  In the first part of this paper (Sections 1-4), we study a standard exchange
economy model with Cobb-Douglas type consumers and give a necessary and
sufficient condition for the existence of an odd period cycle in the
Walras-Samuelson (tatonnement) price adjustment process. We also give a
sufficient condition for a price to be eventually attracted to a chaotic
region. In the second part (Sections 5 and 6), we investigate ergodic
properties of the price dynamics showing that the existence of chaos is not
necessarily bad. (The future is still predictable on average.) Moreover,
supported by a celebrated work of Avila et al. (Invent. Math., 2003), we
conduct a sensitivity analysis to investigate a relationship between the
ergodic sum (of prices) and the speed of price adjustment. We believe that our
methods in this paper can be used to analyse many other chaotic economic
models.
