The Consumer Problem

1
The Consumer Problem and the Budget
Constraint Overheads
2
The fundamental unit of analysis in consumption
economics is the individual consumer
3
The underlying assumption in consumption analysis
is that all consumers possess a preference
ordering
which allows them to rank alternative states of
the world.
4
The behavioral assumption in consumption analysis
is
that consumers make choices consistent with their
underlying preferences
5
The main constraint facing consumers in
determining which goods to purchase and consume is
the amount of income that they can spend
This is called the budget constraint
6
The Consumer Problem
The consumer problem is to maximize
the satisfaction that comes from the consumption
of various goods
subject to the amount of income
the consumer has to spend.
7
The Consumer Problem
satisfaction
Maximize
subject to
income
8
Definition of the budget constraint
A consumers budget constraint identifies
which combinations of goods and services
the consumer can afford with a limited budget,
at given prices
9
Notation
Income - I
Quantities of goods - q1, q2, . . . qn
Prices of goods - p1, p2,. . . pn
Number of goods - n
10
Budget constraint with 2 goods
11
Budget constraint with n goods
12
Example
Income I 1.20
q1 Reeses Pieces
q2 Snickers
p1 price of Reeses Pieces 0.30
p2 price of Snickers 0.20
13
Graphical Analysis of Budget Set
5
Reeses
4
3
2
1
0
0
1
2
3
4
5
6
7
Snickers
14
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
15
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
4 Reeses -- 0 Snickers
Cost 4 x 0.30 0 x 0.20 1.20
16
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
0 Reeses -- 6 Snickers
Cost 0 x 0.30 6 x 0.20 1.20
17
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
2 Reeses -- 3 Snickers
Cost 2 x 0.30 3 x 0.20 1.20
18
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
2 Reeses -- 1 Snickers
Cost 2 x 0.30 1 x 0.20 .80
19
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
3 Reeses -- 3 Snickers
Cost 3 x 0.30 3 x 0.20 1.50
20
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
There are many different combinations
Only some combinations are feasible
21
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
Some combinations exactly exhaust income
22
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
We say these points lie along the budget line
23
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
Or on the boundary of the budget set
24
Graphical Analysis of Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
Points inside or on the line are affordable
25
Graphical Analysis of Budget Set
Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
Points outside the line are not affordable
26
Slope of the Budget Constraint - q1 h(q2)
So the slope is
-p2 / p1
27
Graphical Analysis of Budget Set
5
q1
4
?q1 2
3
2
1
0
0
1
2
3
4
5
6
7
q2
3 Snickers -- 2 Reeses
0 Snickers -- 4 Reeses
28
Graphical Analysis of Budget Set
5
q1
4
?q1 2
3
2
1
0
0
1
2
3
4
5
6
7
q2
3 Snickers -- 2 Reeses
0 Snickers -- 4 Reeses
29
Numerical Example
I 1.20, p1 0.30, p2 0.20
30
Budget Constraint - 0.3q1 0.2q2 1.20
q1
5
4
Not Affordable
3
2
Affordable
1
q2
5
6
7
4
3
2
1
31
Budget Constraint - 0.3q1 0.2q2 1.20
q1
Double prices and income
5
Budget Constraint - 0.6q1 0.4q2 2.40
4
3
2
Not Affordable
1
Affordable
q2
5
6
7
4
3
2
1
32
Budget Constraint - 0.3q1 0.2q2 1.20
q1
Double p1 from 0.3 to 0.6
5
Budget Constraint - 0.6q1 0.2q2 1.20
4
3
2
1
Affordable
q2
5
6
7
4
3
2
1
33
Just to review how to solve
Budget Constraint - 0.6q1 0.2q2 1.20
34
Budget Constraint - 0.3q1 0.2q2 1.20
q1
Raise p2 from 0.2 to 0.3
5
Budget Constraint - 0.3q1 0.3q2 1.20
4
3
2
Affordable
1
q2
5
6
7
4
3
2
1
35
Change in Income
Budget Constraint0 - 0.3q1 0.2q2 1.20
36
Change in Price of Good 1 (price rises)
Budget Constraint0 - 0.3q1 0.2q2 1.20
Budget Constraint1 - 0.6q1 0.2q2 1.20
37
Change in Price of Good 1 (price falls)
Budget Constraint0 - 0.3q1 0.2q2 1.20
Budget Constraint1 - 0.24q1 0.2q2 1.20
38
Change in Price of Good 2 (price rises)
Budget Constraint0 - 0.3q1 0.2q2 1.20
Budget Constraint1 - 0.30q1 0.30q2 1.20
39
The End
40
Graphical Analysis of Budget Set
Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2
41
Graphical Analysis of Budget Set
Budget Set
5
q1
4
3
2
1
0
0
1
2
3
4
5
6
7
q2