Is Dynamic Stability of Walrasian Equilibrium Achieved Through Falling Target Utilities?
通过一个纯交换经济的例子，证明哈恩过程的假设（QPQ和HA）在自愿交易下可能不一致，并质疑下降目标效用作为非试探过程稳定性证明的有效性。
It is known that if disequilibrium trade occurs according to the assumptions of the Hahn Process, Walrasian stability is achieved by means of falling target utilities. This paper shows, by means of an example in a pure exchange economy, that the assumptions of the Hahn Process are not necessarily mutually consistent. After Scaif (1960) showed that the tatonnement process is not necessarily stable, attempts to establish stability of Walrasian equilibrium turned towards nontatonnement models, in particular the Hahn Process. If the assumptions of the Hahn Process (hereinafter labelled QPQ and HA) are satisfied, dynamic stability is established by means of a declining Lyapounov function constructed as a sum of individual target utilities. The Hahn Process was introduced by Hahn and Negishi (1962) and subsequent developments are reviewed by Arrow and Hahn (1971), Hahn (1982) and Fisher (1983).2 In this paper, an example is provided in which QPQ and HA cannot remain consistent with voluntary trade prior to equilibrium. An attempt is made to overcome this problem by assigning the role of money to the numeraire good, but this does not succeed because the exhaustion of money stocks can not be prevented. These results cast doubt on the usefulness of the falling target utilities condition as a means of proving non-tatonnement stability.