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 #11

Tuesday, February 17, 2004

LECTURE 11Revealed Preference

Budget Lines

Consumer TheoryConsumer Choice

Consumers select bundles of consumption goods given their Preferences and subject to their budget constraint.

Consumer preferences over goods and services are represented by a utility function, U(x,y).

Budget Constraint: PXX + PYY ≤ B.

A Simple Model of a Consumer Budget

2 goodsGood x (i.e., soft drink)Good y (i.e., pizza)

2 PricesPrice of good x, Px

Price of good y, Py

Fixed Income or Budget, B

The Consumer Budget Constraint

Total expenditures on goods x and y cannot exceed the consumer’s income (consumer’s budget).

Expenditures on good x = Pxx.

Expenditures on good y = Pyy.

Total Expenditures = Pxx + Pyy.

Total expenditures must be less than or equal to the consumer’s budget.

Pxx + Pyy ≤ B.

The Consumer’s Budget Set

The Consumer’s budget set is the set of consumption bundles composed of goods x and y such that total expenditures are less than or equal to the consumer’s budget.

Budget Set = { (x,y) | Pxx + Pyy ≤ B } .

The Consumer’s Budget Line

Pxx + Pyy = B

Isolate y: y = B/Py – (Px/Py)xThe y intercept = B/Py

The slope = ∆y/ ∆ x = - (Px/Py)

Isolate x: x = B/Px – (Py/Px)yThe x intercept = B/Px

The slope = ∆ x/ ∆ y = - (Py/Px)

Quantity of Good y

Quantity of Good x

B/Py

B/Px

Slope = ∆ y/ ∆ x = - Px/Py

Budget Line: y = B/Py – (Px/Py)x

Budget Line: An Example

Price of good y = $2 per unit

Price of good x = $1 per unit

Budget = $100

$1x + $2y = $100

y = 50 – 0.5x

x = 100 – 2y

Quantity of Good y

Quantity of Good x

B/Py

=$100/$2=50

B/Px = $100/$1 = 100

Slope = ∆ y/∆ x = - Px/Py = -$1/$2

Budget Line: y = B/Py – (Px/Py)xy = 50 – 0.5 x

Quantity of Good y

Quantity of Good x

B/Py

B/Px

Budget Set ={ (x,y) | Pxx +Pyy ≤ B}

Budget Set

Quantity of Good y

Quantity of Good x

B/Py

B/Px

Slope = - Px/Py

Income IncreasesB/Py

B/Px

Quantity of Good y

Quantity of Good x

B/Py

B/Px

Slope = - Px/Py

Income Decreases

B/Py

B/Px

Quantity of Good y

Quantity of Good x

B/Py

B/Px

Slope = - Px/Py

Price of Good x Increases

B/Px

Slope = - Px/Py

Quantity of Good y

Quantity of Good x

B/Py

B/Px

Slope = - Px/Py

Price of Good x Decreases

B/Px

Slope = - Px/Py

Quantity of Good y

Quantity of Good x

B/Py

B/Px

Slope = - Px/Py

Price of Good y Increases

B/Py

Slope = - Px/Py

Quantity of Good y

Quantity of Good x

B/Py

B/Px

Slope = - Px/Py

Price of Good y Decreases

B/PySlope = - Px/Py

Quantity of Good y

Quantity of Good x

B/Py

B/Px

Slope = - Px/Py

What happens if income doubles and prices double?

Quantity of Good y

Quantity of Good x

•A

•Z

•L

•W

•O•M

•R

•N •V

Quantity of Good y

Quantity of Good x

•A

Point A is dominatedby points in this set.

Point A dominatespoints in this set.

Assumptions about Consumers

Consumers are rational.

Consumers prefer more to less.Nonsatiation

Preferences (tastes) are stable.

Choice vs. Preference

Quantity of Good y

Quantity of Good x

•A

•Z

•L

•O

•R

Is A preferred to Z? Or, is Z preferred to A?Is A preferred to L? Or, is L preferred to A?Is A preferred to R? Or, is R preferred to A?Is A preferred to O? Or, is O preferred to A?

Quantity of Good y

Quantity of Good x

•A

•Z

•L •O

•M

•R•V

Budget Line: Year 2003

Consumer Choice: Year 2003

Consumption Bundle A isRevealed Preferred to R, O,M, etc.

Quantity of G

ood y

Quantity of Good x

•A


Suppose the consumer chooses consumptionbundle A in the year 2003.

Quantity of G

ood y

Quantity of Good x

•A


Budget Line:Year 2004

Is the consumer better off or worse off in 2004?

•L

•W

•R

Are goods x and y normalor inferior?

0

Quantity of G

ood y

Quantity of Good x

•A




•R

•W

•L

Are goods x and y normalor inferior?

0

Quantity of G

ood y

Quantity of Good x

•A




•M

•L

•W

0

Quantity of G

ood y

Quantity of Good x




•J

•L

•W0

•R•A

Quantity of G

ood y

Quantity of Good x

•A




•J

•L

•M

0

University of Hawai‘i at Mānoa Department of Economics

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