A Markovian Model Market - Akerlof's Lemmons and the Asymmetry of Information

In this work we study an economic agent based model under different asymmetric information degrees. This model is quite simple and can be treated analytically since the buyers evaluate the quality of a certain good taking into account only the quality of the last good purchased plus her perceptive capacity \beta . As a consequence the system evolves according to a stationary Markovian stochastic process. The value of a product offered by the seller increases with quality according to the exponent \alpha, which is a measure of technology. It incorporates all the technological capacity of production systems such as education, scientific development and techniques that change the productivity growth. The technological level plays an important role to explain how the asymmetry of information may affect the market evolution in this model. We observe that, for high technological levels, the market can control adverse selection. The model allows us to compute the maximum asymmetric information degree before market collapse. Below this critical point the market evolves during a very limited time and then dies out completely. When \beta is closer to 1(symmetric information), the market becomes more profitable for high quality goods, although high and low quality markets coexist. All the results we obtained from the model are analytical and the maximum asymmetric information level is a consequence of an ergodicity breakdown in the process of quality evaluation.