Dynamic Macroeconomics with Imperfect Competition
This thesis was stimulated throughout the time of my participation in a research project on Dynamic Macroeconomics, supported by the German Research Foundation (DFG). The starting point was the central question of how to integrate price setting firms in a
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Managing Editors: Prof. Dr. G. Fandel Fachbereich Wirtschaftswissenschaften Fernuniversitat Hagen Feithstr. 140/AVZ II, D-58084 Hagen, Germany Prof. Dr. W. Trockel Institut fUr Mathematische Wirtschaftsforschung (IMW) Universitat Bielefeld Universitatsstr. 25, D-33615 Bielefeld, Germany
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Springer-V erlag Berlin Heidelberg GmbH
Leo Kaas
Dynamic Macroeconomics with Imperfect Competition
Springer
Author Dr. Leo Kaas Institute for Advanccd Studies Department of Economics Stumpergasse 56 A- I06Q Vienna- Austria
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Kaas. Lea . 1969Oyna~lc laeroecona.les wlth llperfect ceepetltlan I Leo Kaas. p. c~ . -- (Leeture notes In aeona.les and ~athelatlea systels 4751 Includes blbl10graphlcal referenees (p. l. ISBN 978-3-540-66029-3
ISBN 978-3-642-56479-4 (eBook)
DOI 10.1007/978-3-642-58479-4 . 1. Coopetltton, Ieperfaet--Hltha~atleal eadels. 2_ Haeroeconolles--HathtllatlCal ~ode1s. 3. Equl11brlu. lEconOllcs)-Hathelatlcal eodels. I. Tltle . II. Ser les. HB238. K33 1999 338.6' 048--dc2 1 99-34450 CIP
ISSN 0075-8442 ISBN 978-3-540-66029-3 This work is subject 10 copyright. Ali rights are reserved, whether the whole or part of Ihe material is concerne 1fj(sj, 'ljJj(a, sj)). But then sf E Rj(at-I; 'ljJ!) for all t ~ 1 implies lim
t-too
1fj (
sf , 'ljJ! (at-I, sf) )
> tlim 1f j (sj,'ljJ!(at-l,sj)) -too
= 1f j (sj,'ljJj(a,sj))
a contradiction. (ii) Take the IOFs ('ljJj)jEJ of Definition 2. Define
L1
by
L1 (lit-I)
'ljJj and arbitrary and consistent if ht- I i= li t- I (for instance, by adaptive outcome expectations L1 (ht-I)(at-I, si) = a~_1 + A(at-I a~_I)). Then clearly (s, a, lit)t?1 is a trajectory of (2.3)-(2.5).
D
As an illustration of this result, consider a monopolist who believes in a linear inverse demand curve with intercept a and negative slope -b. A consistent learning process may be defined by fixing one parameter a or
b and updating of the other parameter. The resulting learning dynamics would have different steady states depending on the fixed parameter. One can think as well of learning processes with updating of both parameters and which have a continuum of steady states. This is the case in models where the monopolist estimates the parameters with an OLS method, cf. Rampa (1989). It is a consequence of the above result that further assumptions on the
learning process have to be imposed in order to select among the set of subjective equilibria by learning dynamics. An agent's learning process
2.4. LEARNING DYNAMICS
25
reflects his subjective perception of the economy and cannot be fixed "objectively" by an outside observer. All one can do is to exclude too stupid agents by imposing consistency or rationality requirements on the learning process. It is, however, not clear if there exist learning processes which select (locally) objective equilibria independently of the true outcome function. This will be discussed briefly in the following. A first observation is that if it were assumed that agents not only observe past histories of
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