The fifth Workshop MDEF (Modelli Dinamici in Economia e Finanza) will be held in Urbino from 25 to 27 of September 2008. On Thrusday 25th, I am presenting the following work:
A Mulitproduct Monopolist with Local Knowledge of Demand
(with J. Tuinstra and F. Wagener)
…following there is an abstract
We study a learning model for a quantity setting monopolist that has incomplete knowledge of the demand for the n goods she produces. In each period, the monopolist produces a certain quantity of each commodity and observes the set of corresponding market clearing prices as well as the matrix of (cross-)price effects at those quantities. From this information she estimates a linear demand system for her products, consisting of n linear subjective demand curves. On the basis of this estimated demand system the monopolist updates her perceived profit maximizing vector of quantities, and so on. The model is a generalization of Naimzada and Ricchiuti (2008), who study this learning process for a single-product monopolist (that is, n=1). Our analysis is richer because it allows for studying the effects of complements and substitutes on stability of the learning model.
As in Tuinstra (2004) and Bischi et al. (2006), we show that there is a one-to-one relationship between steady states of the learning process and critical points of the objective profit function. Moreover, we show that every local minimum of the objective profit function is an unstable steady state of the learning process. Local maxima, on the other hand, may correspond to either locally stable or unstable steady states of the learning process, depending upon the curvature of the demand system. We show, by means of numerical simulations, that the learning process may lead to complicated behavior and endogenous fluctuations.