Economics 111.3 Winter 14

February 28th, 2014Lecture 17

Ch. 9 Ordinal Utility:

Indifference Curve Analysis

MRS

• MRS stands for Marginal Rate of Substitution

Combining Indifference Curves and Budget Line: Equilibrium at Tangency

• The goal for a consumer is to get as high on an indifference curve as possible, given her income constraint.

Which one of the following statements about Figure 9.3.2 is true?

Which one of the following statements about Figure 9.3.2 is true?

Consumer’s Equilibrium: a recap• The utility-maximizing rule: a consumer

with a fixed income and facing given market prices of goods will achieve maximum satisfaction (utility) when the marginal utility of the last dollar spent on each good is exactly the same as the marginal utility of the last dollar spent on any other good.

In Equilibrium, at point X, MRS = -PB/PA

If we move along I3, Memo:UA/ A =MUA

UB/ B =MUB

Thus,UA=A*MUA

UB=B*MUB

UA + UB = 0

-A/B =MRS=MUB/MUA

𝑴𝑹𝑺=𝑴𝑼𝒙𝑴𝑼𝒚

In Equilibrium, at point X, MRS = -PB/PA

Y

X

𝑴𝑹𝑺=𝑴𝑼𝒙𝑴𝑼𝒚

𝑰𝒏𝒆𝒒𝒖𝒊𝒍𝒊𝒃𝒓𝒊𝒖𝒎 ,𝑴𝑹𝑺=𝑴𝑼𝒙𝑴𝑼𝒚

=𝑷𝒙𝑷𝒚

Study Question• A consumer decides not to buy a VCR when

her income is $20,000. However, when her income rises to $30,000, she decides to buy one. In a single diagram, draw the budget lines and indifference curves to illustrate this situation (assume the VCR costs $300 in both time periods). Be sure to label your diagram completely.

Derivation of the Demand Curve, Income: $12

What happens if the price of B increases to

$1.50?

What happens if the price of B increases to

$1.50?Q

ua

nti

ty o

f A

Quantity of B

12

10

8

6

4

2

0

2 4 6 8 10 12

X I4

I1

I2I3

Derivation of the Demand Curve

New budget line reflects

the price change

New budget line reflects

the price change

Qu

an

tity

of

A

Quantity of B

12

10

8

6

4

2

0

2 4 6 8 10 12

I2I3

I1

I4X

PB=$1.50

Qu

an

tity

of

A

Quantity of B

12

10

8

6

4

2

0

2 4 6 8 10 12

Derivation of the Demand Curve

New budget line reflects the price

change

New budget line reflects the price

change

I2I3

I1

I4X

PB=$1.00

PB=$1.50

Qu

an

tity

of

A

Quantity of B

12

10

8

6

4

2

0

2 4 6 8 10 12

Derivation of the Demand Curve

New equilibrium point is X'

New equilibrium point is X'

X'

I2I3

I1

I4X

PB=$1.00

PB=$1.50

Qu

an

tity

of

A

Quantity of B

12

10

8

6

4

2

0

2 4 6 8 10 12

Derivation of the Demand Curve

A consumer’s demand curve can be viewed as a summary of the optimal decisions that arise from

his or her budget constraint and indifference

curves.

A consumer’s demand curve can be viewed as a summary of the optimal decisions that arise from

his or her budget constraint and indifference

curves.X'

I2I3

I1

I4X

Qu

an

tity

of

A

Quantity of B2 4 6 8 10 12

X'

I2I3I1

I4

X

PB QB$1.00 6

$1.50 3

2

46

10

12

8

Pri

ce

of

B

Quantity of B2 4 6 8 10 12

$0.50$1.00$1.50

DB

The Effect of Price Change

The Effect of Price Change• A fall in the price of a good has

two effects:

1. Consumers will tend to buy more of the good that has become cheaper and less of those goods that are now relatively more expensive.

2. Because one of the goods is now cheaper, consumers enjoy an increase in real purchasing power.

INCOME AND SUBSTITUTION EFFECTS

• Substitution effect Change in consumption of a good associated with a change in its price, with the level of utility held constant.

• Income effect • Change in consumption

of a good resulting from an increase in purchasing power, with relative prices held constant.

The Substitution Effect of Price Change

– The substitution effect is the effect of a change in price on the quantity bought when the consumer remains on the same indifferent curve.

– When the relative price falls, the consumer always substitutes more of that good for other goods.

– The substitution effect is the first reason why the demand curve slopes downward.

The total effect of a change in price is given theoretically by the sum of the substitution effect and the income effect