Example 2.
Here consumer 1 benefits from more bargaining power to the detriment of consumer 2.
Consumer 3 either gains or loses. Household h is still endowed with ωh = (1, 0). But
now each member i = 1, 2 has Cobb-Douglas preferences with utility representation
ui(xi, yi) = xiγiyi1-γi , 0 < γi < 1.
The household maximizes
U au 2-α = ( X11 y 11-γ 1 )α ( x Y2 y1-γ2 ¢1-α
αγ1 (1-α)γ2 α(1-γ1) (1-α)(1-γ2)
= x1 x2 y1 y2 .
Again, α and 1-α lend themselves as measures of relative bargaining power of consumer
1 and consumer 2, respectively.
Household k has the single member 3, with the same consumer characteristics as before.
We obtain:
Fact 2 A shift of bargaining power from consumer 2 to consumer 1 benefits consumer
1 and harms consumer 2, who ends up consuming less of both commodities.
In Example 2 there is more substitutability in the economy than in Example 1.
Example 3 exhibits less substitutability than Example 1, because the preferences of
consumer 3 will be altered from Cobb-Douglas to Leontieff. It turns out that the lack
of substitution by consumer 3 necessitates a major price adjustment to re-equilibrate
the market after bargaining power within household h has shifted. As a result, we
observe a drastic price effect: When bargaining power within their household changes,
the equilibrium utilities of consumers 1 and 2 are moving in the same direction.
Example 3.
Here a shift of bargaining power from consumer 2 to consumer 1 benefits both con-
sumers to the detriment of consumer 3. This example is identical with Example 1,
except that consumer 3 now has Leontief preferences with utility representation
u3(x3, y3) = min(x3, y3).
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