II) Demand Functions

Question 1

What is the Marshallian demand function?

Answer 1

By maximizing utility over the budget set, the consumer chooses the quality consumed of each good i, g_i as a function of the prices p and the income level x.

Question 2

What does mean that the Marshallian demand function is homogeneous of degree zero in prices and incomes?

Answer 2

g_i(λp, λx) = g_i(p, x)

It reflects the absence of money illusion: the nominal price doesn’t influence consumption.

Question 3

What will happen to the vector of consumption when x changes?

Answer 3

it also changes through the income expansion path.

Question 4

When x changes, what happen to every good i?

Answer 4

The consumption of every good i changes.

This is the Engel curve of good i.

Question 5

If x increases, what will happen to at least one consumption?

Answer 5

One consumption at least must increase

In the other way around when x go down.

Question 6

What are the different categories of goods?

Answer 6

• Normal
  
  • Luxury
  • Necessities
• Inferior

Question 7

What happent to a normal good when x increases?

Answer 7

The consumption increases.

Question 8

What happens to an inferior good when x raises?

Answer 8

The consumption decreases.

Question 9

What is the characteristics of luxury goods?

Answer 9

The consumption increases faster than x.

Question 10

What is the characteristic for necessities?

Answer 10

The consumption increases more slowly x.

Question 11

What the utility if elasticty?

Answer 11

It is a quatitative estimation of the effect of a change of x on consumption.

Question 12

On which parameters depends the elasticity?

Answer 12

1. Change of x (x-x’)
2. The unit in which x and consumption are measured.

Question 13

How is analyzed an elasticty?

Answer 13

How one percent of change of income affects the consumption of the good in percentage.

Question 14

What’s the formula for elasticity?

(elasticity of consumption with respect to income)

Answer 14

Question 15

What is the elasticity for the different types of goods?

Answer 15

• inferior: η_i(p,x)<0
• normal: η_i(p,x)>0
  
  • luxury: η_i(p,x)>1
  • necessity: 1>η_i(p,x)>0

Question 16

What are the 2 effects if a price p_i rises?

Answer 16

• 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.

Question 17

What is a Giffen good?

Answer 17

Income effect positive and greater than ⎟substituion effect ⎪

↑ p may result in ↑d

Question 18

What’s the formula fo the elasticity of prices on demand?

Answer 18

Usually, the demand function is decreasing and

e_i(p,x) < 0

Question 19

What if ↑p_j => ↑q_i ?

Answer 19

i and j are substitutes.

Question 20

What if ↑p_j => ↓q_i ?

Answer 20

Goods i and j are complements.

Question 21

What is the formula for cross price elasticity?

Answer 21

Question 22

What happen to e_ij if the 2 goods are:

Substitutes?

Complements?

Answer 22

Substitutes: e_ij > 0

Complements: e_ij < 0

Question 23

What does mean the consumer surplus?

Answer 23

WHen a consumer buys units of a products, he “gains” the price of all the units above. This is because of marginal costs.

Question 24

What do we do to obtain the market demand?

Answer 24

We add all the individual demands for this market.

Question 25

When are preferences homothetic?

Answer 25

If along any ray, the MRS between any pair of goods remains constant.

MRS_ij(λq₁, λq₂) = MRS_ij(q₁, q₂) For any q₁, q₂, λ.

Question 26

What is the other name for homothetic preferences?

Answer 26

The MRS is homogeneous of degree zero.

Question 27

What do look like homothetic preferences?

Answer 27

Question 28

How is denoted an optimal consumption of q?

Answer 28

q^*

Question 29

What happen to the income expansion path if the preferences are homothetic?

Answer 29

It is a straigh line.

Question 30

What happen to the Marshallian demands if preferences are homothetic?

Answer 30

They are linear in income.

=> The sum of demand only depend on the sums of income. The agregation of demands is exact.

Question 31

The agregation of demand is exact only if?

Answer 31

The marshallian demands are linear in income.

Question 32

What are the other preferences that satisfies the exact agregation of demand?

Answer 32

Homothetic preferences, pure substitutes or pure complements.

Question 33

What is indirect utility?

Answer 33

It is the maximal utility.

Question 34

What is the particularity of indirect utility?

Answer 34

It is homogeneous of degree zero.

Question 35

What are the 2 effects of a raise of prices on consumption?

Answer 35

Substitution effect (negative)

Income effect (negative or positive)

Question 36

Summary of Chapter 2:

Answer 36

Question 37

Summary of Chapter 2 2:

Answer 37