II) Demand Functions Flashcards
What is the Marshallian demand function?
By maximizing utility over the budget set, the consumer chooses the quality consumed of each good i, gi as a function of the prices p and the income level x.
What does mean that the Marshallian demand function is homogeneous of degree zero in prices and incomes?
gi(λp, λx) = gi(p, x)
It reflects the absence of money illusion: the nominal price doesn’t influence consumption.
What will happen to the vector of consumption when x changes?
it also changes through the income expansion path.
When x changes, what happen to every good i?
The consumption of every good i changes.
This is the Engel curve of good i.
If x increases, what will happen to at least one consumption?
One consumption at least must increase
In the other way around when x go down.
What are the different categories of goods?
- Normal
- Luxury
- Necessities
- Inferior
What happent to a normal good when x increases?
The consumption increases.
What happens to an inferior good when x raises?
The consumption decreases.
What is the characteristics of luxury goods?
The consumption increases faster than x.
What is the characteristic for necessities?
The consumption increases more slowly x.
What the utility if elasticty?
It is a quatitative estimation of the effect of a change of x on consumption.
On which parameters depends the elasticity?
- Change of x (x-x’)
- The unit in which x and consumption are measured.
How is analyzed an elasticty?
How one percent of change of income affects the consumption of the good in percentage.
What’s the formula for elasticity?
(elasticity of consumption with respect to income)
What is the elasticity for the different types of goods?
- inferior: ηi(p,x)<0
- normal: ηi(p,x)>0
- luxury: ηi(p,x)>1
- necessity: 1>ηi(p,x)>0
What are the 2 effects if a price pi rises?
- Substitution effect, always negative => ↓ consumption of good i.
- Income effect: negative if the good is normal, but may be positive if the good is inferior.
What is a Giffen good?
Income effect positive and greater than ⎟substituion effect ⎪
↑ p may result in ↑d
What’s the formula fo the elasticity of prices on demand?
Usually, the demand function is decreasing and
ei(p,x) < 0
What if ↑pj => ↑qi ?
i and j are substitutes.
What if ↑pj => ↓qi ?
Goods i and j are complements.
What is the formula for cross price elasticity?
What happen to eij if the 2 goods are:
Substitutes?
Complements?
Substitutes: eij > 0
Complements: eij < 0
What does mean the consumer surplus?
WHen a consumer buys units of a products, he “gains” the price of all the units above. This is because of marginal costs.
What do we do to obtain the market demand?
We add all the individual demands for this market.
When are preferences homothetic?
If along any ray, the MRS between any pair of goods remains constant.
MRSij(λq1, λq2) = MRSij(q1, q2) For any q1, q2, λ.
What is the other name for homothetic preferences?
The MRS is homogeneous of degree zero.
What do look like homothetic preferences?
How is denoted an optimal consumption of q?
q*
What happen to the income expansion path if the preferences are homothetic?
It is a straigh line.
What happen to the Marshallian demands if preferences are homothetic?
They are linear in income.
=> The sum of demand only depend on the sums of income. The agregation of demands is exact.
The agregation of demand is exact only if?
The marshallian demands are linear in income.
What are the other preferences that satisfies the exact agregation of demand?
Homothetic preferences, pure substitutes or pure complements.
What is indirect utility?
It is the maximal utility.
What is the particularity of indirect utility?
It is homogeneous of degree zero.
What are the 2 effects of a raise of prices on consumption?
Substitution effect (negative)
Income effect (negative or positive)
Summary of Chapter 2:
Summary of Chapter 2 2:
