Transcript ndifference Curve Analysis

Consumption
Country pct
Australia
Banglad.
Brazil
Canada
Egypt
Germany
Japan
Thailand
U.K.
U.S.
61.9
67.3
61.9
56.7
74.2
57.8
62.4
56.1
65.8
67.8
GDP
21240
1590
7300
20000
1270
24920
33780
2110
22790
34100
amount
13147
1070
4519
11340
942
14403
21078
1183
14995
23119
Country
GDP
per
Capita
Health
Expenditur
e per
Capita
Life
Expec
t.
Average
Years in
Poor
Health
Prevalence of
HIV
Albania
3600
144
72
9.4
0.01
Bangladesh
1590
57
61
8.2
0.02
Brazil
7300
482
67
8.4
0.57
China
3920
176
70
7.4
0.07
660
27
42
8.6
10.63
24920
2642
77
6.5
0.10
800
22
47
11.5
5.06
8010
368
66
6.6
0.18
34100
4433
77
6.9
0.61
Ethiopia
Germany
Nigeria
Russian Fed.
United
States
Source: World Bank website,
http://www.worldbank.org/data/databytopic/class.htm, on April 29, 2002.
Notes: GDP (for 2000) is via the purchasing power parity method; health care expenditures per capita were found by applying the 1990-98 average percentage of GDP spent
on health care; life expectancy is estimated from birth; years spent in poor health and HIV are World Bank health risk indicators; HIV figures represent the percent of adults
estimated to carry the virus.
Indifference Curve Analysis
1. Develop indifference curves
2. Develop budget constraint
3. Some basic analysis: a. changes in
prices; b. changes in income;
c. the Engels Curve
4. The Food Stamps Problem
Indifference curve:
A collection of points for which the
consumer is indifference between
each of them and some reference
point.
Typically shown in the context of a two
good world on a two-dimensional graph.
.
OG
Indifference
curve
.B
D
A
.
C
.E
.F
Food
What sense does the indifference
curve make? A heuristic approach.
OG
Food
The c onsumer’s preference map is
the set of all his indifference c urves.
Here several m ore are shown
Determinants of Consumer Preferences
Experience
Demonstration effects
Advertising
Conspicuous consumption
The axiomatic approach to indifference
curves is a search for a minimum set
of assumptions regarding consumer
behavior through which to generate
indifference curves.
Standard axioms:
1. More is preferred to less—nonsatiation
2. Completeness—all points in a relation
3. Transitivity– A  B; B  C;  A  C
Og
A
.C
B
U1
U2
.
.
Food
Why indifference curves
cannot cross (and still obey
the axioms for preferences).
The marginal rate of substitution and the
shapes and kinds of indifference curves.
Perfect substitutes
Perfect complements
Steepness, what does it mean
Do they shift or stay in place?
OG
U1
B
A
U1
Food
The axioms imply that indifference
curves must be unbroken, ie
continuous.
These two sets of indifference curves represent people
who differ in their relative willingness to trade
food for medicine. Which one is hungry? Careful.
The budget equation:
B = pogOG + pfF
OG = B/pog – pf/pogF
Meaning: The budget equation will depict
a curve in OG-Food space that is downward
sloping (note: its derivative –pf/pog is
negative).
OG
Budget constraint
B/p f
Food
If budget is B, then the most OG
possible to buy is B/p o, and similarly
the most Food possible is B/p f . The
budget constraint connects these
two intercepts.
OG
A
B
C
Food
As the price of Food falls, the budget
constraint shifts from A to B and then
to C.
OG
Food
C
B
A
As income increases, the budget
constraint shifts outward parallely
OG
. E
UE
Budget
line
Food
Consumer equilibrium
in indifference curve analysis
Utility, a quantitative measure of satisfaction.
a. utility is constant along an indifference curve.
OG
Indifference
curve
.B
.
D
A
.
C
.E
.F
Food
What sense does the indifference
curve make? A heuristic approach.
b. higher indifference curves yield higher utility.
c. utility is treated as ordinal in most cases
“ordinal” measures are like 1st, 2nd, 3rd, etc
“cardinal” numbers are like 1.0, 3.6, 7.1 etc
(utility numbers are really “cardinal but arbitrary”)
Jeremy Bentham and Utilitarianism
1748-1832.
For Bentham, utility was:
1. Metric (also called Cardinal,
remember--today we think its ordinal).
2. Interpersonally comparable.
Bentham was extremely optimistic in
these beliefs.
If utility were metric, then society could
correctly identify and measure exactly how
happy or well-off America was, or Detroit,
or this classroom. It would be scientific.
Nevertheless his utilitarianism proved useful
in bringing reforms:
1. Prisons were made more humane.
2. Insane asylums were made more humane.
Who was Jeremy Bentham? And, what
does he look like?
Notice I said "what does he look like.
Note: Although Bentham lived and wrote
back in the 18th Century you can see
what he looks like. Notice I said he.
Jeremy
Bentham
as he still
appears in a
glass case in
University
College of
London, which
he helped to
found.
Applying calculus to find an expression
for the slope of the other curve, the
indifference curve:
OG/F = - (U/F) /(U/OG)
or, using an equivalent notation:
OG/F = - MUf/ MUog
OG
. E
UE
Budget
line
Food
Consumer equilibrium
in indifference curve analysis
At an equilibrium, tangency implies that
the slope of the budget constraint equals
the slope of the indifference curve: Hence,
Consumer equilibrium requires that
pf/pog = MUf /MUog
or
MUf /pf = MUog /pog
In words: The marginal utility per dollar
of expenditure must be equal for each good.
OG
E1
E3
.
E2
.
.
Food
F1
F3
As income increases, Food demanded
increases. This is shown in indifference
curve analysis as successive, new
equilibria.
Income
Engel’s Curve
F1
F2
F3
Food
Consider the shape of the Engels
Curve as related to the income
elasticity of demand.
OG
B
A
Food Stamps Problem
budget constraint
Food
0
C
D
When the eligible person is given AB
worth of Food Stamps, this extends
her budge constraint to ABD.
OG
Food Stamps Problem
budget constraint
B
A
E’
.
E
.
Food
0
D
C
A case of a Food Stamps
recipient for whom the Stamps
could just as well have been
in cash (rather than “in-kind ”).
OG
.
E’’
B
A
Food Stamps Problem
Ucash budget constraint
UFStamps
.E
Food
0
D
C
A case of a Food Stamps
recipient for whom the Stamps
could just as well have been
in cash (rather than “in-kind ”).