Bargaining Power and Equilibrium Consumption



(1 - αh) TT 2^ ʌ Uh2(xh2) - λh = 0

Uh2 (xh2 )

Using the budget constraint and the first-order conditions yields

1 ττ' TU ʌ (л      2Jw2(whP1 + wh - xh 1 P1)      n

αh Uh ((x 1 ) Uh 1( xh 1)   (1   αh ) U hDlrD +w2   11 np p1   0

Uh1(xh1)                     Uh2whP1 +wh - xh1 P1

or

1 αh F1 (xh 1) = F2 (w1 P1 + wh - xh 1P1) ∙ P1                 (24)

1 - αh 1    1       2                     1

where F1 ln Uh1 and F2 ln Uh2 . F10 and F20 are strictly decreasing functions.
Hence, for a given
P1 , a higher (equal) αh requires a higher (identical) consumption of
good 1 to preserve (24). This shows (i) and (ii).

By the same argument, an increase of αh raises ceteris paribus the aggregate de-
mand for good 1. Further examination of (24) shows that for fixed bargaining power
parameters, aggregate demand for good 1 is a decreasing function of
P1. Consequently,
if only
αh is increased, then the equilibrium price Pb1 rises and the equilibrium con-
sumption of all first members except
h1 is reduced. Finally, market clearing implies
that the equilibrium consumption of
h1 goes up. This shows (iii) and, by symmetry,
(iv).

31



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