Dynamics of a Price Adjustment Model with Distributed Delay

Luca Guerrini (), Martin Anokye, Albert L. Sackitey and John Amoah-Mensah
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Luca Guerrini: Department of Management, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy
Martin Anokye: Department of Mathematics, University of Cape Coast, Cape Coast P.O. Box 046, Ghana
Albert L. Sackitey: Department of Mathematics, University of Cape Coast, Cape Coast P.O. Box 046, Ghana
John Amoah-Mensah: Department of Computer Science, Sunyani Technical University, Sunyani P.O. Box 206, Ghana

Mathematics, 2024, vol. 12, issue 20, 1-12

Abstract: This paper deals with the stability and occurrence of Hopf bifurcation of a distributed delay differential cobweb model using the chain trick technique. This is a generalized form of the fixed delay cobweb model to which it is compared using the same parameter values. The results from the delay distribution showed that whenever less weight ( γ = 0.146 ) is put on past prices, the current equilibrium price is adjusted upwards while the reverse is observed when a higher weight ( γ = 0.186 ) is put on the previous price. It is also observed that if the initial price is set below/above the equilibrium price, the price adjustment either affects the consumers or benefits the suppliers. However, the fixed delay cobweb model does not display the consumers or suppliers benefits of the price dynamics in either direction. These are unique, underlying patterns in price dynamics discovered when using a distributed delay model compared to traditional fixed delay cobweb models. Furthermore, our model challenges the traditional cobweb model’s requirement for divergence, as it is based on the weight assigned to past prices rather than the relationship between the elasticities of supply and demand, which is the determining factor in the classical model. Based on these insights, we recommend that future price adjustment models incorporate distributed delays, as they reveal more intricate price dynamics and provide a more comprehensive understanding of market behavior than fixed delay models.

Keywords: cobweb model; distributed delay; price; stability switch (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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