Although the actual h is a natural number we can treat equilibrium consumption levels
as functions of real-valued parameters and obtain
∩γ*
dxh 1
∂h
dyh 2
∂h
for h = 1,... ,h;
for h = 1,... ,h;
χh'h 1
∂h
dyh 2
∂h
for h = h + 1,... ,n;
for h = h + 1,... ,n.
Since xh 1 > 1, yh2 < 2 for h = 1,..., h and x*h 1 < 1 ,yh2 > 2 for h = h + 1,..., n,
we obtain the following utility changes:
N The first-members of households with bargaining power α + ε suffer a utility
loss if the same bargaining power shift occurs in other households as well. Each
member of the sociological group “first-members” benefits from an increase in
his own bargaining power but is harmed if others gain more bargaining power as
well.
N The second-members in households with bargaining power 1 - α - ε suffer a utility
loss but less so if other individuals of his sociological group experience the same.
The second member in households with power 1 - α benefits if the bargaining
power of other “second-members” decreases.
In sum, each individual of a sociological group benefits if he can increase his bar-
gaining power, but suffers if others in his group achieve the same. Each individual of
a sociological group is harmed by a decrease in its bargaining power, but less if other
individuals of his group experience the same decrease.
A complete shift of bargaining power has no effect on utilities of any individuals
since we are again in an equilibrium with no trade. Bargaining power changes are
completely offset by the corresponding shifts in equilibrium prices.
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