1. University of Hawai‘i at Mānoa Department of Economics
ECON 130 (003): Principles of Economics (Micro)
Gerard Russo
Lecture #11
Tuesday, February 17, 2004

2. LECTURE 11
Revealed Preference
Budget Lines

3. Consumer Theory Consumer Choice
Consumers select bundles of consumption goods given their Preferences and subject to their budget constraint.
Consumer preferences over goods and services are represented by a utility function, U(x,y).
Budget Constraint: PXX + PYY ≤ B.

4. A Simple Model of a Consumer Budget
2 goods
Good x (i.e., soft drink)
Good y (i.e., pizza)
2 Prices
Price of good x, Px
Price of good y, Py
Fixed Income or Budget, B

5. The Consumer Budget Constraint
Total expenditures on goods x and y cannot exceed the consumer’s income (consumer’s budget).
Expenditures on good x = Pxx.
Expenditures on good y = Pyy.
Total Expenditures = Pxx + Pyy.
Total expenditures must be less than or equal to the consumer’s budget.
Pxx + Pyy ≤ B.

6. The Consumer’s Budget Set
The Consumer’s budget set is the set of consumption bundles composed of goods x and y such that total expenditures are less than or equal to the consumer’s budget.
Budget Set = { (x,y) | Pxx + Pyy ≤ B } .

7. The Consumer’s Budget Line
Pxx + Pyy = B
Isolate y: y = B/Py – (Px/Py)x
The y intercept = B/Py
The slope = ∆y/ ∆ x = - (Px/Py)
Isolate x: x = B/Px – (Py/Px)y
The x intercept = B/Px
The slope = ∆ x/ ∆ y = - (Py/Px)

8. Budget Line: y = B/Py – (Px/Py)x
Quantity of Good y
Budget Line: y = B/Py – (Px/Py)x
B/Py
Slope = ∆ y/ ∆ x = - Px/Py
B/Px
Quantity of Good x

9. Budget Line: An Example
Price of good y = $2 per unit
Price of good x = $1 per unit
Budget = $100
$1x + $2y = $100
y = 50 – 0.5x
x = 100 – 2y

10. Budget Line: y = B/Py – (Px/Py)x y = 50 – 0.5 x
Quantity of Good y
Budget Line: y = B/Py – (Px/Py)x
y = 50 – 0.5 x
B/Py
=$100/$2
=50
Slope = ∆ y/∆ x = - Px/Py = -$1/$2
B/Px = $100/$1 = 100
Quantity of Good x

11. Budget Set Budget Set ={ (x,y) | Pxx +Pyy ≤ B} B/Py B/Px
Quantity of Good y
Budget Set ={ (x,y) | Pxx +Pyy ≤ B}
B/Py
Budget Set
B/Px
Quantity of Good x

12. Income Increases B/Py B/Py Slope = - Px/Py B/Px B/Px
Quantity of Good y
Income Increases
B/Py
B/Py
Slope = - Px/Py
B/Px
B/Px
Quantity of Good x

13. Income Decreases B/Py Slope = - Px/Py B/Py B/Px B/Px
Quantity of Good y
Income Decreases
B/Py
Slope = - Px/Py
B/Py
B/Px
B/Px
Quantity of Good x

14. Price of Good x Increases
Quantity of Good y
Price of Good x Increases
B/Py
Slope = - Px/Py
Slope = - Px/Py
B/Px
B/Px
Quantity of Good x

15. Price of Good x Decreases
Quantity of Good y
Price of Good x Decreases
B/Py
Slope = - Px/Py
Slope = - Px/Py
B/Px
B/Px
Quantity of Good x

16. Price of Good y Increases
Quantity of Good y
Price of Good y Increases
B/Py
Slope = - Px/Py
B/Py
Slope = - Px/Py
B/Px
Quantity of Good x

17. Price of Good y Decreases
Quantity of Good y
Price of Good y Decreases
Slope = - Px/Py
B/Py
B/Py
Slope = - Px/Py
B/Px
Quantity of Good x

18. What happens if income doubles and prices double?
Quantity of Good y
What happens if income doubles and prices double?
B/Py
Slope = - Px/Py
B/Px
Quantity of Good x

19. Quantity of Good y •W •Z •R •N •A •V •L •O •M
Quantity of Good x

20. •A Point A is dominated by points in this set. Point A dominates
Quantity of Good y
Point A is dominated
by points in this set. •A
Point A dominates
points in this set.
Quantity of Good x

21. Assumptions about Consumers
Consumers are rational.
Consumers prefer more to less.
Nonsatiation
Preferences (tastes) are stable.
Choice vs. Preference

22. •R •Z •A •L •O Quantity of Good y
Is A preferred to Z? Or, is Z preferred to A?
Is A preferred to L? Or, is L preferred to A?
Is A preferred to R? Or, is R preferred to A?
Is A preferred to O? Or, is O preferred to A? •R •Z •A •L •O
Quantity of Good x

23. •Z •V •R •A •L •O •M Consumption Bundle A is
Quantity of Good y
Consumer Choice: Year 2003 •Z •V
Consumption Bundle A is
Revealed Preferred to R, O,
M, etc. •R •A •L •O •M
Budget Line: Year 2003
Quantity of Good x

24. •A Suppose the consumer chooses consumption bundle A in the year 2003.
Quantity of Good y •A
Budget Line: Year 2003
Quantity of Good x

25. •W •R •A •L Are goods x and y normal or inferior?
Is the consumer better off or worse off in 2004?
Quantity of Good y
Are goods x and y normal
or inferior? •W
Budget Line:
Year 2004 •R •A •L
Budget Line: Year 2003
Quantity of Good x

26. •W •A •R •L Are goods x and y normal or inferior?
Is the consumer better off or worse off in 2004?
Quantity of Good y
Are goods x and y normal
or inferior?
Budget Line:
Year 2003 •W •A •R •L
Budget Line: Year 2004
Quantity of Good x

27. •M •W •A •L Is the consumer better off or worse off in 2004?
Quantity of Good y •M
Budget Line:
Year 2004 •W •A •L
Budget Line: Year 2003
Quantity of Good x

28. •L •J •A •R •W Quantity of Good y
Is the consumer better off or worse off in 2004? •L
Budget Line:
Year 2004 •J •A •R •W
Budget Line: Year 2003
Quantity of Good x

29. •M •A •L •J Is the consumer better off or worse off in 2004?
Quantity of Good y
Budget Line:
Year 2004 •M •A •L •J
Budget Line: Year 2003
Quantity of Good x