Title: Microeconomics / Q1 / lecture2

Q: commodity vector
A: commodity bundle, is denoted by x.  It is a “list” of the individual commodities
in a specific bundle.  It is complete in
that it indicates how much of all L commodities are in the bundle

Q: commodity space
A: all the consumption
bundles that the consumer could possibly consume, subject to physical
constraints

Q: consumption set
A: Denoted by X. Subset of the consumption space. Whose elements
are all the consumption bundles that the consumer
could possibly consume, subject to physical constraints
1. it is convex

Q: budget constraint
A: p∙x = p_1x_1 + p_2x_2 + … + p_Lx_L ≤ w
1.  The L commodities (goods and services) are all traded in a market at given prices, denoted by the vector p.
2.  These prices cannot be influenced by any individual consumer; that is, all consumers are price takers.

Q: Walrasian budget set
A: also known as the competitive budget set), which can be denoted as
is the set of all feasible consumption bundles for the consumer who faces prices p and has a wealth of w. A formal definition of the consumption bundles that the consumer can afford.
It is also convex.

Q: consumer’s problem
A: Given prices p and wealth w, choose a consumption bundle x from B_p,w

Q: Walrasian demand
correspondence, x(p, w) (Marshallian demand function)
A: a relationship that assigns a set of chosen consumption bundles for every possible value of p and w. also called the Marshallian demand function. we will usually assume that there is a single unique consumption bundle for each (p, w) pair
1. Homogeneous degree zero
2. satisfies Walras' law.

Q: two assumptions about the Walrasian
demand correspondence
A: homogenous of degree zero and it satisfies Walras’ law

Q: homogenous of degree
zero
A: The intuition here is that the consumer does not suffer from “money illusion”; if prices and wealth increase or decrease by the same proportion, then there is no reason to change his or her consumption bundle.  More formally, such a change in prices and wealth does not change the consumer’s feasible consumption bundles (that is B_p,w = B_αp,αw) and thus his or her choice should not change.
Important:

Q: Walras’ law
A: The Walrasian demand correspondence satisfies Walras’ law for any α > 0, x(αp, αw) = x(p, w) for any values of p and w.
the consumer spends all the wealth that he or she has, which is reasonable to assume for most people (most people do not reach a “satiation point”).  It is sometimes called the “adding up restriction”.  This assumption should be interpreted flexibly.

Q: Engel function denoted by x([latex]$\bar{p}$[/latex], w)
A: illistrates wealth effects (often called income effects). Let’s fix prices at [latex]$\bar{p}$[/latex] and see how the
consumer’s demand for each good changes as wealth increases for the entire vector of goods, x.

Q: wealth expansion path (also known as the income expansion path)
A: The changes in demand for all L goods as w increases.

Q: wealth effect (also known as the income effect)
A: derivative of the Engel function for good ℓ, ∂x_ℓ( , w)/∂w

Q: normal good
A: the price-wealth pair (p, w) if ∂x_ℓ(p, w)/∂w ≥ 0

Q: inferior good
A: price-wealth pair (p, w), which is defined as if ∂x_ℓ(p, w)/∂w < 0

Q: price effects
A: how demand changes as prices vary

Q: Offer Curve
A: shows how the demand for two goods changes as the prices change

Q: Elasticity
A: percentage change in the demand for good ℓ in response to a (small) percentage change in the price of good k (which could be good ℓ) or wealth.
This form reflects the homogeneity assumption: the same percentage increase in prices and wealth will lead to no change in consumption.

Q: Cournot aggregation condition
A: If the Walrasian demand function satisfies Walras’ law, then for all p and w
It is the differentiating the expression p·x(p, w) = w with respect to prices.
Matrix notation: p·D_px(p, w) + x(p, w)^T = 0^T
^
1.  Total expenditure cannot change in response to a change in prices (you need to cut back on something when the price of good k increases).
2.  Total expenditure must change by an amount equal to any change in wealth.

Q: Engel aggregation condition
A: differentiating p·x(p, w) = w with respect to w.
p·D_wx(p, w) = 1
1.  Total expenditure cannot change in response to a change in prices (you need to cut back on something when the price of good k increases).
2.  Total expenditure must change by an amount equal to any change in wealth.

Cournot and Engel Elasticity functions

Q: wealth expansion path
A: The changes in demand for all L goods as w increase