On the control of a dynamical system defined by a decreasing one-dimensional set-valued function

Document Type : Original Article


1 Department of Industrial Engineering, Eastern Mediterranean University, Famagusta, Mersin 10, Turkey

2 Department of Economics, Edutus College, Tatabánya, Hungary


Agricultural production can be described by discrete time as there is harvest in every year only once. The agricultural production is uncertain because of the weather and the ever changing technology. At the same time, the sector prefers stability which is reflected in the small changes in the prices. The uncertainty of the price may be modeled by a set-valued function in a single product market. The independent variable is the price expectation of the producer which is the future value of the price estimated by the producer. It can be assumed that the set-valued function is decreasing because in the case of higher price expectation, greater quantity appears on the market and thus the real market price becomes the lower. The stability of the market may require some control. In this paper the existence of an appropriate control to reach a target interval and to keep the trajectory in the interval is investigated from mathematical point of view. Necessary and sufficient conditions are given for the existence of the viable solution. The “striped structure” of the dynamical system is explored as well.


Ahmad, H. F. (2015). Endogenous price expectations as reference points in auctions. Journal of Economic Behavior & Organization, 112, 46-63.
Bacsi, Z., & Vizvári, B. (1999). Modelling chaotic behaviour in agricultural pricesusing a discrete deterministic nonlinear price model. Annals of Operations Research, 89, 125-148
Flåm, S. D., & Kaniovski, Y. M. (2002). Price expectations and cobwebs under uncertainty. Annals of Operations Research, 114(1), 167-181.
Freeland, C. (2009). The credit crunch according to Soros. Financial Times, 30(01).
Gennaioli, N., Ma, Y., Shleifer, A. (2015). Expectations and Investment. National Bureau of Economics, NBER Working Paper No. 21260.
Dr. Agrarwissenschaften. Thesis, Zentrum für Entwicklungsforschung, Landwirtschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität, Bonn. Mekbib Gebretsadik Haile, Volatility of International Food Prices (Impacts on Resource Allocation and on Food Supply Response), 2015.
Kenyon, D. E. (2001). Producer ability to forecast harvest corn and soybean prices. Review of Agricultural Economics, 23(1), 151-162.
Keynes, J.M. The General Theory of Employment, Interest and Money, Macmillen, London, on page 156. 1963.
Imre, K., & Tibor, K. (1982). On the possibility of the realization of farming advantages in the Hungarian society (in Hungarian). Valóság, 6, 45-55. 
Kovács, G., Mureşan, M., & Vizvári, B. (2001). On a new approach of the price expectations of producers. Szigma, No. 1-2, 1-11.
Kovács, G., Mureşan, M., & Vizvári, B. (2002). Remarks on multifunction-based dynamical systems. Dynamical Systems and Applications, 11, 325-332.
Nerlove, M. (1958). Adaptive expectations and cobweb phenomena. The Quarterly Journal of Economics, 72(2), 227-240.
Masuku, M. B., Sukati, M. C., & Rugambisa, J. I. (2017). Supply Response of Milk Producers to Economic and Non-Economic Factors in Swaziland. Journal of Agricultural Studies, 5(4), 14-34.
Szidarovszky, F., & Molnár, S. (1994). Adaptive and extrapolative estimations in a special discrete dynamic producer-consumer model. Szigma, 25, 221-227.