微观经济学-清华大学课件Ch5Choice消费者最优选择

x*1
am (ab)p1
x1
Rational Constrained Choice
When x1* > 0 and x2* > 0 and (x1*,x2*) exhausts the budget, and indifference curves have no
‘kinks’, the ordinary demands are obtained by solving:
p1x1* + p2x2* = m (b) the slope of the budget constraint, -p1/p2, and the slope of the indifference curve containing (x1*,x2*) are equal at (x1*,x2*).
x2
(x1*,x2*) is interior.
(a) (x1*,x2*) exhausts the
budget; p1x1* + p2x2* = m.
x2*Βιβλιοθήκη Baidu
x1*
x1
Rational Constrained Choice
x2
(x1*,x2*) is interior .
(b) The slope of the indiff.
(a) p1x1* + p2x2* = y
curve at (x1*,x2*) equals the slope of the budget
constraint. x2*
x1*
x1
Rational Constrained Choice
(x1*,x2*) satisfies two conditions: (a) the budget is exhausted;
So the MRS is
M R S d d x x 1 2 U U / /x x 1 2 b a x x 1 1 a a x 1 b 2 x b 2 1 a b x x 1 2 .
At
(x1*,x2*),
a b
MRpS1=x-1p*1/p2
p2
x
* 2
so
(A)
Computing Ordinary Demands a Cobb-Douglas Example.
Computing Ordinary Demands a Cobb-Douglas Example.
Suppose that the consumer has Cobb-Douglas preferences.
U (x1,x2)x1 axb 2
Computing Ordinary Demands a Cobb-Douglas Example.
So the MRS is
M R S d d x x 1 2 U U / /x x 1 2 b a x x 1 1 a a x 1 b 2 x b 2 1 a b x x 1 2 .
Computing Ordinary Demands a Cobb-Douglas Example.
Chapter Five
Choice 消费者最优选择
Where Are We Doing in This Chapter?
After modeling a consumer’s choice set and his preference (represented by utility functions), we now put them together and model how he/she makes optimal choice.
Affordable bundles
x1
Rational Constrained Choice
The most preferred affordable bundle is called the consumer’s ORDINARY DEMAND at the given prices and budget. Ordinary demands will be denoted by x1*(p1,p2,m) and x2*(p1,p2,m).
U (x1,x2)x1 axb 2
is
( ) (x * 1 ,x * 2 )(a a m b )p 1 ,(a b m b )p 2.
Computing Ordinary Demands -
a Cobb-Douglas Example.
x2
U (x1,x2)x1 axb 2
x
* 2
bm
(a b )p 2
Rational Constrained Choice
When x1* > 0 and x2* > 0 the demanded bundle is INTERIOR. If buying (x1*,x2*) costs $m then the budget is exhausted.
Rational Constrained Choice
Suppose that the consumer has Cobb-Douglas preferences.
Then
U (x1,x2)x1 axb 2
M U1x U 1ax1 a1xb 2
M U2x U 2bx1 axb 21
Computing Ordinary Demands a Cobb-Douglas Example.
In mathematical terms, this is a constrained maximization problem;
In economics, this is a rational choice problem.
Rational Constrained Choice
x2
More preferred bundles
(x1*,x2*) also exhausts the budget so
p1x* 1p2x* 2m . (B)
Computing Ordinary Demands a Cobb-Douglas Example.
So we have discovered that the most preferred affordable bundle for a consumer with Cobb-Douglas preferences