Abstract:
The paper is intended to use mathematical models for controlling fluctuations in the price of maize by employing a nonlinear continuous time delay differential equation derived from linear demand and nonlinear supply functions of price. The delay parameters reflect the realities prevailing at the local market. 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. 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 buffer, then price oscillations would be drastically reduced as shown in this paper. The study is, also, an improvement on the work done by earlier workers, whose discrete time models are limiting cases of the delay buffer stock model used in this study. The efficiency of a buffer system is proven to be dependent on delay variation suitably enough to be used by buffer stock operators. It is noted that, the farther the buffer stock delay and supply delay are reduced, the more stable the price becomes and the effects of buffer stock are felt more by stakeholders. The results of the analysis provide an average stable price of maize as GH¢ 30.49 compared to the actual average price of GH¢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 excess supply is kept in stock and when needed it is released in the next market period. The standard deviation also is reduced to 0.1602 compared to the original 29.48 before the application of buffer stock scheme. Thus, before the application of buffer stock scheme, price oscillated between two price points and could not converge. This affirms the fact that buffer stock acts as a reserve against short term shortages and dampens excessive fluctuations. We draw inferences from this study that researchers should rather use continuous time nonlinear delay models as they reflect the realities in most real-life economic problems
