Abstract
Market collapse is one of the most dramatic events in economics. Such a catastrophic event can emerge from the nonlinear interactions between the economic agents at the micro level of the economy. Transient chaos might be a good description of how a collapsing market behaves. In this work, we apply a new control method, the partial control method, with the goal of avoiding this disastrous event. Contrary to common control methods that try to influence the system from the outside, here the market is controlled from the bottom up by one of the most basic components of the market—the firm. This is the first time that the partial control method is applied on a strictly economical system in which we also introduce external disturbances. We show how the firm is capable of controlling the system avoiding the collapse by only adjusting the selling price of the product or the quantity of production in accordance to the market circumstances. Additionally, we demonstrate how a firm with a large market share is capable of influencing the demand achieving price stability across the retail and wholesale markets. Furthermore, we prove that the control applied in both cases is much smaller than the external disturbances.
Highlights
Economic dynamics constitute an important research field in economics
When the firm prevents the crash: Avoiding market collapse with partial control have shown that this macro state of collapse can be avoided acting on the macro level of the market when a powerful firm had influenced the quantity demanded using the partial control method
A firm with high market power might influence the demand by intervening directly in the market, buying the excess supply, or just by investing in advertising to encourage the consumption in the market. It is more remarkable how the agents at the micro level have avoided the macro state of collapse by changing their behaviors using the partial control strategy
Summary
Economic dynamics constitute an important research field in economics. Many models have been developed to explain the motion of economic variables such as the price, the demand or the GDP, giving rise to different dynamical behaviors, like periodic orbits, strange attractors and equilibrium states. This model produces the following dynamics: equilibria points, periodic orbits and chaotic behavior which for some parameter values becomes transient In this situation the trajectories of the price, the demand or the supply are chaotic some time until they eventually collapse. The main results of this paper are that the firm can successfully control the trajectories of the price by only changing the gross margin at each time step preventing a market collapse It can rationalize the quantity supplied with the same purpose. The iterative map for Dn is as follows, Dnþ1 1⁄4 a À b
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