The Use of Functional Differential Equations in the Model of the Meat Market with Supply Delay

Abstract

In economic applications, we have to make the assumption that relations between the variables vary with time. One of the possible ways of incorporating the process dynamics into the model is to describe the model by functional equations. The paper is based on the assumption that the balance between the demand and supply can be successfully expressed by a model described by differential equations, even if the goods are supplied with a certain delay. The equation is solved by modern theory. Theoretical results are illustrated by an example, with concrete results presented in graphical form. The solution is presented by modern computer simulation and the Maple system is used. The authors come to the conclusion that a delay in the supply of goods can cause an oscillation in the price. On the other hand, it is possible to define conditions under which the solution is monotonous.

A Mathematical Model of Financial Bubbles: A Behavioral Approach

“…Thus, the modelling methodology must incorporate and link two aspects, namely social contagion or herd behavior and the asset price. Since the basic economic model determining the price of an asset is that of supply and demand [17], it is reasonable to use this model as a link between herd behaviors and asset prices. In other words, the proposed mathematical model presented in Section 3 uses, on the one hand, a basic economic model of supply and demand to describe the dynamics of the price of an asset and, on the other hand, an epidemiological approach to describe the dynamics of contagious behaviors, which, in turn, affect the supply and demand and, ultimately, the price of an asset.…”

“…This phase of excess supply is referred to as a negative bubble [3] or collapse regime [9]. As can be inferred from the work of Bobalová and Novotná [17], a decrease in demand and increase in supply would cause the asset price to reverse trend and begin to decrease. As such, during the collapse regime portion of a financial bubble, the asset is subject to a precipitous drop in price [9].…”

“…Based on the assumption of economic equilibrium, where a stable asset price is attained by the balance of supply and demand, the following Evans price equilibrium model [17,[20][21][22], which describes the rate of change of price with respect to time as a function of the difference between demand and supply, is used:…”

“…where the parameter τ > 0 characterizes the effect of the bull population on the price elasticity of demand, and d 2 (0) = −d * 2 (with d * 2 > 0) denotes the basal price elasticity of demand. Now, let us turn our attention to the autonomous demand (d 1 ), which is the quantity of the asset demanded when prices equal zero [17]. Assuming that this quantity increases according to the number of optimists and that the contribution of each optimist/bull in the market toward autonomous demand is the same, the autonomous demand function reflecting its dependence on the optimist population can be written in the following form:…”

“…Note that the dynamics of the social contagion component of the full model (17) expressed by its last four equations (or equivalently by Equation ( 14)) is independent of the dynamics of the asset price expressed by its first equation (or equivalently by Equation ( 10)). Thus, in order to carry out the stability analysis, we first find the steady state (( N, T, Ū, Q)) of Equation (14).…”