In this paper a linear cobweb model is developed to study the phenomenon of commodity price fluctuations and then a buffer stock incorporated into the model to stabilize the price of fresh tomatoes in Ghana. The model performed on the assumptions that fresh tomatoes have no equal substitutes, and that there is no foreign competition and also no exogenous shocks needed to generate price fluctuations.The analysis detected that the slope of the demand function of price was smaller than the slope of the supply function of price curve implying that the price and quantity supplied of the fresh tomatoes would oscillate around a fixed price and quantity and also spiral outward.The "Keep Supply at Average" (KSA) buffer scheme achieved price and quantity stability in the short run. The mean price of the scheme was GH¢17.31, very close to actual price mean of Gh¢ 13.40 in the first 16 quarters. The standard deviation of the scheme price also dropped to 1.2 from 9.13 during price stabilization compared to 14.60 of actual price mean.In the long run the scheme price went up to Gh¢ 18.22, an increase of Gh¢ 0.91 and it is clear that in long run buffer system will fail unless the average supply is reviewed regularly.The scheme price trend equation indicated that with the implementation of the buffer scheme, the average quarterly price of fresh tomatoes increased by only 0.05.

The paper studies the dynamics of a full delay-logistic population model incorporated with a proportionate harvesting function. The study discusses the stability of the model in comparison with the well-known Hutchinson logistic growth equation with harvesting function using the rate of harvesting as a bifurcation parameter to determine sustainable harvesting rate even at a bigger time delay of τ = 3.00 . In all cases, the Hutchinson equation with harvesting was forced to converge to equilibrium using an additional and a different time delay parameter, a deficiency previous researchers have failed to address when the Hutchinson model is used for this purpose. The population fluctuations are catered for with this model making the estimated maximum sustainable growth and harvest reflect realities as this model drastically reduces time-delay associated oscillations compared to the well-known Hutchinson delayed logistic models. The numerical simulations were be done using the MatLab Software.

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