Dynamics of equilibrium prices with differential and delay differential equations using characteristic equation techniques

Abstract

This study compares differential model to delay differential model in terms of their qualitative behaviour with respect to equilibrium price changes using roots of characteristic equation techniques. The equilibrium states of both price adjustment models were simulated using inputs from same source. The study found that irrespective of initial prices set for the system, the current price of the differential model would always move monotonically towards the equilibrium price defined for the system. However, the current price of the delay- differential model will fluctuate and move away from the initial prices due to the delay parameter associated with the supply, then gradually decrease and turn towards the defined system equilibrium price. Results from the study also showed that current prices in the delay-differential model are not predictable at the initial stage due to the time delay parameter in the supply function of price. On the other hand, current prices in their counterpart models without delay are predictable, as they always converge to the equilibrium price points defined in the system. Since most economic and physical systems are time delay inherent, it is recommended that such systems are modeled using delay-differential equations to reflect realities of the phenomena