University of Hawai‘i at Mānoa Department of Economics
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University of Hawai‘i at Mānoa Department of Economics ECON 130 (003): Principles of Economics (Micro) http://www2.hawaii.edu/~lindoj Gerard Russo Lecture #12 Thursday, February 19, 2004
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University of Hawai‘i at Mānoa Department of Economics. ECON 130 (003): Principles of Economics (Micro) http://www2.hawaii.edu/~lindoj Gerard Russo Lecture #12 Thursday, February 19, 2004. LECTURE 12. Ordinal and Cardinal Utility Utility Functions Indifference Curves - PowerPoint PPT Presentation
Transcript of University of Hawai‘i at Mānoa Department of Economics
University of Hawai‘i at MānoaDepartment of Economics
ECON 130 (003): Principles of Economics (Micro)
http://www2.hawaii.edu/~lindoj
Gerard Russo
Lecture #12
Thursday, February 19, 2004
LECTURE 12Ordinal and Cardinal Utility
Utility Functions
Indifference Curves
Marginal Rate of SubstitutionConsumer OptimizationConsumer Choice and Income ChangesDerivation of Consumer Demand
Application: Transfers in Cash vs. Transfers in Kind
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.
Example: Topographical Map
Elevation1000 meters
Elevation 2000 meters
Elevation4000 meters
Quantity of G
ood y
Quantity of Good x
I0
I0
I1
I2
I2
I1
Indifference Curve Map
0
Direction of Preference
Quantity of G
ood y
Quantity of Good x
A•
•B
Z•
M•
L•
R•
U0
U2
U2
U1
U0
U1
0
Qu
antity of G
ood y
e.g., Au
tomob
ile Tran
sportation
Quantity of Bad xe.g., Air Pollution
Direction of Preference? U0
U0
U1
U1
U2
U2
0
Qu
antity of B
ad y
e.g., Garb
age
Quantity of Bad xe.g., Viral Disease
Direction of Preference?
U0
U0
U1
U1
U2
U2
0
Qu
antity of B
ad y
e.g., Poison
Ivy
Quantity of Good xe.g., Music CDs
Direction of Preference?
U0
U0
U1
U1
U2
U2
0
Quantity of G
ood y
Quantity of Good x
∆y
∆x
The Slope of an Indifference Curve= ∆y/∆x = -MUx/MUy = MRS= Marginal Rate of Substitution
U0
U0
0
Quantity of G
ood y
Quantity of Good x
U0
U1U2
U2
U1
U0
Slope of the indifferencecurve = -MUx/MUy.
Slope of the budget line = -Px/Py
0
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
Quantity of G
ood y
Quantity of Good x
U0
U1U2
U2
U1
U0
The Optimal Choice is Consumption Bundle A. –Px/Py = -MUx/MUy.
A•
0 xA
yA
The Optimal Condition
-Px/Py = -MUx/MUy
Px/Py = MUx/MUy
MUy/Py = MUx/Px
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.
Quantity of G
ood y
Quantity of Good x
U0
U1U2
U2
U1
U0
Px/Py = MUx/MUy
A•
Px/Py < MUx/MUy
Px/Py > MUx/MUy
L•
Z•
0
Quantity of G
ood y
Quantity of Good x
U0
U1U2
U2
U1
U0
A•
B•C•
Are goods x and y normalor inferior?
0
Quantity of G
ood y
Quantity of Good x
U0
U1U2
U2
U1
U0
A•
B•C•
Income-Consumption Path.
0
Quantity of G
ood y
Quantity of Good x
U0
U1U2
U2
U1
U0
Income-Consumption Path:Homothetic Preferences
0
Quantity of G
ood y
Quantity of Good x
A•
B•
C•
U0
U0
U1
U1
U2
U2
Are goods x and y normalor inferior?
0 xA
yA
xB
yB
Quantity of G
ood y
Quantity of Good x
A•
B•
C•
U0
U0
U1
U1
U2
U2
Are goods x and y normalor inferior?
0 xC
yC
xB
yB
Quantity of G
ood y
Quantity of Good x
U0
U1U2
U2
U1
U0
A•B•
A decrease in the priceof good x changes theoptimum from point A topoint B.
0
y
xPx
x
A• B• •C
xA
xA
xB
xB
xC
xC
•A'
•B'
•C'
PA
PB
PC Demand Curve
Derivation of a Consumer Demand Curve
Quantity of A
lcoholic Beverage
Quantity of Food
Application: Transfers in Cash versus Transfers in Kind.
Budget Line Before Transfer
Budget Line After TransferA• •B
•C
