the Real Rate of Interest, and the Natural Rate of Unemployment," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 4(2), pages 429-480.
    4. Chryssi Giannitsarou, 2003. "Heterogeneous Learning," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 885-906, October.
    5. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    6. Guse, Eran A., 2005. "Stability properties for learning with heterogeneous expectations and multiple equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1623-1642, October.
    7. Ramon Marimon & Ellen McGrattan, 1993. "On adaptive learning in strategic games," Economics Working Papers 24, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, January.
    9. Seppo Honkapohja & Kaushik Mitra, 2006. "Learning Stability in Economies with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 284-309, April.
    10. Sethi, Rajiv & Franke, Reiner, 1995. "Behavioural Heterogeneity under Evolutionary Pressure: Macroeconomic Implications of Costly Optimisation," Economic Journal, Royal Economic Society, vol. 105(430), pages 583-600, May.
    11. Branch, William A., 2002. "Local convergence properties of a cobweb model with rationally heterogeneous expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 63-85, November.
    12. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    13. Sethi, Rajiv, 1996. "Endogenous regime switching in speculative markets," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 99-118, March.
    14. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
    15. Evans, George W. & Honkapohja, Seppo & Marimon, Ramon, 2001. "Convergence In Monetary Inflation Models With Heterogeneous Learning Rules," Macroeconomic Dynamics, Cambridge University Press, vol. 5(01), pages 1-31, February.
    16. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
    17. Lucas, Robert E, Jr, 1973. "Some International Evidence on Output-Inflation Tradeoffs," American Economic Review, American Economic Association, vol. 63(3), pages 326-334, June.
    18. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    19. repec:cup:macdyn:v:2:y:1998:i:3:p:287-321 is not listed on IDEAS
    20. Evans, George W & Ramey, Garey, 1992. "Expectation Calculation and Macroeconomic Dynamics," American Economic Review, American Economic Association, vol. 82(1), pages 207-224, March.
    21. Hommes, Cars & Sorger, Gerhard, 1998. "Consistent Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 2(03), pages 287-321, September.
    22. Taylor, John B, 1977. "Conditions for Unique Solutions in Stochastic Macroeconomic Models with Rational Expectations," Econometrica, Econometric Society, vol. 45(6), pages 1377-1385, September.
    23. Branch William & McGough Bruce, 2004. "Multiple Equilibria in Heterogeneous Expectations Models," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-16, December.
    24. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    25. Heinemann, Maik, 2000. "Convergence Of Adaptive Learning And Expectational Stability: The Case Of Multiple Rational-Expectations Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 4(03), pages 263-288, September.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Marketing models; Optimal control; Innovation diffusion; Micro-level models; Random search algorithms;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sce:scecf4:100. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/sceeeea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.