A pitchfork bifurcation in the tatonnement process
This note extends the example of Gale (1963) by considering the continuous time tatonnement process for a class of two agent, two commodity exchange economies, parametrized by a number Âµ∈(0,1). We demonstrate that as the parameter passes a threshold value Âµ* the unique, globally stable competitive equilibrium loses local stability while two new locally stable equilibria appear. Intuitively, as Âµ increases the income effect become increasingly more important relative to substitution effect, and eventually overwhelms the latter. As the parameter Âµ approaches 1, the economy tends to the example considered by Gale, as does the limiting behavior of the tatonnement.
Volume (Year): 10 (1997)
Issue (Month): 3 ()
|Note:||Received: February 28, 1996; revised version August 5, 1996|
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