Bargaining Power and Equilibrium Consumption

(i) x_h ∈ EB_h(p) for h = 1, . . . , n, and

(ii) ^P_ixi =ω.

Thus, in a competitive equilibrium among households (p; x), each household makes
an efficient choice under its budget constraint and markets clear. Efficient choice by
the household refers to the individual consumption and welfare of its members, not
merely to the aggregate consumption bundle of the household.

Nash Bargaining. An efficient household choice under a budget constraint may
be the outcome of maximizing a function of the form

Wh(xh) = Sh(Uh1(xh), . . .

^, Uhm(h) (xh))^,

subject to the budget constraint. A special case thereof is a Nash-bargained house-
hold decision. In this case, Sh assumes the form

m(h)

Sh(Uh1,..., Uhm(h)) = ^YUh^αm^hm,                         (1)

m=1

with the provision that αhm ≥ 0 and Uhm ≥ 0 for m = 1, . . . , m(h). The bargaining
weight α_hm measures the relative bargaining power of individual i = hm within
household h. In the sequel, we shall concentrate on two-person households, i.e. m(h) =
2. We assume αh1, αh2 > 0 and αh1 + αh2 = 1.

The assumption of Nash-bargained and, hence, efficient household decisions serves
us well for the present inquiry into the consequences of shifts of bargaining power.
The empirical question of whether collective household decisions are Nash-bargained,
indeed, has gotten a fair amount of attention, in particular in the debate between
Chiappori (1988b, 1991) on the one side and McElroy and Horney (1981, 1990) on the
other side (see Bergstrom (1997) for discussions). There has been a growing number of
empirical studies performing empirical tests of the collective rationality approach which
nests Nash bargaining models as particular cases (Udry (1996), Fortin and Lacroix
(1997), Browning and Chiappori (1998), Chiappori, Fortin and Lacroix (2002), among
others).

Two qualifying comments are warranted. First, the interpretation of the maximands
of Sh as Nash-bargained outcomes assumes that for each member of a multi-person

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