Abstract
In this paper we will evaluate the significance of the inclusion of “dynamics” in profit maximization for widely used demand functions. Specifically we will consider both linear and log-linear demand models. Using these demand functions we will obtain closed form solutions for optimum prices (dynamic market inverse elasticity laws). The optimum price in a market governed by dynamic demand response is different from the one within a static response framework; we will relate the differences to specific characteristics of the demand function. One focus of this work will be to develop intuitive explanations for our conclusion regarding the relative size of the optimum price in static and dynamic markets.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz M, Stegun IA (1965) Handbook of mathematical functions. Dover, New York
Almon S (1965) The distributed lag between capital appropriation and net expenditures. Econometrica 33:178–196
Aminzadeh F (1987) Pricing policy in dynamic markets and a generalization of the Ramsey rule. ZOR-B 31:B1-B29
Aminzadeh F (1981) Optimum pricing policy for dynamic markets —I: monopoly case. IEEE CS-M 1/4:18–24
Aminzadeh F, Chikte SD (1986) Effects of regulatory delays and uncertainty on pricing decisions. ZOR 30:B65-B76
Aminzadeh F (1987) Parameter Identification of a linear dynamic model (a state space approach). ZOR-B 31
Elton EJ, Gruber MJ, Lieber Z (1975) Valuation, optimum investment and financing for the firm subject to regulation. The Journal of Finance 30/2:401–425
Franklin F (1885) Proof of a theorem of Tschebyscheff's on definite integrals. American Journal of Mathematics 7:377–379
Houthakker HS, Taylor LD (1970) Consumer demand in the United States, analysis and projections. Harvard University Press, Cambridge, Massachusetts
Koyck LM (1954) Distributed lags and investment analysis. North-Holland Publishing Company, Amsterdam
Leiderman L (1981) The demand for money under rational expectations of inflation. International Economic Review 22/3:679–681
Maddala GS (1977) Econometrics. McGraw-Hill Book Co, New York
Nahmias S (1979) Simple approximation for a variety of dynamic lead time lost-sales inventory models. Operations Research 27/5:904–924
Robinson B, Lakhani C (1975) Dynamic price models for new product planning. Management Science 21/10:1113–1117
Sakawa Y, Hashimoto Y (1978) Control of envirionmental pollution and economic growth modeling and numerical solution. Applied Mathematics and Optimization, vol 4, pp 385–400. Springer-Verlag, New York
Sims CA (1974) Distributed lags. In: Intrilgator MD, Kendrick D (eds) Frontiers in quantitative economics, vol II. North-Holland Publishing Co, pp 289–332
Solow RM (1960) On a family of lag distributions. Econometrica 28:393–406
Tang JT, Thompson GL (1983) Oligopoly models for optimal advertising when production costs obey a learning curve. Management Science 24/9:1087–1101
Taylor LD (1980) The demand for telephone service: A survey and critique of the literature. Ballinger, Cambridge, Massachusetts
Author information
Authors and Affiliations
Additional information
This work was completed when the author was with Bell Laboratories, USA.
Rights and permissions
About this article
Cite this article
Aminzadeh, F. Application of a dynamic market inverse elasticity law with linear and log-linear demand models. Zeitschrift für Operations Research 31, B173–B191 (1987). https://doi.org/10.1007/BF01258648
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01258648