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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.


University of hawai i at m noa department of economics

Example: Topographical Map

Elevation

1000 meters

Elevation

4000 meters

Elevation

2000 meters


University of hawai i at m noa department of economics

I2

Quantity of Good y

I1

Indifference Curve Map

I0

Direction of Preference

I2

I1

I0

0

Quantity of Good x


University of hawai i at m noa department of economics

U2

Quantity of Good y

U1

U0

L•

R•

Z•

A•

U2

M•

B

U1

U0

0

Quantity of Good x


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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.


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

Quantity of Good y

U2

U1

Income-Consumption Path.

U0

C•

B•

U2

A•

U1

U0

0

Quantity of Good x


University of hawai i at m noa department of economics

Quantity of Good y

U2

U1

U0

U2

U1

U0

0

Income-Consumption Path:

Homothetic Preferences

Quantity of Good x


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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


University of hawai i at m noa department of economics

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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