When the supply is the reflection of the supplier expectations, chaos is overpowering the market

For economists, a problem known as: uncertainty of demand forecast, is a recurrent shortcoming they have to contend with daily when it comes to predicting future demand. This issue mainly arises when a firm has to decide on the number of units they need to produce of a certain product before knowing how many products the market will demand in the next sales season. The accuracy of predicting future demand will soon be vital for the survivability of any firm entangled in a dynamic market environment. Several models and statistical based approaches have already been proposed, including; the economic order quantity and linear regression. Recently, agent-based modelling has emerged as a popular technique amongst academics and industry researchers to face demand uncertainty in the markets. Unfortunately, it has not been used to resolve market issues as the one described earlier.

Recently, Professor Miguel A.F. Sanjuán at Universidad Rey Juan Carlos in Spain with Asaf Levi (PhD Candidate) and Dr. Juan Sabuco (currently a Postdoctoral Research Assistant at the Mathematical Institute of the University of Oxford) conducted a study to numerically analyze a simple dynamical model that describes the firm’s behavior under uncertainty of demand. They have focused on modeling a market where one firm was a price maker operating under uncertainty of demand using a discrete dynamical system, where consumers obey the law of demand. In addition, they have studied the dynamics of the model proposed and how it changes when some key parameters are varied. Their work is currently published in the research journal, Communications in Nonlinear Science and Numerical Simulation.

The modeling approach that they propose assumes a firm whose commercial activity consists in producing or buying some stocks of a certain good with the purpose of selling them to obtain profits, but operating under uncertainty of demand. The model proposed takes two basic assumptions. First, the firm is the only one that sets and adjusts the price in light of circumstances. Second, the main goal of the firm is to sell all the produced products and satisfy the overall demand. With these two assumptions the authors have studied two possible scenarios: the naive supplier and the cautious and optimistic supplier.

The authors observed that in both scenarios, the model was capable of reproducing a large variety of dynamics such as equilibrium, cycles, chaos, and even catastrophic dynamics under the simple and reasonable economic assumptions presumed. They also noted that the price elasticity of demand and the gross margin could play an essential role in the market crash.

In summary, Professor Miguel Sanjuán and his collaborators have successfully introduced a supply based on demand model studying two types of firm behaviors, the naive supplier and the cautious and optimistic supplier. Generally, they have observed that very small changes in the price elasticity of demand have the potential to lead to very different global dynamics assuming a monotonic demand function. They also emphasize the notion of “final bifurcation means market collapse”, illustrating the importance of transient chaos in economics. Altogether, their work has demonstrated the huge influence of the gross margin, M, on the market dynamics.