University of Hawai

1
University of Hawaii at ManoaDepartment 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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LECTURE 12

• 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

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Utility Function

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

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Example Topographical Map
Elevation 1000 meters
Elevation 4000 meters
Elevation 2000 meters
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I2
Quantity of Good y
I1
Indifference Curve Map
I0
Direction of Preference
I2
I1
I0
0
Quantity of Good x
6
U2
Quantity of Good y
U1
U0
L
R
Z
A
U2
M
B
U1
U0
0
Quantity of Good x
7
U2
Quantity of Good y e.g., Automobile Transportation
U1
U0
Direction of Preference?
U2
U1
U0
0
Quantity of Bad x e.g., Air Pollution
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Quantity of Bad y e.g., Garbage
U0
Direction of Preference?
U1
U2
U0
U1
U2
0
Quantity of Bad x e.g., Viral Disease
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Quantity of Bad y e.g., Poison Ivy
Direction of Preference?
U0
U1
U2
U0
U1
U2
0
Quantity of Good x e.g., Music CDs
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The Slope of an Indifference Curve ?y/?x
-MUx/MUy MRS Marginal Rate of Substitution
U0
Quantity of Good y
?y
?x
U0
0
Quantity of Good x
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Quantity of Good y
U2
U1
Slope of the indifference curve -MUx/MUy.
U0
U2
U1
U0
0
Quantity of Good x
Slope of the budget line -Px/Py
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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

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Quantity of Good y
U2
U1
U0
The Optimal Choice is Consumption Bundle A.
Px/Py -MUx/MUy.
yA
A
U2
U1
U0
0
xA
Quantity of Good x
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The Optimal Condition

• -Px/Py -MUx/MUy
• Px/Py MUx/MUy
• MUy/Py MUx/Px

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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.

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Quantity of Good y
U2
U1
Px/Py lt MUx/MUy
U0
Px/Py MUx/MUy
Z
A
U2
U1
L
U0
0
Px/Py gt MUx/MUy
Quantity of Good x
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Quantity of Good y
U2
U1
Are goods x and y normal or inferior?
U0
C
U2
B
A
U1
U0
0
Quantity of Good x
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Quantity of Good y
U2
U1
Income-Consumption Path.
U0
C
U2
B
A
U1
U0
0
Quantity of Good x
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Quantity of Good y
U2
U1
U0
U2
U1
U0
0
Income-Consumption Path Homothetic Preferences
Quantity of Good x
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U2
Quantity of Good y
Are goods x and y normal or inferior?
U0
U1
C
U2
yB
B
yA
A
U1
U0
0
xA
xB
Quantity of Good x
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U2
Quantity of Good y
Are goods x and y normal or inferior?
U0
U1
C
yC
U2
yB
B
A
U1
U0
0
xC
xB
Quantity of Good x
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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
0
Quantity of Good x
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Derivation of a Consumer Demand Curve
y
C
B
A
xA
xB
x
Px
xC
PA
A'
PB
B'
Demand Curve
C'
PC
xA
xB
xC
x
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Quantity of Alcoholic Beverage
Application Transfers in Cash versus Transfers
in Kind.
Budget Line After Transfer
A
B
C
Quantity of Food
Budget Line Before Transfer