Bargaining Power and Equilibrium Consumption

will prevail for instance, if the economy is replicated and the same shift in bargaining
power occurs in all households that are replicas of h. This brings us back to the facts
motivating this inquiry, namely enhanced influence and more specifically increased
intra-household bargaining power of women in contemporary industrialized societies
as compared with their situation in those societies during the first half of the 20th
century or their current situation in “traditional” societies. Such changes occur in
many households and, thus, price effects may be drastic.

4 Examples

In this section, we illustrate the propositions and striking effects of the last section
by means of examples. The entire population consists of a total of three consumers,
two belonging to household h and one forming a one-person household denoted k.
To capture widespread shifts in bargaining power in a large finite population, one
can consider h as a prototype of a two-person household and k as representative of a
one-person household. Literally, one can think in terms of replica economies derived
from the basic economies under consideration, with an equal number of two-person
households like h and one-person households like k .

Throughout this section, there are always two goods: ` = 2. The second good
serves as num´eraire. The symbols x, x1 , x2 , . . . , xi , . . . denote quantities of the first
good. The symbols y, y 1, y 2,... ,y_i,... denote quantities of the second good. c* stands
for the equilibrium consumption bundle of a generic person (individual, consumer) i.
All consumers fulfill condition E2, i.e., absence of externalities.

To simplify the exposition of the later examples, we consider first an auxiliary ex-
ample of an economy consisting of two one-person households, g and k . The respective
consumers are named 0 and 3.

Example 0.

The initial endowments are ω0 = (1, 0) and ω3 = (0, 1). The utility representations are
u₀ = u₀(x₀, y₀) = x₀^αy₀^1-α, with 0 < α < 1, and

u3 = u3 (x3, y3) = x₃^1/2y₃^1/2.

After normalizing the price of the second good, market equilibrium is unique. The

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