Aggregation

Question 1

For what types of preference does the Wealth Expansion path are parallel and stright?

Answer 1

1) Identical homothetic preference

2) quasilinear preferences (with the same numraire)

Question 2

A set of consumers has parallel and straight wealth-expansion paths iff …

Answer 2

Every preference admits an indirect utility of the Gorman Form with identical wealth coefficient:
vi = ai(p) + bi(p)*w

Question 3

The aggregate demand satisfies the WARP iff…

Answer 3

for x(p1, w1) ≠ x(p2,w2) and p1x(p2,w2) ≤ w1
Then
p2x(p1,w1) > w2

Question 4

What is the uncompensated Law of the Demand?

Answer 4

(p2 - p1)*[x(p2, wi) - x(p1, wi)] ≤ 0

Question 5

Uncompensated Law of the Demand implies…

Answer 5

Compensated Law of the Demand

Question 6

Compensated Law of the Demand is equivalent to

Answer 6

WARP

Question 7

If xi(p, w) satisfies Uncompensated Law of the demand then

Answer 7

Dp xi(p,w) is negative Semi-deinite

Question 8

If Dp x(p,w) is negative definite then

Answer 8

It satisfies Uncompensated Law of the Demand

Question 9

If each individual demand satisfies ULD, then

Answer 9

The aggregate demand satisfies ULD

Question 10

If the preference is homothetic then

Answer 10

Satisfies ULD

Question 11

If all preferences have utility function in the form v(p,w) in the Gorman form, then

Answer 11

There exists a utility function that yields aggregate demand as the solution to the UMP

Question 12

When a positive representative consumer exists?

Answer 12

if there is a rational preference that generates a Walrasian demand function that coincides with the aggregate demand

Question 13

What is a social welfare function?

Answer 13

is a function W that assigns a utility value to each possible vector (u1,…ui) of utility leves for the i consumer in the economy

Question 14

The optimal wealth distribution solves:

Answer 14

max w1,…,wi {W(v1(p,w1),…, vi(p,wi)) | Σ wi ≤ w}

Question 15

What is a normative representative consumer

Answer 15

If the wealth allocation used to cnstruct the aggregate demand solves the optimal weath distribution problem

Question 16

If each indirect utility is in the Gorman Form, then

Answer 16

Any wealth distribuition rule is optimal for the utilitarian social welfare function Σui
Moreover preferences ofthe associate representatice consumer are indepndent of the choice of w

Question 17

Como podemoes escrever a ULD em formato diferencial?

Answer 17

dp * dx ≤ 0

Question 18

Apresente a derivada total de x

Answer 18

dx = Dpx(p,w)dp + Dwx(p,w)dw

Question 19

No caso da Lei da Demanda não compensada qual o valor do diferencial total de x?

Answer 19

dx = Dpx(p,w)dp

Uma vez que não há alteração de w

Question 20

Apresente o teorema do valor médio

Answer 20

existe c ∈(a,b) tal que

b-a) h’(c) = h(b) - h(a

Question 21

Quando a demanda agregada pode ser escrita como função da riqueza agregada?

Answer 21

Quando a utildade indireta está no formato de Gorman

Question 22

O que é o formato de Gorman?

Answer 22

v(p,w) = a(p) + b(p)*w

Question 23

Quando existe um agente representativo?

Answer 23

Quando as utilidades indiretas estão no formato de Gorma e apresentam o mesmo coeficiente de riqueza

Question 24

No caso de indvíduos idênticos exste um agente representativo?

Answer 24

Sim