1. University of Hawai‘i at Mānoa Department of Economics
ECON 130 (003): Principles of Economics (Micro)
Gerard Russo
Lecture #12
Thursday, February 19, 2004

2. LECTURE 12 Application: Transfers in Cash vs. Transfers in Kind
Ordinal and Cardinal Utility
Utility Functions
Indifference Curves
Marginal Rate of Substitution
Consumer Optimization
Consumer Choice and Income Changes
Derivation of Consumer Demand
Application: Transfers in Cash vs. Transfers in Kind

3. Utility Function
Consumer Utility is a function of the quantity of goods x and y consumed.
U=U(x,y)
One dependent variable, U, and two independent variables, x and y.
The function U(x,y) is three-dimensional.

4. Example: Topographical Map
Elevation
1000 meters
Elevation
4000 meters
Elevation
2000 meters

5. Indifference Curve Map I0
Quantity of Good y I1
Indifference Curve Map I0
Direction of Preference I2 I1 I0
Quantity of Good x

6. L• R• Z• A• M• • B U2 Quantity of Good y U1 U0 U2 U1 U0
Quantity of Good x

7. U2
Quantity of Good y
e.g., Automobile Transportation U1 U0
Direction of Preference? U2 U1 U0
Quantity of Bad x
e.g., Air Pollution

8. Quantity of Bad y
e.g., Garbage U0
Direction of Preference? U1 U2 U0 U1 U2
Quantity of Bad x
e.g., Viral Disease

9. Quantity of Bad y
e.g., Poison Ivy
Direction of Preference? U0 U1 U2 U0 U1 U2
Quantity of Good x
e.g., Music CDs

10. The Slope of an Indifference Curve = ∆y/∆x = -MUx/MUy = MRS
Quantity of Good y U0
The Slope of an Indifference Curve
= ∆y/∆x = -MUx/MUy = MRS
= Marginal Rate of Substitution ∆y ∆x U0
Quantity of Good x

11. Slope of the indifference curve = -MUx/MUy.
Quantity of Good y U2 U1
Slope of the indifference
curve = -MUx/MUy. U0 U2 U1 U0
Quantity of Good x
Slope of the budget line = -Px/Py

12. OPTIMAL CONSUMER CHOICE
The Consumer maximizes utility subject to the budget constraint.
The optimum is characterized by the equality of the slopes of the budget line and the indifference curve.
-Px/Py = -MUx/MUy

13. yA xA The Optimal Choice is Consumption Bundle A. –Px/Py = -MUx/MUy.
Quantity of Good y U2 U1 U0
The Optimal Choice is Consumption Bundle A. –Px/Py = -MUx/MUy. yA A• U2 U1 U0 xA
Quantity of Good x

14. The Optimal Condition -Px/Py = -MUx/MUy Px/Py = MUx/MUy
MUy/Py = MUx/Px

15. Diminishing Marginal Utility
An increase (decrease) in the consumption of good x decreases (increases) the marginal utility of good x.
If x goes up, MUx goes down. If x goes down, MUx goes up.
An increase (decrease) in the consumption of good y decreases (increases) the marginal utility of good y.
If y goes up, MUy goes down. If y goes down, MUy goes up.

16. Px/Py < MUx/MUy Px/Py = MUx/MUy Z• A• L • Px/Py > MUx/MUy
Quantity of Good y U2 U1
Px/Py < MUx/MUy U0
Px/Py = MUx/MUy Z• A• U2 U1 L • U0
Px/Py > MUx/MUy
Quantity of Good x

17. Are goods x and y normal or inferior? C• B• A• Quantity of Good y U2
Quantity of Good x

18. Income-Consumption Path.
Quantity of Good y U2 U1
Income-Consumption Path. U0 C• B• U2 A• U1 U0
Quantity of Good x

19. Income-Consumption Path: Homothetic Preferences
Quantity of Good y U2 U1 U0 U2 U1 U0
Income-Consumption Path:
Homothetic Preferences
Quantity of Good x

20. yB yA xA xB Are goods x and y normal or inferior? C• B• A• U2
Quantity of Good y
Are goods x and y normal
or inferior? U0 U1 C• U2 yB B• yA A• U1 U0 xA xB
Quantity of Good x

21. yC yB xC xB Are goods x and y normal or inferior? C• B• A• U2
Quantity of Good y
Are goods x and y normal
or inferior? U0 U1 C• yC U2 yB B• A• U1 U0 xC xB
Quantity of Good x

22. A decrease in the price of good x changes the optimum from point A to
Quantity of Good y U2 U1
A decrease in the price
of good x changes the
optimum from point A to
point B. U0 B• U2 A• U1 U0
Quantity of Good x

23. Derivation of a Consumer Demand Curvey •C B• A• xA xB Px xC x PA
•A' PB
•B'
Demand Curve PC
•C' xA xB xC x

24. Budget Line After Transfer
Quantity of Alcoholic Beverage
Application: Transfers in Cash
versus Transfers in Kind.
Budget Line After Transfer A• •B •C
Budget Line Before Transfer
Quantity of Food