TY - JOUR
T1 - A geometric study of shareholders' voting in incomplete markets
T2 - Multivariate median and mean shareholder theorems
AU - Crès, Hervé
PY - 2006/10
Y1 - 2006/10
N2 - A simple parametric general equilibrium model with S states of nature and K < S firms is considered. Since markets are incomplete, at a (financial) equilibrium shareholders typically disagree on whether to keep or not the status quo production plans. Hence each firm faces a genuine problem of social choice. The setup proposed in the present paper allows to study these problems within a classical (Downsian) spatial voting model. Given the multidimensional nature of the latter, super majority rules with rate ρ ∈ [1/2, 1] are needed to guarantee existence of politically stable production plans. A simple geometric argument is proposed showing why a 50%-majority stable production equilibrium exists when K=S-1. When the degree of incompleteness is more severe, under more restrictive assumptions on agents' preferences and the distribution of agents' types, equilibria are shown to exist for rates ρ smaller than Caplin and Nalebuff (Econometrica 59: 1-23, 1991) bound of 0.64: they obtain for production plans whose span contains the 'ideal securities' of all K mean shareholders.
AB - A simple parametric general equilibrium model with S states of nature and K < S firms is considered. Since markets are incomplete, at a (financial) equilibrium shareholders typically disagree on whether to keep or not the status quo production plans. Hence each firm faces a genuine problem of social choice. The setup proposed in the present paper allows to study these problems within a classical (Downsian) spatial voting model. Given the multidimensional nature of the latter, super majority rules with rate ρ ∈ [1/2, 1] are needed to guarantee existence of politically stable production plans. A simple geometric argument is proposed showing why a 50%-majority stable production equilibrium exists when K=S-1. When the degree of incompleteness is more severe, under more restrictive assumptions on agents' preferences and the distribution of agents' types, equilibria are shown to exist for rates ρ smaller than Caplin and Nalebuff (Econometrica 59: 1-23, 1991) bound of 0.64: they obtain for production plans whose span contains the 'ideal securities' of all K mean shareholders.
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U2 - 10.1007/s00355-006-0138-7
DO - 10.1007/s00355-006-0138-7
M3 - Article
AN - SCOPUS:33748525236
SN - 0176-1714
VL - 27
SP - 377
EP - 406
JO - Social Choice and Welfare
JF - Social Choice and Welfare
IS - 2
ER -