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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

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university of hawai i at m noa 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 12
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
utility function
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.
slide4
Example: Topographical Map

Elevation

1000 meters

Elevation

4000 meters

Elevation

2000 meters

slide5
I2

Quantity of Good y

I1

Indifference Curve Map

I0

Direction of Preference

I2

I1

I0

0

Quantity of Good x

slide6
U2

Quantity of Good y

U1

U0

L•

R•

Z•

A•

U2

M•

B

U1

U0

0

Quantity of Good x

slide7
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

slide8
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

slide9
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

slide10
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

slide11
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

optimal consumer choice
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
slide13
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

the optimal condition
The Optimal Condition
  • -Px/Py = -MUx/MUy
  • Px/Py = MUx/MUy
  • MUy/Py = MUx/Px
diminishing marginal utility
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.
slide16
Quantity of Good y

U2

U1

Px/Py < MUx/MUy

U0

Px/Py = MUx/MUy

Z•

A•

U2

U1

L

U0

0

Px/Py > MUx/MUy

Quantity of Good x

slide17
Quantity of Good y

U2

U1

Are goods x and y normal

or inferior?

U0

C•

B•

U2

A•

U1

U0

0

Quantity of Good x

slide18
Quantity of Good y

U2

U1

Income-Consumption Path.

U0

C•

B•

U2

A•

U1

U0

0

Quantity of Good x

slide19
Quantity of Good y

U2

U1

U0

U2

U1

U0

0

Income-Consumption Path:

Homothetic Preferences

Quantity of Good x

slide20
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

slide21
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

slide22
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

slide23
Derivation of a Consumer

Demand Curve

y

•C

B•

A•

xA

xB

Px

x

xC

PA

•A'

PB

•B'

Demand Curve

PC

•C'

xA

xB

xC

x

slide24
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

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