Dynamics of price stabilization with buffer stock: an application of cobweb model using delay differential equation: (the case of maize supply in Ghana)

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July 28, 2016
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This study is intended to use mathematical models for controlling fluctuations in the price of maize by employing a nonlinear continuous time delay diff erential equation derived from linear demand and nonlinear supply functions of price. These models are formulated from parameters estimated from real economic data of maize price demand and production in the Ashanti Region of Ghana through the use of regression methods. The data is obtained from the Ministry of Food and Agriculture, Statistical Directorate Kumasi-Ghana, pertaining to years from 1994 to 2013. The results of the study are connected to the assertion that commodity price is dependent on planting time, storage time, relaxation time and total production time. It is proven that if all these individual time segments are combined as one for supply delay to make up total storage time, which is the delay for the bu er, then price oscillations would be drastically reduced. Also the study is an improvement on the work done by earlier researchers, whose discrete time models are limiting cases of the delay bu er stock model used in this study. The effi ciency of a bu er system is proven to be dependent on delay variation suitable enough to be used by bu er stock operators. It is noted that, the more the bu er stock delay and supply delay are reduced in connection with the type of price scheme operated in the bu er stock scheme, the more stable the price becomes and the eff ects of bu er stock are felt more by stakeholders. The results of the analysis provide an average stable price of maize as GHC 30.49 compared to the actual average price of GHC 30.27. The equilibrium price in turn provides the average equilibrium weight of 2931.6 and 8217.6 metric tons for demand and supply respectively. The average excess supply that constitutes the stocks in the bu er is also given as 5286 metric tons and they are kept in stock for the next market period (i.e planting period). When at another period (i.e during harvesting period) demand exceeds supply then the appropriate diff erence is released from the bu er to the market in order to keep price in equilibrium. The standard deviation is also reduced to 0.1602 compared to the original 29.48 before the application of bu er stock scheme. Thus, before the application of bu er stock scheme, price oscillated between two price points and could not converge. This affi rms the fact that bu er stock acts as a reserve against short- term shortages and dampens excessive fluctuations. Inferences are drawn from this study that researchers should rather use continuous time nonlinear delay models as they reflect the realities prevailing in most real-life economic problems. While continuous time delay di fferential bu er stocks models or equations could be applied in managing unstable market price of maize irrespective of the type of the supply function it is integrated with, being it linear or nonlinear, the discrete time bu er stock models instead work well with linear supply functions.
A thesis submitted to the Department of Mathematics,Kwame Nkrumah University of Science and Technology in partial fufillment of the requirement for the degree of Master of Philosophy (Applied Mathematics), 2016