The Consumer Problem and the Budget Constraint Overheads.
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Transcript of The Consumer Problem and the Budget Constraint Overheads.
![Page 1: The Consumer Problem and the Budget Constraint Overheads.](https://reader035.fdocuments.net/reader035/viewer/2022062907/5a4d1b7a7f8b9ab0599b8b38/html5/thumbnails/1.jpg)
The Consumer Problem
and the Budget Constraint
Overheads
![Page 2: The Consumer Problem and the Budget Constraint Overheads.](https://reader035.fdocuments.net/reader035/viewer/2022062907/5a4d1b7a7f8b9ab0599b8b38/html5/thumbnails/2.jpg)
The fundamental unit of analysis
in consumption economics is the
individual consumer
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The underlying assumption in
consumption analysis is that all
consumers possess a preference
ordering which allows them to rank
alternative states of the world.
![Page 4: The Consumer Problem and the Budget Constraint Overheads.](https://reader035.fdocuments.net/reader035/viewer/2022062907/5a4d1b7a7f8b9ab0599b8b38/html5/thumbnails/4.jpg)
The behavioral assumption in
consumption analysis is
that consumers make choices consistent
with their underlying preferences
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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
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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
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The Consumer Problem
Maximize satisfaction
subject to
income
![Page 8: The Consumer Problem and the Budget Constraint Overheads.](https://reader035.fdocuments.net/reader035/viewer/2022062907/5a4d1b7a7f8b9ab0599b8b38/html5/thumbnails/8.jpg)
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
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Notation
Income - I
Quantities of goods - q1, q2, . . . qn
Prices of goods - p1, p2,. . . pn
Number of goods - n
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Budget constraint with 2 goods
p1q1 p2q2 I
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p1q1 p2q2 p3q3 pn qn I
Budget constraint with n goods
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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
![Page 13: The Consumer Problem and the Budget Constraint Overheads.](https://reader035.fdocuments.net/reader035/viewer/2022062907/5a4d1b7a7f8b9ab0599b8b38/html5/thumbnails/13.jpg)
Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7Snickers
Reese’s
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Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
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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
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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
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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
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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
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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
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Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
There are many different combinationsOnly some combinations are feasible
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Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
Some combinations exactly exhaust income
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Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
We say these points lie along the budget line
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Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
Or on the boundary of the budget set
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Graphical Analysis of Budget Set
012345
0 1 2 3 4 5 6 7q2
q1
Points inside or on the line are affordable
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Graphical Analysis of Budget SetBudget Set
012345
0 1 2 3 4 5 6 7q2
q1
Points outside the line are not affordable
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
![Page 38: The Consumer Problem and the Budget Constraint Overheads.](https://reader035.fdocuments.net/reader035/viewer/2022062907/5a4d1b7a7f8b9ab0599b8b38/html5/thumbnails/38.jpg)
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
![Page 39: The Consumer Problem and the Budget Constraint Overheads.](https://reader035.fdocuments.net/reader035/viewer/2022062907/5a4d1b7a7f8b9ab0599b8b38/html5/thumbnails/39.jpg)
The End
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Graphical Analysis of Budget SetBudget Set
012345
0 1 2 3 4 5 6 7q2
q1
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Graphical Analysis of Budget SetBudget Set
012345
0 1 2 3 4 5 6 7q2
q1