Household behavior and individual autonomy: an extended Lindahl mechanism

We present a comprehensive model of household economic decision covering both full cooperation and noncooperation as well as semi-cooperative cases, varying with income distribution and a parameter vector <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\theta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">θ</mi> </mrow> </math> </EquationSource> </InlineEquation> representing degrees of individual autonomy with respect to the public goods. In this model, the concept of “household <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\theta $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="italic">θ</mi> </mrow> </math> </EquationSource> </InlineEquation>-equilibrium” is introduced through the reformulation of the Lindahl equilibrium for Nash implementation and its extension to semi-cooperation. Existence is proved and some generic properties derived. An example is given to illustrate. An important benefit of this approach is to allow for a compact and unified investigation of the testable (local) restrictions of household demand. A particular decomposition of the pseudo-Slutsky matrix is derived and the testability of the various models discussed. Copyright Springer-Verlag Berlin Heidelberg 2014