In this paper we develop an heterogenous agents model of asset price and inventory with a market maker who considers the excess demand of two groups of agents that employ the same trading rule (i.e. fundamentalists) with different beliefs on the fundamental value. The dynamics of our model is driven by a bi-dimensional discrete non-linear map. We show that the market maker has a destabilizing role when she actively manages the inventory. Moreover, inventory share and the distance between agents' beliefs strongly influence the results: market instability and periodic, or even, chaotic price fluctuations can be generated. Finally, we show through simulations that endogenous fluctuations of the fractions of agents may trigger to instability for a larger set of the parameters.
In this paper, we analyze a heterogeneous agent model in which the fundamental exchange rate is endogenously determined by the real markets. The exchange rate market and the real markets are linked through the balance of payments. We have analytically found that there exists at least a steady state in which the exchange rate is at its fundamental value and incomes of both countries are equal to the autonomous components times the over-simplified multiplier (as in the Income-Expenditure model). That steady state can be unique and always unstable when all agents act as contrarians, while when agents act as fundamentalists is unique but its stability depends on the reactivity of actors of the market. Finally, we show that the (in)stability of the economic system depends on both the reactivity of the markets and that of different type of agents involved.