Bargaining Power and Equilibrium Consumption

household, the individual’s reservation utility level is zero. The choice of disagreement
points for intra-household bargaining is somewhat controversial and depends on the
assumed inside or outside options of household members. In Gersbach and Haller
(2002), we consider for example an exit option, that is the possibility that a household
member leaves, forms a single household and maximizes utility at the going market
prices. Such an outside option would complicate notation and the formal analysis, but
not alter the qualitative implications. Therefore, we opt here for a price-independent
reservation utility which we normalize to zero solely for computational convenience.
After a logarithmic transformation of the form (1), this household decision mechanism
proves equivalent to the maximization of a utilitarian social welfare function for the
household, where the bargaining weights become welfare weights.

Second, although maximization of the Nash product (1) describes the way in which
the household reaches an efficient collective decision, it would be a grave mistake to
attribute further meaning to the maximal value of (1) and to changes of it. Normative
statements always refer to individuals, either one by one, identifying gainers and losers,
or as constituents of society. Pareto-optimality and Pareto-improvements are defined
in the standard fashion.

For welfare comparisons between societies which differ only with respect to the
bargaining power of individuals in households, one can rely on a modified version of
the first welfare theorem. With the possibility of multi-person households and intra-
household externalities, the crucial property of the classical version of the first welfare
theorem, local non-satiation needs to be adapted. The modified property stipulates
that each household’s efficient choices under its budget constraint lie on the household’s
“budget line”. Haller (2000) calls this property budget exhaustion. He shows the
validity of the first welfare theorem for economies with the budget exhaustion property.

Except for subsection 3.2 the economies and corresponding examples in the paper
all have unique competitive equilibria and possess the budget exhaustion property.
Therefore, equilibrium allocations are Pareto-optimal and comparative statics moves
the economy from one Pareto-optimum to another one. Consequently, if a household
member gains from a shift in bargaining power, then someone else inside or outside the
household must lose.

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