1. and the Budget Constraint
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. This is called the budget constraint
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
Maximize
satisfaction
subject to
income

8. 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

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 = Reese’s Pieces q2 = Snickers
p1 = price of Reese’s Pieces = $0.30
p2 = price of Snickers = $0.20

13. Graphical Analysis of Budget Set5
Reese’s 4 3 2 1 1 2 3 4 5 6 7
Snickers

14. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2

15. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
4 Reese’s Snickers
Cost = 4 x x = $1.20

16. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
0 Reese’s Snickers
Cost = 0 x x = $1.20

17. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
2 Reese’s Snickers
Cost = 2 x x = $1.20

18. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
2 Reese’s Snickers
Cost = 2 x x = $.80

19. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
3 Reese’s Snickers
Cost = 3 x x = $1.50

20. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
There are many different combinations
Only some combinations are feasible

21. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
Some combinations exactly exhaust income

22. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
We say these points lie along the budget line

23. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
Or on the boundary of the budget set

24. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2
Points inside or on the line are affordable

25. Graphical Analysis of Budget Set5 q1 4 3 2 1 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 Set5 q1 4
q1
q1 = 2 3 2
q2 = - 3 1 1 2 3 4 5 6 7 q2
3 Snickers Reese’s
0 Snickers Reese’s

28. Graphical Analysis of Budget Set5 q1 4
q1 = 2 3 2
q2 = - 3 1 1 2 3 4 5 6 7 q2
3 Snickers Reese’s
0 Snickers Reese’s

29. Numerical Example
I = $1.20, p1 = 0.30, p2 = 0.20

30. Not Affordable Budget Constraint - 0.3q1 + 0.2q2 = $1.20 Affordable q15 4
Not Affordable 3 2
Affordable 1 q2 1 2 3 4 5 6 7

31. Not Affordable Budget Constraint - 0.3q1 + 0.2q2 = $1.20
Double prices and income 5
Budget Constraint - 0.6q q2 = $2.40 4 3 2
Not Affordable 1
Affordable q2 1 2 3 4 5 6 7

32. Not Affordable Budget Constraint - 0.3q1 + 0.2q2 = $1.20
Double p1 from 0.3 to 0.6 5
Budget Constraint - 0.6q q2 = $1.20 4
Not Affordable 3 2 1
Affordable q2 1 2 3 4 5 6 7

33. Just to review how to solve
Budget Constraint - 0.6q q2 = $1.20

34. Budget Constraint - 0.3q1 + 0.2q2 = $1.20
Raise p2 from 0.2 to 0.3 5
Budget Constraint - 0.3q q2 = $1.20 4 3 2
Not Affordable
Affordable 1 q2 1 2 3 4 5 6 7

35. Change in Income Budget Constraint0 - 0.3q1 + 0.2q2 = $1.205 6 7 4 3 2 q1 q2
Budget Constraint q q2 = $1.20
Budget Constraint q q2 = $0.60

36. Change in Price of Good 1 (price rises)5 6 7 4 3 2 q1 q2
Budget Constraint q q2 = $1.20
Budget Constraint q q2 = $1.20

37. Change in Price of Good 1 (price falls)5 6 7 4 3 2 q1 q2
Budget Constraint q q2 = $1.20
Budget Constraint q q2 = $1.20

38. Change in Price of Good 2 (price rises)1 5 6 7 4 3 2 q1 q2
Budget Constraint q q2 = $1.20
Budget Constraint q q2 = $1.20

39. The End

40. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2

41. Graphical Analysis of Budget Set5 q1 4 3 2 1 1 2 3 4 5 6 7 q2