Monopolist optimum pricing and advertising policies for diffusion models of new product innovations

Optimal Control Applications and Methods

Volumn 19, Issue 2, 1998, Pages 111-136

  Mesak, Hani I ^a   Clark, James W ^b  

^a LOUISIANA TECH UNIVERSITY   (United States)

^b NORTHEASTERN STATE UNIVERSITY   (United States)

Author keywords

Diffusion models of innovation; Non linear least squares; Optimal advertising; Optimal price; Pontryagin's maximum principle

Indexed keywords

LEAST SQUARES APPROXIMATIONS; MARKETING; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

PONTRYAGIN'S MAXIMUM PRINCIPLE;

OPTIMAL CONTROL SYSTEMS;

EID: 0032028672     PISSN: 01432087     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1099-1514(199803/04)19:2<111::aid-oca622>3.0.co;2-m     Document Type: Article

References (85)

1. Bass, F. M., 'A new product growth model for consumer durables', Management Sci., 15, 215-227 (1969).
2. Mahajan, V., E. Muller and F. M. Bass, 'New product diffusion models in marketing: a review and directions for research', J. Marketing, 54, 1-26 (1990).
3. Gatignon, H. and T. S. Robertson, 'A propositional inventory for new diffusion research', J. Consumer Res., 11, 859-867 (1985).
4. Mahajan, V. and R. A. Peterson, Models for Innovation Diffusion, Sage, Beverly Hills, CA, 1985.
5. Kalish, S. and S. K. Sen, 'Diffusion models and the marketing mix for single products', in Mahajan, V. and Y. Wind (eds), Innovation Diffusion Models of New Product Acceptance, Ballinger, Cambridge, MA, 1986, pp. 87-115.
6. Dockner, E., G. Feichtinger and G. Sorger, 'Interaction of pricing and advertising under dynamic conditions', in DGOR Operations Research Proceedings, Springer, Berlin, 1989, pp. 547-554.
7. Robinson, B. and C. Lakhani, 'Dynamic price models for new product planning', Management Sci., 10, 1113-1122 (1975).
8. Dolan, R. J. and A. P. Jeuland, 'Experience curves and dynamic demand models: implications for optimal pricing strategies', J. Marketing, 45, 52-62 (1981).
9. Clarke, F. H., M. N. Darrough and J. Heineke, 'Optimal pricing strategies policy in the presence of experience effects', J. Business, 55, 517-530 (1982).
10. Kalish, S., 'Monopolist pricing with dynamic demand and production cost', Marketing Sci., 31, 1569-1585 (1983).
11. Feichtinger, G., 'Saddle point analysis in a price-advertising model', J. Economic Dyn. Control, 4, 319-340 (1982).
12. Jørgensen, S., 'Optimal control of a diffusion model of new product acceptance with price-dependent total market potential', Opt. Control Appl. Meth., 4, 269-276 (1983).
13. Jeuland, A. P. and R. J. Dolan, 'An aspect of new product planning: dynamic pricing', in Zoltners, A. (ed.), TIMS Studies in the Management Sciences, Special Issue on Marketing Planning Models, 1982, pp. 1-21.
14. Parker, P. M., 'Price elasticity dynamics over the adoption life cycle', J. Marketing Res., 24, 358-367 (1992).
15. Kamakura, W. and S. K. Balasubramanian, 'Long-term view of the diffusion of durables', Int. J. Res. Marketing, 5(1), 1-13 (1988).
16. Jain, D. C. and R. C. Rao, 'Effect of price on the demand for durables: modeling, estimation and findings', J. Business Economic Statist., 8, 163-170 (1990).
17. Chow, G. C., 'Technological change and the demand for computers', Amer. Economic Rev., 1117-1130 (1967).
18. Horsky, D., 'A diffusion model incorporating product benefits, price, income, and information', Marketing Sci., 9, 342-365 (1990).
19. Dodson, J. A. and E. Muller, 'Models of new product diffusion through advertising and words of mouth', Management Sci., 24, 1568-1578 (1978).
20. Horsky, D. and L. S. Simon, 'Advertising and the diffusion of new products', Marketing Sci., 1, 1-18 (1983).
21. Ozga, S. A., 'Imperfect markets through lack of knowledge', Quart. J. Economics, 74, 29-52 (1960).
22. Stigler, G., 'The economics of information', J. Political Economics, 69, 213-225 (1961).
23. Dockner, E. and S. Jørgensen, 'Optimal advertising policies for diffusion models of new product innovations in monopolistic situations', Management Sci., 34, 119-130 (1988a).
24. Simon, H. and K. H. Sebastian, 'Diffusion and advertising: the German telephone company', Management Sci., 33, 451-466 (1987).
25. Nerlove, K. and K. J. Arrow, 'Optimal advertising policy under dynamic conditions', Economica, 39, 129-142 (1962).
26. Spremann, K., 'Hybrid product life cycles and the Nerlove-Arrow theorem', Working Paper, Abt. Wirtschaftswessenschagten, Universitat Ulm. D-7900 Ulm, Federal Republic of Germany, 1981.
27. Thompson, G. L. and J. T. Teng, 'Optimal pricing and advertising policies for new product oligopoly models', Marketing Sci., 3, 148-168 (1984).
28. Teng, J. T. and G. L. Thompson, 'Optimal strategies for general price-advertising models', in Feichtinger, G. (ed.), Optimal Control Theory and Economic Analysis 2. Elsevier, North Holland, 1985, pp. 183-195.
29. Kalish, S., 'A new product adoption model with pricing, advertising and uncertainty', Management Sci., 31, 1569-1585 (1985).
30. Bass, F. M., T. V. Krishnan and D. C. Jain, 'Why the Bass model fits without decision variables', Marketing Sci., 13, 203-223 (1994).
31. Feichtinger, G., R. F. Hartl and S. P. Sethi, 'Dynamic optimal control models in advertising: recent development', Management Sci., 40(2), 195-226 (1994).
32. Feichtinger, G. and R. Hartl, 'Optimal pricing and production in an inventory model', European J. Oper. Res., 19, 45-56 (1985).
33. Bass, F. M., 'The relationship between diffusion rates, experience curves, and demand elasticities for consumer durable technological innovations', J. Business, 53, S51-S67 (1980).
34. Kalish, S. and G. L. Lilien, 'Optimal price subsidy policy for accelerating the diffusion of innovation', Marketing Sci., 2, 407-420 (1983).
35. Mesak, H. I., 'Impact of anticipated competitive entry and cost experience on optimal strategic pricing of technological innovations', Comput. Oper. Res., 17(1), 27-37 (1990).
36. Jørgensen, S. and G. Zaccour, 'Optimal production, inventory and pricing with cost and demand learning effects', Working paper, Dept. of Management, Odense University, 1996.
37. Dockner, E. and S. Jørgensen, 'Optimal pricing strategies for new products in dynamic oligopolies', Marketing Sci., 7, 251-334 (1988b).
38. Piconni, M. J. and C. L. Olson, 'Advertising decision rules in a multibrand environment: optimal control theory and evidence', J. Marketing Res., 15, 82-92 (1979).
39. Pontryagin, L. D., The Mathematical Theory of Optimal Processes, Interscience, New York, 1962.
40. Sethi, S. P. and G. L. Thompson, Optimal Control Theory: Applications to Management Science, Martinus Nijhoff, Boston, MA, 1981.
41. Mangasarian, O. L., 'Sufficient conditions for the optimal control of nonlinear systems', J. SIAM Control, 4, (1966).
42. Arrow, K. J. and M. Kurz, Public Investment, the Rate of Return, and Optimal Fiscal Policy, John Hopkins, Baltimore, 1970.
43. Kamien, M. I. and N. L. Schwartz, Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management, North-Holland, New York, 1981.
44. Glaister, S., Mathematical Models for Economists, Basil Black well, New York, 1984.
45. Schmalensee, R., The Economics of Advertising, North-Holland, Amsterdam, 1972.
46. Feichtinger, G. and R. F. Hartl, Optimale Kontralle Oekonomischer Prozesse, deGruyter, Berlin, 1986.
47. Dorfman, R. and P. O. Steiner, 'Optimal advertising and optimal quality', Amer. Economic Rev., 4, 826-836 (1954).
48. Jain, D., 'Marketing mix effects on the diffusion of innovations', Working Paper, Northwestern University, Kellogg Graduate School of Management, 1992.
49. Parsons, L. and R. L. Schultz, Marketing Models and Econometric Research, North-Holland, New York, NY, 1976.
50. Naert, P. and P. Leeflang, Building Implementable Marketing Models, Martinus Nijhoff, Boston, MA, 1978.
51. Lilien, G. L. and P. Kotler, Marketing Decision Making, Harper and Row, New York, 1983.
52. Mahajan, V., E. Muller and R. A. Kerin, 'Introduction strategy for new products with positive and negative word-of-mouth', Management Sci., 30, 1389-1404 (1984).
53. Easingwood, C., V. Mahajan and E. Muller, 'A nonsymmetric responding logistic model for technological substitution', Technol. Forecasting Social Change, 20, 199-213 (1981).
54. Easingwood, C., V. Mahajan and E. Muller, 'A non-uniform influence innovation diffusion model of new product acceptance', Marketing Sci., 2, 273-296 (1983).
55. Dockner, E. and S. Jørgensen, 'New Product Advertising in Dynamic Oligopolies', ZOR-Methods and Models of Operations Research, 36, 459-473, 1992.
56. Bass, F. M. and A. V. Bultez, 'A note on optimal strategic pricing of technological innovations', Marketing Sci., 1, 371-378 (1982).
57. Moorthy, K. S., 'Theoretical modelling in marketing', J. Marketing, 57, 92-106 (1993).
58. Sorger, G., 'Competitive dynamic advertising: a modification of the case game', J. Economic Dyn. Control, 13, 55-80 (1989).
59. Chintagunta, P. K. and N. J. Vilcassim, 'An empirical investigation of advertising strategies in a dynamic duopoly', Management Sci., 38(9), 1230-1244 (1992).
60. Chintagunta, P. K., 'Investigating the sensitivity of equilibrium profits to advertising dynamics and competitive effects', Management Sci., 39(9), 1146-1162 (1993).
61. SAS Institute, SAS/ETS User's Guide, Version 5 Edition, SAS Institute, Cary, NC, 1984.
62. Sultan, F., J. V. Farely and D. R. Lehmann, 'A meta-analysis of diffusion models', J. Marketing Res., 27, 70-77 (1990).
63. Srinivasan, V. and C. H. Mason, 'Nonlinear least squares estimation of new product diffusion models', Marketing Sci., 5, 169-178 (1986).
64. Holak, S. L. and S. K. Reddy, 'Effects of television and radio advertising ban: a study of the cigarette industry', J. Marketing, 50, 219-227 (1986).
65. Balasubramanian, S. K. and D. C. Jain, 'Simple approaches to evaluate competing non-nested models in marketing', Int. J. Res. Marketing, 11(1), 53-72 (1994).
66. Takada, H. and D. Jain, 'Cross-national analysis of diffusion of consumer durable goods in Pacific Rim Countries', J. Marketing, 55, 48-54 (1991).
67. Parsons, L. J., 'The product life cycle and time-varying advertising elasticities', J. Marketing Res., 9, 476-480 (1975).
68. Arora, R., 'How promotion elasticities change', J. Advertising Res., 19, 57-62 (1979).
69. Tellis, G. J., 'The price elasticity of selective demand: a meta-analysis of econometric analysis of sales', J. Marketing Res., 25, 331-341 (1988).
70. Jones, J. M. and C. J. Ritz, 'Incorporating distribution into new product diffusion models', Int. J. Res. Marketing, 8, 91-112 (1991).
71. Narasimhan, R., S. Ghosh and D. Mendez, 'A dynamic model of product quality and pricing decisions on sales response', Decision Sci., 24(5), 893-908 (1993).
72. Menezes, M. A. J. and I. S. Currim, 'Approach for determination of warranty length', Int. J. Res. Marketing, 9, 177-195 (1992).
73. Lilien, G. L., A. G. Rao and S. Kalish, 'Bayesian estimation and control of detailing effort in a repeat purchase environment', Management Sci., 27(5), 493-507 (1981).
74. Dockner, E. and G. Feichtinger, 'Dynamic advertising and pricing in an oligopoly: a Nash equilibrium approach', in Basar, T. (ed.), Dynamic Games and Applications in Economics, Lecture Notes in Economics and Mathematical Systems, vol. 265, Springer, Berlin, 1986, pp. 238-251.
75. Olson, J. A. and S. Choi, 'A product diffusion model incorporating repeat purchases', Technol. Forecasting Social Change, 27, 385-397 (1985).
76. Bayus, B., 'Accelerating the durable replacement cycle with marketing mix variables', J. Product Innovation Management, 5, 216-226 (1988).
77. Mesak, H. I. and W. D. Berg, 'Incorporating price and replacement purchases in new product diffusion models for consumer durables', Decision Sci., 26(4), 425-449 (1995).
78. Erickson, G. M., 'A model of advertising competition', J. Marketing Res., 22, 297-304 (1985).
79. Erickson, G. M., Dynamic Models of Advertising Competition, Kluwer, Boston, 1991.
80. Rao, R. C. and F. M. Bass, 'Competition, strategy, and price dynamics: a theoretical and empirical investigation', J. Marketing Res., 22, 283-296 (1985).
81. Eliashberg, E. and A. P. Jeuland, 'The impact of competitive entry in developing market upon dynamic pricing strategies', Marketing Sci., 5, 20-36 (1986).
82. Parker, P. M. and H. Gatignon, 'Specifying competitive effects in diffusion models: an empirical analysis', Int. J. Res. Marketing 11, 17-39 (1994).
83. Horsky, D. and K. Mate, 'Dynamic advertising strategies of competing durable good producers', Marketing Sci., 7, 356-367 (1988).
84. Eliashberg, E. and R. Chatterjee, 'Stochastic issues in innovation diffusion models', in Mahajan, V. and Y. Wind (eds), Innovation Diffusion Models of New Product Acceptance, Ballinger, Cambridge, MA, 1986, pp. 151-199.
85. Chen, Y. M. and D. C. Jain, 'Dynamic monopoly pricing under a Poisson-type uncertain demand', J. Business, 65(4), 593-616 (1992).