Transcript Review Class Three - Sun Yat

Review Class Three
Outline
 A typical consumer will satisfy himself as
much as possible with limited resources.
 Three factors of demand:
 price, income and preference
 Now we can obtain the demand function,
and carry out the comparative statics.
Demand function
 Arithmetical method: maxux1 , x2 s.t. p1 x1  p2 x2  m
 Eg. Given the utility function that
1

 
u( x1 , x2 )  ( x1  x2 ) ,0    1
 Seek for the demand function arithmetically?
1
1
 Solution :
y  p2 1
y  p1 1
x2  
, x1  


p1 1  p2 1
p1 1  p2 1
Demand function




Key point:
Lagrangian method
Two properties:
1)
MU
p
i
MU j
 2)

i
pj
MU i MU j


pi
pj
Demand function
 Warning: the preceding two properties only hold
for the tangency case.
 In order to obtain the demand, we can also use
the geometrical tools.
 Find the highest IC in the budget set!
 Interior solution: Tangency case and kinky case
 Boundary solution:
 Some examples
Choosing tax
 The government can choose the lumpsum tax rather than quantity tax to let the
typical consumer feel better with its tax
revenue constant.
Comparative statics(1)
 How does the demand of one good
change corresponding to the change in
income with the prices constant?
 Def. income offer curve and Engle curve
 For different types of goods
 For different types of preferences (H.M)
Comparative statics(1)
 Def. normal goods(p97) and inferior
goods(p98)
 Def. luxury goods and necessary
goods(p101)
 To make the def. more clearly, we can
impose the def. of income elasticity of
demand.
Comparative statics(1)
 Arithmetical form:
dQ
I
Q
Q


dI
dI
I
dQ
 Geometrical meaning:
 The ratio of the slope of the ray and the slope of
the tangent line of some point on the Engle
curve.
Comparative statics(1)
 Strict def.
 Normal goods:
 Inferior goods:
 Luxury goods:
 Necessary goods:
 0
 0
 1
  0,1
Comparative statics(1)
 Distinguish the normal and inferior goods
in the figures of income offer curve and
Engle curve
 Distinguish the luxury and necessary
goods in the figures of income offer curve
and Engle curve
Comparative statics(1)
 Eg. Income offer curve and Engle curve of
the Quasilinear case
 Eg. Homothetic preference:
 Income offer curve and Engle curve of it
are both the rays through the origin.
Comparative statics(2)
 How does the demand of one good
change corresponding to the change in its
price with the income and price of the
other good constant?
 Def. price offer curve and personal
demand curve
 For different types of goods
 For different types of preferences (H.M)
Comparative statics(2)
 Def. of ordinary goods and Giffen goods
 Def. of substitutes and complements
 In order to describe the def. more clearly,
we can use the def. partial derivatives.
Comparative statics(2)




Ordinary goods
Giffen goods
Substitutes
Complements
Q1
0
p1
Q1
0
p1
Q2
0
p1
Q2
0
p1
 Distinguish the ordinary and Giffen goods in the
figures of price offer curve and demand curve
Comments on Exercises
 Thank you