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 µ∈(0,1). We demonstrate that as the parameter passes a threshold value µ* the unique, globally stable competitive equilibrium loses local stability while two new locally stable equilibria appear. Intuitively, as µ increases the income effect become increasingly more important relative to substitution effect, and eventually overwhelms the latter. As the parameter µ 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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