Working paper N. 729 Febbraio 2016
Ahmad K. Naimzada
Department of Economics, Quantitative Methods and Business Strategy, University of Milano-Bicocca
Serena Sordi
Department of Economics and Statistics, University of Siena
Abstract
The simple pure exchange model with two individuals and two goods by Day and Pianigiani (1991), extensively analyzed by Day (1994, Ch. 10) and taken up again by Mukherjy (1999), is discussed and extended with the purpose of showing that chaos in a discrete tâtonnement process of this kind can be controlled if the auctioneer uses a smooth, nonlinear formulation of the price evolution process such that the price adjustment is a sigmoid-shaped function of the excess demand, with given upper and lower limits. This formulation o¤ers some advantages over previous speci
cations. In particular, given the speed of adjustment and the excess demand function, we show that, acting on the lower and/or upper limits that constrain price dynamics, the auctioneer can (i) stabilize the dynamics, (ii) reduce the complexity of the attractor and (iii) increase the economic signi
cance of the adjustment process.
Keywords
Price adjustment, tâtonnement, chaos, control
Jel Codes
C62, D50
