Title: Microeconomics / Q1 / lecture8

Q: Aggregate Demand
A: The sum of the individual demands of all consumers in an economy
x(p, w) = xi(p, wi(p, w)) is generated by a positive representative consumer with an aggregate indirect utility function

Q: under what conditions can we “simplify” the aggregate
demand function x(p, w1, w2, ... wI) so that instead of
being a general function of the entire distribution of
wealth it is a function of only prices and total wealth:
A: For this (“simplification”) property to hold in all
possible situations, aggregate demand must be identical
for any two distributions of wealth that have the same
total wealth. That is, for two distributions of wealth,

Q: Redistirbution of wealth
A: No change in cummulative weatlh when redistribution!
For this to be true:
Then:
This works if and only if a redistribution of wealth between any two people, i and j, has no effect on aggregate demand. Therefore the partial w of person i and the partial of w to person j are equal.

Q: What restrictions on preferences lead to demand functions that have this characteristic?
A: Two examples are: 1. Everyone has the same homothetic preferences; and 2. Everyone has quasi-linear preferences for the same good. These are special cases of a more general assumption about preferences:

Q: How is the Gorman form restrictive?
A: The requirement that changes in the distribution of
income will have no effect on aggregate demand is quite
unrealistic

Q: can aggregate demand be modeled in a less restrictive (more realistic) way by (other than the Gorman form) allowing for some other (aggregate) variables in the aggregate demand function?
A: One possibility is the variance of the distribution of wealth.
Another approach is to model aggregate demand as a
function of only prices and average (or total) wealth,
which implicitly puts limits on the possible distributions
of wealth that could occur in the economy.

When can aggregate demand be written as a function of only prices and aggregate wealth?

Q: When can we measure aggregate welfare using the aggregate demand function and the welfare measurement methods discussed in Lecture 7 that were used for individual consumers?
A: 1. make assumption of how wealth is distributed (For each individual i, the sum of w_i(p,w) = w))
2. Demand is continuous and homogeneous degree 0, and satisfy Walras law

A positive representative consumer

Q: Bergson-Samuelson social welfare function
A: a social welfare function that aggregates the welfare of each member of the population into an aggregate welfare function for society as a whole.

Q: social indirect utility function
A: denoted by v(p, w). The following proposition shows that this social
indirect utility function can be used to “produce” a
positive representative consumer for the aggregate
demand function.

normative representative consumer

Q: Bottom Line on representative consumers
A: If a normative representative consumer
exists, then a positive representative consumer exists, but
not vice versa. For a normative representative consumer to
exist, you need to assume (impose) a social welfare function
and that a social planner distributes wealth to maximize it.

Q: There are two “special cases” where
rational individuals can form households for which
rational behavior will hold:
A: Everyone in the household has the same preferences; 2. A “dictator” makes all
household decisions. These cases are called “unitary
models”. There is a lot of evidence contradicting the
unitary model (Alderman et al., 1995). Thus, economists
have developed models of intra-household allocation.
This lecture presents one of the first models, by Browning,
et al (1994).

Q: exclusive good
A: Goods that are used
by only one person in the household, and we know which
person it is.

Q: assignable private good
A: one for which we have information on consumption at
the individual (as opposed to the household) level.