Summary
This paper gives an overview to the state-of-art of applying control theory to the analysis of the dynamics of the firm. Three types of models are considered: one firm facing a certain environment, one firm facing a stochastic environment and with a risk of bankruptcy, and models of duopolies. In spite of the limits of these control theory models, they are useful to improve the understanding of important microeconomic phenomena and to explain to students or to junior managers how to combine policies through time to define an efficient strategy. An extended bibliography is given.
Zusammenfassung
Dieses Manuskript gibt einen Über-blick über den Stand der Forschung zur Anwendung der Kontrolltheorie bei der Analyse der Unternehmens-dynamik. Drei Modellarten werden betrachtet: ein Unternehmen in einer gewissen Umwelt, ein Unternehmen in einer stochastischen Umwelt mit der Möglichkeit des Bankrotts und Modelle, bei denen das Unternehmen in Konkurrenz zu einem anderen steht. Trotz der Grenzen dieser kontrolltheoretischen Modelle sind sie nützlich bei der Verbesserung des Verständnisses von bedeutenden mikroökonomischen Phänomena und wenn man Studenten oder Jungmanagern erklären will, wie man Politiken im Verlauf der Zeit kombiniert um eine wirksame Strategie zu entwickeln.
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References
Arrow KJ (1968) Optimal capital policy with irreversible investment. In: Wolfe J (ed) Value, capital and growth.Essays in honour of J. Hicks. Edinburgh University Press, Edinburgh, pp 1–19
Arrow KJ, Beckmann M, Karlin S (1958) The optimal expansion of the capacity of a firm. In: Studies in the mathematical theory of inventory and production. Stanford University Press, Stanford
Arrow KJ, Karlin S (1958) Smoothed production plans. In: Studies in the mathematical theory of inventory and production. Stanford University Press, Stanford
Bain J (1956) Barriers to new competition. Harvard University Press, Cambridge
Bensoussan A, Hurst G, Näslund B (1974) Management applications of modern control theory. North Holland, Amsterdam
Bensoussan A, Lesourne J (1980) Optimal growth of a self-financing firm in an uncertain environment. In: Applied stochastic control in econometrics and management science. North Holland, Amsterdam
Bensoussan A, Lesourne J (1982) Optimal growth of a firm facing a risk of bankruptcy. Infor Can J Oper (to appear in 1982)
Bensoussan A, Lesourne J (1981) Growth of firms: a stochastic control theory approach. In: Unternehmensplanung, Springer, Berlin Heidelberg New York
Brechling F (1975) Investment and employment decisions. Manchester University Press, Manchester
Case JH (1979) Economics and the competitive process. New York univ. press New York
Catinat M (1979) Stratégie optimale de stockage et d'investissement en avenir incertain. Ann INSEE, no 36:85–129
Deal KR (1975) Differential games solution to the problem of determining the optimal timing of advertising expenditures. Unpublished Ph.D. Dissertation, State University of New York at Buffalo, Buffalo
Deal KR (1979) Optimizing advertising expenditures in a dynamic duopoly. Oper Res 27:no4
Deal KR, Zionts S (1973) A differential games solution to the problem of determining the optimal timing of advertising expenditures. Proc. Second Annual Northeast Regional AIDS Conference (Kingston, RI, 1973) American Institute of Decision Sciences, Altanta, GA
Deal K, Sethi SP, Thompson G (1979) A bilinear-quadratic differential game in advertising. In: Liu PT, Sutinen JG (eds) Control theory in mathematical economics. Proc. of the Third Kingston Conference, Part B. Marcel Dekker, New York
Dehez P, Jacquemin A (1975) A note on advertising policy under uncertainty and dynamic conditions. J Ind Econ 24:73–78
Dorfman R, Steiner P (1954) Optimal advertising and optimal quality. Am Economic Rev 44:no 5
Eisner R, Strotz R (1963) Determinants of business investment. In: Commission on money and credit. Impacts of monetary policy. Prentice Hall, Englewood Cliffs, NJ, pp 59–337
Ekman E (1978) Some dynamic models of the firm. Stockholm, The Economic Research Institute at the Stockholm School of Economics, EFI
Feichtinger G (1980) Saddlepoint analysis in a price advertising model. Paper presented at the workshop on “The Dynamics of the Firm”, E.I.A.S.M., Brussels
Feichtinger G (1981) A differential game for market entrance. Technische Universität Wien. Paper presented at the DGOR Meeting, Göttingen
Gaskins D (1971) Dynamic limit pricing and optimal pricing under threat of entry. J Econ Theory 3:306–322
Gould JR (1968) Adjustment costs in the theory of investment of the firm. Rev Econ Studies 35:47–55
Gould JR (1970) Diffusion processes and optimal advertising policy in microeconomics foundations of employment and inflation theory. MacMillan, London
Hartmann R (1972) The effects of price and cost uncertainty on investment. J Econ Theory 5:258–266
Hochman E, Hochman O, Razin A (1973) Demand for investment in productive and financial capital. Eur Econ Rev 4:67–83
Horowitz I (1970) A note on advertising and uncertainty. J Ind Econ 18:151–160
Hughes W (1970) A theory of firm growth with applications to United States Oil Corporations. Unpublished D.B.A. Dissertation, Bloomington, Indiana University
Ireland N (1972) Concentration and the growth of market demand: A comment on Gaskins limit pricing model. J Econ Theory 5:303–305
Jacquemin A (1973) Optimal control theory and advertising policy. Metroeconomica 25:200–206
Jacquemin A (1975) Economie industrielle européenne. Dunod, Paris
Jacquemin A, Thisse J (1972) Recent applications of optimal control theory to industrial organizations. Working paper 7208, Université catholique de Louvain
Jacquemin A, Thisse J (1972) Strategy of the firm and market structure: an application of optimal control theory. In: Cowling K (ed) Market structure and corporate behaviour. Nijoss Leiden
Jorgenson DW (1963) Capital theory and investment behaviour. Am Econ Rev 53:247–259
Jorgenson DW, Stephenson JA (1969) Issues in the neoclassical theory of investment behaviour. Rev Econ Statistics 51:no 3
Jørgensen S (1980) A survey of some diffential games in advertising. Paper presented at the Workshop on the “Dynamics of the Firm”, E.I.A.S.M., Brussels
Jørgensen S (1980) A differential games solution to a logarithmic advertising model. Working paper, Copenhagen School of Economics and Business Administration
Kamien M, Schwartz N (1971) Limit pricing and uncertain entry. Econometrica 39:411–459
Kamien M, Schwartz N (1968) Optimal induced technical change. Econometrica, 36:1–17
Kamien M, Schwartz N (1974) Risky research and development with rivalry. Ann Econ Soc Meas 3:no 1
Kamien M, Schwartz N (1975) Market structure and innovation: a survey. J Econ Liter 13:1–37
Leban R (1982) Employment and wage strategies of the firm over a business cycle. J Econ Dyn Control (to appear in 1982)
Leban R, Lesourne J (1980) The investment and Employent policy of the firm through a business cycle. Eur Econ Rev 13:43–80
Leban R, Lesourne J (1982) Adaptive strategies of the firm through a business cycle. J Econ Dyn Control (to appear in 1982)
Leitmann G (1977) Many player differential games. In Hage-dorn P, Knobloch HW, Olsder GJ (eds) Differential games and applications. Proceedings of a Workshop, Enschede 1977. Lecture Notes in Control and Information Sciences, vol 3. Springer, Berlin Heidelberg New York
Leitmann G (1974) Cooperative and non-cooperative many players differential games. International Center for Mechanical Sciences, Udine. Courses and Lectures no 190. Springer, Berlin Heidelberg New York
Lesourne J (1973) Modèles de croissance des entreprises. Dunod, Paris
Lesourne J (1976) Optimal growth of the firm in a growing environment. J Econ Theory 13:118–138
Lesourne J, Leban R (1977) Business strategies in inflationary economies. Rev Econ Studies 44:265–285
Lesourne J, Leban R (1978) La substitution capital-travail au cours de la croissance de l'entreprise. Rev Econ Polit 4:540–564
Lesourne J, Domingues A (1981) Employment policy of a self-financing firm facing a risk of bankruptcy. Laboratoire d'Econométrie du CNAM. Working Paper no 20
Lieber Z (1971) Production over time with increasing marginal costs and linear holding costs. Center for Mathematical studies in Business and Economics, University of Chicago
Liedenpohja Y (1976) On optimal financing, dividends and investment of the firm. Helsinki School of Economics, Helsinki
Liedenpohja Y (1978) Taxes, dividends and capital gains in the adjustment cost model of the firm. Working paper, Vaasa School of Economics and Business Administration, Finland
Lintner J (1965) The valuation of risk assets and the selection of risky investments in stock portefolios and capital budgets. Rev Econ Stat 47:13–37
Lucas JR RE (1967) Adjustment costs and the theory of supply. J Polit Econ 75:321–334
Luptacik M (1980) Optimal price and advertising policy under atomistic competition. Paper presented at the Workshop on the Dynamics of the Firm, E.I.A.S.M., Brussels
Maccini LJ (1973) Delivery lags and the demand for investment. Rev Econ Studies 40:269–281
Magill MJP (1970) On a general economic theory of motion. Lecture Notes in Economics, vol 36. Springer Berlin Heidelberg New York
Marris R (1964) The economic theory of managerial capitalism. MacMillan, London
Martirena-Mantel A (1971) Optimal inventory and capital policy under certainty. J Econ Theory 3:241–253
Masse P (1962) Optimal investment decisions. Prentice Hall, NJ Englewood Cliffs
Miller M, Modigliani F (1961) Dividend policy, growth and the valuation of shares. J Business (Chicago) 34:44–133
Modigliani F (1958) New developments on the oligopoly front. J Polit Econ 66:215–232
Modigliani F, Miller M (1958) The cost of capital, corporation finance and the theory of investment. Am Econ Rev 48:261–297
Modigliani F, Miller M (1963) Corporate income taxes and the cost of capital: a correction. Am Econ Rev 53:439–443
Morland P (1978) Optimal firm behaviour under different fiscal regimes. Eur Econ Rev 11:37–58
Mortensen D (1973) Generalized costs of adjustment and dynamic factor demand theory. Econometrica 41:657–665
Mukundan R, Elsner WB (1975) Linear feedback strategies in non-zero-sum differential games. Int J Systems Sci 6:no 6
Näslund B, Sellstedt B (1972) Optimal marketing policy and life of products. European Institute of Advanced Studies in Management Working Paper 72-4
Nerlove M, Arrow K (1962) Optimal advertising policy under dynamic conditions. Economica 42:129–142
Nickell SJ (1978) The investment decisions of firms. Cambridge University Press, Oxford
Nickell SJ (1974) On the role of expectations in the pure theory of investment. Rev Econ Studies 41:1–20
Nickell SJ (1974) On expectations, government policy and the rate of investment. Economica 41:241–255
Nickell SJ (1975) A closer look at replacement investment. J Econ Theory 10:54–88
Nickell SJ (1977) Uncertainty and lags in the investment decisions of firms. Rev Econ Studies 44:249–263
Nickell SJ (1978) Fixed costs, employment and labour demand over the cycle. Economica 45:329–345
Olsder GJ (1976) Some thoughts about simple advertising models as differential games and the structure of coalitions. In: Ho YC, Mitter SK (eds) Directions in large-scale systems, many-person optimization and decentralized control. Plenum Press, New York
Ozga SA (1960) Imperfect market through lack of knowedge. Qu J Econ 74:29–52
Pashigian P (1968) Limit price and the market share of the leading firm. J Ind Econ (to appear)
Pekelman D (1972) Simultaneous price and production decision. Center for Mathematical Studies in Business and Economics, University of Chicago
Penrose E (1959) The theory of the growth of the firm. Wiley, New York
Phelps E, Winter S (1970) Optimal price policy under atomistic competition In: Microeconomic foundations of employment and inflation theory. MacMillan, London
Robichek A, Myers S (1965) Optimal financing decisions. Préntice Hall, Englewood Cliffs, NJ
Salop SC (1973) Wage differentials in a dynamic theory of the firm J Econ Theory 9:321–343
Sau RK (1979) The optimal rate of investment in a firm. J Finance 24:1–12
Schramm R (1970) The influence of relative prices, production conditions and adjustment costs on investment behaviour. Rev Econ Studies 37:361–376
Schramm R (1966) Optimal adjustment of factors of production and the study of investment behaviour. Carnegie Institute of Technology, Doctoral Dissertation
Schwartz N, Kamien M (1978) Self-financing a research and development project. Am Econ Rev 68:no 63
Sethi SP (1977) Optimal advertising for the Nerlove-Arrow model under a budget constraint. Oper Res Qu 28:683–693
Sethi JP, Lee SC (1979) Optimal advertising for the Nerlove-Arrow model under a replenishable budget. Wirking paper
Sethi SP (1975) Optimal control of a logarithmic advertising model. Oper Res Qu 26:317–321
Stevens GV (1974) On the impact of uncertainty on the value and investment of the neoclassical firm. Am Econ Rev 64:319–336
Stigler G (1961) The economics of informations J Polit Econ 69:213–225
Stiglitz JE (1969) A re-examination of Modigliani-Miller theorem. Am Econ Rev 59:784–793
Thepot J (1979) Politiques de prix et d'investissement d'un duopole en croissance. Working paper 79-42, E.I.A.S.M., Brussels
Thepot J (1981) Dynamic equilibrium of an advertising duopoly in a growing industry. Working paper 81-3, E.I.A.S.M., Brussels
Treadway AB (1970) Adjustment costs and variable inputs in theory of the competitive firm. J Econ Theory 1:329–347
Treadway AB (1969) On rational entrepreneurial behaviour and the demand for investment. Rev Econ Studies 36:227–239
Treadway AB (1967) Rational entrepreunerial behaviour and the dynamics of investment. University of Chicago, Doctoral Dissertation
Treadway AB (1971) The rational multivariate flexible accelerator. Econometrica 39:845–856
Van Loon P (1980) Employment in a monopolistic firm. Paper presented at the Workshop on “The Dynamics of the Firm”, E.I.A.S.M., Brussels
Vidale ML, Wolfe MB (1957) An operations research study of sales response to advertising. Oper Res 5:370–381
Wickens MR (1974) Towards a theory of the labour market. Economica 41:278–294
Wong RE (1975) Profit maximization and alternative theories: a dynamic reconciliation. Am Econ Rev 65:689–694
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Lesourne, J., Leban, R. Control theory and the dynamics of the firm. OR Spektrum 4, 1–14 (1982). https://doi.org/10.1007/BF01837019
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DOI: https://doi.org/10.1007/BF01837019