6 Concluding Remarks
The current analysis is confined to a general equilibrium model of a pure exchange
economy with a fixed household structure and Nash-bargained household decisions
for a select two-person household. General comparative statics as well as numerical
examples lend support to the following conclusions. As a rule, a consumer benefits
from more bargaining power at the expense of her fellow household member and the
other consumer(s). However, in a closed economy, a shift of bargaining power within
a significant number of two-person households may cause drastic price effects. As a
consequence, both members of such a household may benefit from or both members
may be harmed by a shift of internal bargaining power. In exceptional cases, it can
happen that a household member is unaffected.
The current analysis further shows that the aggregate equilibrium consumption of
a household can be positively affected by a shift of internal bargaining power. This
suggests the possibility that a sophisticated household might succeed in an attempt
to manipulate the market outcome, not by misrepresenting endowments or individual
preferences, but by misrepresenting the internal bargaining power. To illustrate this
novel way of manipulation, which is not yet documented in the literature, let us re-
consider Example 2. Suppose the household pretends that the bargaining power of the
first consumer is higher than it actually is and they submit the corresponding excess
demands to the market. If γ1 > γ2, i.e. if the first good is relatively more important
to the first consumer, they will end up with a higher aggregate amount of the first
good and the same amount of the second good in equilibrium. Whether or not both
gain from a successful manipulation depends on the internal distribution of aggregate
consumption. If they divided the goods in accordance with their pretended bargaining
power, put their money where their mouth is, then consumer 1 would gain and con-
sumer 2 would lose from manipulation. If they divide the goods according to the true
bargaining power — which fixes a proportional sharing rule for each of the goods —
then both gain from manipulation. As noted before, quasi-linear preferences rule out
spill-overs and, consequently, this kind of manipulation.
To reiterate, the current model assumes a fixed household structure and pure ex-
change. Removing any of these restrictions leads to a host of new important issues,
which are left to future research.
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