[01] Pranvera Mulla, Faculty of Natural Sciences, Department of Applied Mathematics, University of Tirana, Branch Sarande, Sarande, Albania. [02] Eglantina Xhaja, Faculty of Natural Sciences, Department of Applied Mathematics, University of Tirana, Tirane, Albania. [03] Erand Mulla, Department of Economics, University College London, London, UK.

Agriculture in Albania is a sector which exhibits big fluctuations of prices and production. The priority given to this sector in the light of the overall development of Albanian economy, reveals the necessity of orientating the market and production towards a stable equilibrium in order to facilitate the process of policy-making. The main aim of this paper is to study the stability of prices and production by using nonlinear models of difference equations. Starting from the logistic function, it is argued the its discrete version is nonlinear and the recurrent graphical method is a cobweb method; the stability of equilibrium point is studied and it is shown that the model satisfies the stability conditions with real economic data on agricultural products. After studying its stability through numerical methods, the logistic model is used to make predictions on prices.

Difference Equations, Stability, Logistic Model, Cobweb Model, Agriculture

[01] Anokye M., Oduro F., (2013). Cobweb with buffer stock for the stabilization of tomato prices in Ghana, Journal of Management nad Sustainability. 3 (1). pp. 155-165. [02] FinkenstädtB., and Kuhbier P., (1992). Chaotic dynamics in agricultural markets. Springer. 37(1)pp 73-96. [03] Bohner M., Warth H., (2008). Logistic dynamic equations in population models. Missouri University of Science and Technology. http://atlasconferences.com/c/ a/w/w/46.htm [Accessed January, 2013]. [04] Boussard, J.M., and Gérard, F., (1994). Stabilisation des prix et offreagricole in: M. Benoit-cattin, M. Griffon and P. Guillaumonteds (eds), Economics ofagricultural policies in developing countries. Paris: RFSP. Pp. 319-335. [05] Zhang, Q., Liu, J. and Luo, ZH, (2015)Dynamical behavior of a third-order rational fuzzy difference equation Advances in Difference Equations. 108(1). pp. 1-18. [06] Finkenstadt, B., (1995), Nonlinear Dynamics in Economics: A theoretical and Statistical Approach to Agricultural Markets: Lecture Notes in Economics and Mathematical System. Journal of Economic Literature. 34(4). [07] Gonze, G., (2013) The logistic equation, Belgium, pp.1-22. [08] Hommes, C. H., (1994),Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand, Journal of Economic Behaviour & Organization, 24(3) pp.315-335. [09] Hommes, C., (2013), Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems. Cambridge: Cambridge University Press. [10] Neusser, K., (2008). Difference Equations for Economists:http://www.vul.unibe.ch/studies/3107_e/DifferenceEquations.pdfMatsumoto A. (1999). Preferable disequilibrum in a nonlinear cobweb economy. Annals of Operations Research, 89. pp.101-123. [11] Mulla, P., (2012). Modelimimatematik i disaproblemevedhestabiliteti i tyre: Modeli Cobweb. Albanian Socio Economic Review. 2(71). pp.75-82. [12] Mulla, P.,Xhaja,E.,Hoxha, F., (2014). The numerical simulation of nonlinear cobweb model in MATLAB. The Albanian Journal of Natural and Technical Sciences. 36(1). [13] Mulla, P., Vegetable price fluctuation in Albania: A nonlinear model for its study. Mediterranean Journal of Social Sciences. 5(2). Pp. 477-482. [14] Mulla, P. 2014. The stability of solutions of difference equations and applications in economics. PhD. Thesis. Faculty of natural Sciences, Albania. [15] Drejtoria e Bujqësisë e RrethitSarandëdheMinistria e Bujqësisë,UshqimitdheMbrojtjessëKonsumatorit: Vjetaristatistikor. Instituti i Statistikave:www.instat.gov.al [Accessed December, 2014]. [16] Republika e shqipërisë, Instituti i statistikave. 2013www.instat.gov.al. [Accessed November, 2014]. [17] Ramos, R. A. (2013). Logistic function as a forecasting model: It’s application to business and economics, International Journal of Engineering and Applied Sciences.2(3). Pp. 29-36. [18] Agarwal, P.R., El-Sayed, AMA., and Salman SM., (2013). Fractional-order Chua’s system: discretization,bifurcation and chaos. Advances in Difference Equations.320(1). pp.1-13.