Bargaining Power and Equilibrium Consumption

a specific sociological group, with added emphasis on inter-household or spill-over ef-
fects. We distinguish between “first members” and “second members” of households.
With particular consumer characteristics, spill-overs are absent: The effects of a change
of bargaining power within a household are confined to that household. With differ-
ent consumer characteristics, spill-overs can occur exactly as described earlier. For
instance, a first member of a household benefits from an increase in own bargaining
power, but loses if ceteris paribus first members of other households gain more bargain-
ing power. In Section 6, we offer concluding remarks.

2 General Equilibrium Model

We consider a finite pure exchange economy. The main departure from the traditional
model is that a household can have several members, each with their own preferences.

Fixed Household Structure.

The population is divided into finitely many households h = 1, . . . , n, with n ≥ 2.
Each household h consists of finitely many members i = hm with m = 1, . . . , m(h),
m(h) ≥ 1. Put I = {hm : h = 1, . . . , n; m = 1, . . . , m(h)}, the finite population of
individuals to be considered.

Commodities, Endowments, and Individual Preferences.

The commodity space is IR' with ' ≥ 1. Household h is endowed with a commodity
bundle ω_h ∈ IR', ω_h > 0. The aggregate or social endowment is ω = hω_h ω_h. A generic
individual i = hm ∈ I has:

• consumption set Xi = IR+;

• preferences £ i on the allocation space X ≡ ∏_j∙∈_j Xj represented by a utility
function U_i : X -→ IR.

The consumption bundle of a generic individual i is denoted by x_i. Let x = (x_i), y =
(yi) denote generic elements of X. For h = 1, . . . , n, define Xh = ^Qm_m⁽₌^h₁⁾ Xhm with
generic elements xh = (xh1, . . . , x_hm(_h)). If x ∈ X is an allocation, then for h = 1, . . . , n,
household consumption is given by x_h = (x_h1 , . . . , x_hm(_h) ) ∈ X_h.

<<   2   3   4   5   6   7   8   >>

More intriguing information