Bargaining Power and Equilibrium Consumption

preferences a multi-person household has no incentive to misrepresent the internal
bargaining power.

Regarding our simplifying assumptions for the neutrality result, interiority and
uniqueness of equilibrium, giving up the first assumption requires to work with Kuhn-
Tucker conditions instead of first order conditions. Without the second assump-
tion, multiple equilibria cannot be ruled out. But a market clearing price system
(p₁ , . . . , p_`-1 , 1) with respect to some array of bargaining power parameters is also
market clearing with respect to all other arrays. Given any such market clearing price
system and the associated equilibrium selection, the conclusion of Proposition 3 con-
tinues to hold.

5.2 Separate Sphere Consumption

We next turn to situations where internal bargaining power changes in a particular
household have spill-over effects on other households. In particular, we examine how
individuals are affected if similar (dissimilar) persons in other households can increase
their bargaining power. We examine an economy like in the last subsection, but with
different individual preferences. We assume households which are homogeneous at the
beginning but undergo large sociological changes thereafter. We assume ` = 2 and that
all households have the same endowment w_h = w = (w¹, w2).

Individuals have separate spheres of consumption, i.e.

The utility functions are assumed to be strictly increasing, strictly concave and
differentiable. The assumption of separate sphere consumption is one convenient way
to divide the society into different sociological groups where individuals are similar
within a group and dissimilar across groups. Here we have two groups, “first members”
(denoted h1) and “second members” (denoted h2) of households. Again household h
maximizes

αh 1-αh

Sh = U_h1 U_h2

where 0 < α_h < 1. We obtain, with ^ denoting again equilibrium values:

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