Bargaining Power and Equilibrium Consumption

The characteristics of household k are as in the previous example, that is the endow-
ment is ω3 = (0, 1) and the utility representation is

u3 (x3, y3) = x₃^1/2y₃^1/2.

Since the aggregate demand function of household h coincides with the demand function
of consumer 0 in Example 0, the equilibrium quantities are

p = 2(1 - α)^, ŋ;

cÎ = (α, 0),
c2 = (о, 2 ),
^c з = (^{1 - α}, 2 ) ∙

Hence as asserted consumer 1 benefits from more bargaining power, to the detriment
of consumer 3. Consumer 2 is unaffected.                                         g

In the example, the first good becomes more valuable to the two-person household
as the bargaining power of the first consumer increases. This boosts the equilibrium
price of the first good and the income of the two-person household endowed with
the first good. The household has become richer both in nominal and real terms.
Since the expenditure on the second good remains constant, the second consumer is
unaffected. But the increase in the residual income to be spent on the first good more
than compensates for the higher price: consumer 1 is better off as a consequence of her
increased bargaining power. As for consumer 3, his nominal income derived from the
possession of the second resource remains constant. Therefore, he has become poorer,
has less purchasing power.

From consumer 2’s perspective, if bargaining power shifts towards her and prices
are fixed, then her welfare is increased. But the resulting price variation offsets her
gain. That consumer 2 is unaffected by a change in bargaining power seems to be
caused by limited substitutability within the two-person household. This is confirmed
by the next example where enhanced bargaining power of consumer 1 translates into
improved welfare for this consumer and welfare losses for consumers 2 and 3.

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