An adjustment process for nonconvex production economies

We consider a slightly adapted version of the general equilibrium model with possibly nonconvex production technologies presented by Villar (1994). Typical for such models is that the behaviour of a producer is modelled by a pricing rule that relates market prices and production vectors - a combination to which we refer as the market condition -with a set of acceptable prices for this producer. We prove the existence of a path of market conditions that links any arbitrarily chosen market condition with an equilibrium market condition. At an equilibrium market condition all markets are cleared and all producers accept the market prices. The adjustment of the market prices and production quantities along the path can be given some economic interpretation as a tatonnement process. Along this process the market prices are adjusted according to the sign of the excess demands on the underlying markets, and the production quantities according to the difference between market prices and acceptable prices. The existence theorem holds for any semi-algebraic version of the model, i.e. all sets and mappings in the model can be described by polynomial (in-)equalities. Any path connecting the initial market condition with an equilibrium market condition can be approximated arbitrarily close by applying a simplicial algorithm. By restarting this algorithm in a different market condition, we may find more than one equilibrium.