Fisher studied if there is an out-of-equilibrium process that rapidly converges to some equilibrium points. He claims that Hahn process has a Lyapounof function and therefore convergent to an equilibrium. How can we understand Fisher's result with Saari and Simon (1978) Effective price mechanisms, Econometrica 46(5), 1097-1125, which claims there is no effective method of calculation that leads to an equilibrium?
Is there someone who is well versed in this topic? Although it is not very popular now, Fisher's book treats the theme that is crucially important for general equilibrium analysis. You can safely assume that the economic state is in equilibrium if you know that any state of the economy converges rapidly to an equilibrium. If not, analyzing equilibrium state risks to be an examination of a state that has no relevance to the actual economy.
Fabio Neves Peracio de Freitas Tosihiro Oka Arrigo Opocher Barkley Rosser
Édgar Hernando Sánchez Cuevas Antonio D'Agata Martín Esteban Seoane Salazar Hiroyasu Uemura Takeshi Ogawa Ricardo Summa Winston W. Chang Gheorghe Zaman
Dear Yoshinori,
I apologize for the delay in responding to your generous comments on my previously published articles. I did not have enough time until now. I answer you now your interesting question.
Saari and Simon's criticisms focus on the adjustment processes known as Walrasian tâtonnement, where 1) there is no exchange, production, or consumption activities during disequilibrium, and 2) prices are adjusted according to the law of supply and demand or Newton's iterative process, explained as if they result from perfectly competitive mechanisms where a Walrasian auctioneer sets the prices. In these cases, the stability results depend on the shape of the excess market demand functions for each commodity. According to the SMD theorem, this presents a significant problem and a huge limitation for such stability results.
In contrast, the Hahn and Fisher adjustment processes are different: 1) they are not Walrasian tâtonnement processes (Hahn's process involves exchanges, and Fisher includes also consumption and production activities), and 2) firms or individuals set prices through more or less monopolistic competitive processes. Most importantly, their stability results do not depend on the shape of the excess market demand functions for each commodity. Therefore, they are not constrained by the SMD theorem.
It is a shame these adjustment processes are not as well known or taught in our economics courses.
Best regards,
Martin
Dear Yoshinori,
I supect, that you want to "prove" that there is no process to arrive at an equilibrium, when the economy is out-of-equtilibrium. Ithink that a waste of time, because equilibrium economics (GE models) have nothing to do with reality. Has anybody observed an economy in equilibrium ( however defined) for a certain period?
Best regards,
Anton
Dear Anton Rainer
you may be too optimistic. Have you ever persuaded a mainstream economist to get out of it? You are right to say that the economy is out of equilibrium, GE or its DSGE variant have nothing to do with reality. As long as you can persuade those economists, it is all right. However, such economists are few. Many will be deaf of your depiction. That is the problem. What do you do?
Martín Esteban Seoane Salazar Tony Aspromourgos Heinz D. Kurz Hiroshi Nishi Hiroyasu Uemura
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