the consumer problem and the budget constraint overheads
DESCRIPTION
The underlying assumption in consumption analysis is that all consumers possess a preference ordering which allows them to rank alternative states of the world.TRANSCRIPT
The Consumer Problem
and the Budget Constraint
Overheads
The fundamental unit of analysis
in consumption economics is the
individual consumer
The underlying assumption in
consumption analysis is that all
consumers possess a preference
ordering which allows them to rank
alternative states of the world.
The behavioral assumption in
consumption analysis is
that consumers make choices consistent
with their underlying preferences
The main constraint facing consumersin determining which goodsto purchase and consume is
This is called the budget constraint
the amount of income that they can spend
The Consumer Problem
The consumer problem is to maximize
the consumer has to spend.
the satisfaction that comes from theconsumption of various goods
subject to the amount of income
The Consumer Problem
Maximize satisfaction
subject to
income
Definition of the budget constraint
A consumer’s budget constraint identifies
which combinations of goods and services
the consumer can afford with a limited budget,
at given prices
Notation
Income - I
Quantities of goods - q1, q2, . . . qn
Prices of goods - p1, p2,. . . pn
Number of goods - n
Budget constraint with 2 goods
p1q1 p2q2 I
p1q1 p2q2 p3q3 pn qn I
Budget constraint with n goods
Example
Income = I = $1.20
q1 = Reese’s Pieces
p1 = price of Reese’s Pieces = $0.30
q2 = Snickers
p2 = price of Snickers = $0.20
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7Snickers
Reese’s
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
4 Reese’s -- 0 Snickers
Cost = 4 x 0.30 + 0 x 0.20 = $1.20
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
0 Reese’s -- 6 Snickers
Cost = 0 x 0.30 + 6 x 0.20 = $1.20
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
2 Reese’s -- 3 Snickers
Cost = 2 x 0.30 + 3 x 0.20 = $1.20
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
2 Reese’s -- 1 Snickers
Cost = 2 x 0.30 + 1 x 0.20 = $.80
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
3 Reese’s -- 3 Snickers
Cost = 3 x 0.30 + 3 x 0.20 = $1.50
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
There are many different combinationsOnly some combinations are feasible
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
Some combinations exactly exhaust income
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
We say these points lie along the budget line
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
Or on the boundary of the budget set
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
Points inside or on the line are affordable
Graphical Analysis of Budget SetBudget Set
012345
0 1 2 3 4 5 6 7q2
q1
Points outside the line are not affordable
Slope of the Budget Constraint - q1 = h(q2)
p1 q1 p2q2 I
p1q1 I p2 q2
q1 Ip1
p2
p1q2
So the slope is -p2 / p1
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
0 Snickers -- 4 Reese’s
q2 = - 3
3 Snickers -- 2 Reese’s
q1q1 = 2
Δq1
Δq2
2 3
23
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
0 Snickers -- 4 Reese’s
3 Snickers -- 2 Reese’s
q1 = 2
Δq1
Δq2
2 3
23
p2
p1
0.200.30
q2 = - 3
Numerical Example
I = $1.20, p1 = 0.30, p2 = 0.20
0.30q1 0.20q2 1.20
0.30q1 1.20 0.20q2
q1 1.200.30
0.200.30
q2
4 23q2
1
5 6 74321
2
3
4
5
Budget Constraint - 0.3q1 + 0.2q2 = $1.20
Affordable
Not Affordable
q1
q2
q1 4 23q2
0.3q1 1.2 0.2q2
1
5 6 74321
2
3
4
5
Budget Constraint - 0.3q1 + 0.2q2 = $1.20
Affordable
Not Affordable
q2
q1 Double prices and incomeDouble prices and income
q1 4 23q2
Budget Constraint - 0.6q1 + 0.4q2 = $2.40
0.6q1 2.4 0.4q2
1
5 6 74321
2
3
4
5
Budget Constraint - 0.6q1 + 0.2q2 = $1.20
Affordable
q2
q1
Not Affordable
Double pDouble p11 from 0.3 to 0.6 from 0.3 to 0.6
q1 2 13q2
Budget Constraint - 0.3q1 + 0.2q2 = $1.20
0.6q1 1.2 0.2q2
Just to review how to solveBudget Constraint - 0.6q1 + 0.2q2 = $1.20
0.60q1 1.20 0.20q2
q1 1.200.60
0.200.60
q2
q1 2 13
q2
1
5 6 74321
2
3
4
5
Budget Constraint - 0.3q1 + 0.3q2 = $1.20
Affordable
q2
q1
Raise pRaise p22 from 0.2 to 0.3 from 0.2 to 0.3
Not Affordable
q1 4 q2
Budget Constraint - 0.3q1 + 0.2q2 = $1.20
0.3q1 1.2 0.3q2
1
5 6 74321
2
3
4
5
q1
q2
Change in Income
Budget Constraint0 - 0.3q1 + 0.2q2 = $1.20
Budget Constraint1 - 0.3q1 + 0.2q2 = $0.60
q1 2 23q2
0.3q1 0.6 0.2q2
Change in Price of Good 1 (price rises)
Budget Constraint0 - 0.3q1 + 0.2q2 = $1.20
1
5 6 74321
2
3
4
5
q1
q2
Budget Constraint1 - 0.6q1 + 0.2q2 = $1.20
Change in Price of Good 1 (price falls)
Budget Constraint0 - 0.3q1 + 0.2q2 = $1.20
Budget Constraint1 - 0.24q1 + 0.2q2 = $1.20
1
5 6 74321
2
3
4
5
q1
q2
Change in Price of Good 2 (price rises)
Budget Constraint0 - 0.3q1 + 0.2q2 = $1.20
Budget Constraint1 - 0.30q1 + 0.30q2 = $1.20
1
5 6 74321
2
3
4
5
q1
q2
The End
Graphical Analysis of Budget SetBudget Set
012345
0 1 2 3 4 5 6 7q2
q1
Graphical Analysis of Budget SetBudget Set
012345
0 1 2 3 4 5 6 7q2
q1