Controlling the Walrasian tatonnement process

Includes bibliographical references (leaves 69-70).In this thesis I examine a discrete-time Walrasian tatonnement process. The criterion for stability is examined in a two good tatonnement process. It is shown that the stability of the system depends upon the speed of adjustment and holdings of endowments as well as preferences. It is then shown that periodic solutions as well as aperiodic or chaotic trajectories occur. The analysis is then extended to multiple agents. Having established the results for the one-dimensional system, the analysis is extended to the case of three goods in which one of the goods is a numeraire. It is shown that similar dynamics to the one dimensional case exist. It is found that if one market acts in a chaotic manner then both markets act in a chaotic manner. Such that markets do not act in a chaotic manner, certain restrictions on the speed of adjustment and the holding of the non-numeraire good with respect to the numeraire good need to be enforced. Following in the footsteps of Uzawa [26], exchange out of equilibrium is examined for the case of one traded good and one numeraire as well as two traded goods and one numeraire. It is found that if any good can be exchanged for any other good there is a direct parallel between the tatonnement process and the nontatonnement process. If the numeraire is treated as a primitive currency then the policy implications differ significantly due to the amount of liquidity in the system