MicroEconomics 5e by besanko braeutigam chapter 05

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Chapter 5

The Theory of Demand

1


Chapter Five Overview

1.
1. Individual
IndividualDemand
DemandCurves
Curves
2.
2. Income
Incomeand
andSubstitution
SubstitutionEffects
Effects&&the
theSlope
SlopeofofDemand
Demand
Applications:
Applications:


 The
TheWork-Leisure

Work-LeisureTrade-of
Trade-of

 Consumer
ConsumerSurplus
Surplus
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••

3.
3. Constructing
ConstructingMarket
MarketDemand
Demand

Chapter Five

2


Chapter Five Overview

The
TheEffects
Effectsof
ofaaChange
ChangeininPrice
Price

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•• Optimal
OptimalChoice
Choice
•• Demand
DemandCurve
Curve

Chapter Five

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Individual Demand Curves

The
ThePrice
PriceConsumption
ConsumptionCurve
CurveofofGood
GoodX:X:

Is the set of optimal baskets for every possible price of

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good x, holding all other prices and income constant.

Chapter Five

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Price Consumption Curves
Y (units)
The price consumption curve for good x can be written as the quantity

PPY ==$4
Y $4
I I==$40
$40

consumed of good x for any price of x. This is the individual’s demand
curve for good x.

10

•
•

•
PX = 1

PX = 2

PX = 4
0

XA=2

XB=10

XC=16
Chapter Five

X (units)

20
6

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Price Consumption Curve


Individual Demand Curve
PX
Individual
IndividualDemand
DemandCurve
Curve

PX = 4

•
•

PX = 2

•

PX = 1
XA

XB

U increasing

X

XC
Chapter Five

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For
ForXX


Individual Demand Curve
Key Points

 The consumer is maximizing utility at every point along the demand curve
 The marginal rate of substitution falls along the demand curve as the price of x falls (if there was an interior
solution).

 As the price of x falls, it causes the consumer to move down and to the right along the demand curve as

The demand curve is also the “willingness to pay” curve – and willingness to pay for an additional unit of X
falls as more X is consumed.

Chapter Five

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utility increases in that direction.


Demand Curve for “X”

Algebraically,
Algebraically, we
we can
can solve
solve for
for the
the individual’s
individual’s demand
demand using
using the
the following
following
equations:
equations:
1.1.ppxxx++ppyyy==I I
x

y

(If(Ifthis
thisnever
neverholds,
holds,aacorner
cornerpoint
pointmay
maybe
besubstituted
substitutedwhere
wherexx==00ororyy==0)0)

Chapter Five

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2.2.MU
= MU /p – at a tangency.
MUx/p
x/pxx = MUyy/pyy – at a tangency.


Demand Curve with an Interior Solution

Suppose that U(x,y) = xy. MUx = y and MUy = x. The prices of x and y
are px and py, respectively and income = I.

We Have:
We Have:

2. x/py = y/px
2. x/py = y/px

Substituting the second condition into the budget constraint, we then have:
Substituting the second condition into the budget constraint, we then have:
3. pxx + py(px/py)x = I or…x = I/2px
3. pxx + py(px/py)x = I or…x = I/2px

Chapter Five

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1. pxx + pyy = I
1. pxx + pyy = I


Change in Income & Demand

Income Consumption Curve

The
The income
income consumption
consumption curve
curve ofof good

good xx isis the
the set
set ofof
optimal
optimalbaskets
basketsfor
forevery
everypossible
possiblelevel
levelofofincome.
income.

We
Wecan
cangraph
graphthe
thepoints
pointson
onthe
theincome
incomeconsumption
consumptioncurve
curve

Chapter Five

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as
aspoints

pointson
onaashifting
shiftingdemand
demandcurve.
curve.

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Income Consumption Curve

Chapter Five
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Engel Curves

The income consumption curve for good x also can be written as
the quantity consumed of good x for any income level. This is the
individual’s Engel Curve for good x. When the income
consumption curve is positively sloped, the slope of the Engel

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Curve is positive.

Chapter Five

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Engel Curves
I ($)

Engel Curve

“X
“Xisisaanormal
normalgood”
good”

92

40

0

10

18

X (units)

24
Chapter Five

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68


Definitions of Goods
• If the income consumption curve shows that the consumer purchases more of good x as her income rises,
good x is a normal good.

• Equivalently, if the slope of the Engel curve is positive, the good is a normal good.

• If the income consumption curve shows that the consumer purchases less of good x as her income rises, good

• Equivalently, if the slope of the Engel curve is negative, the good is an inferior good.

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x is an inferior good.


Definitions of Goods

Example: Backward Bending Engel Curve – a good
can be normal over some ranges and inferior over

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others

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Impact of Change in the Price of a Good

•

Substitution Effect: Relative change in price affects the amount of good that
is bought as consumer tries to achieve the same level of utility

Income Effect: Consumer’s purchasing power changes and affects the
consumer in a way similar to effect of a change in income
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•

Chapter Five

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The Substitution Effect

•

As the price of x falls, all else constant, good x becomes cheaper relative to good
y.

• This

change in relative prices alone causes the consumer to adjust his/ her

•

This effect is called the substitution effect.

•

The substitution effect always is negative.

•

Usually, a move along a demand curve will be composed of both effects.

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consumption basket.


Impact of Change in the Price of a Good
Definition: As the price of x falls, all else constant, purchasing power rises. As the

price of x rises, all else constant, purchasing power falls.

This is called the income effect of a change in price.

The income efect may be positive (normal good) or negative
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(inferior good).

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Impact of Change in the Price of a Good

• If price of a good falls – consumer substitutes into the good to achieve the
same level of utility

• When price falls – purchasing power increases the consumer can buy the
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same amount and still have money left

Chapter Five

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A

Initial Basket
Final Basket
Decomposition Basket

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•
•
•

Clothing

Y

The Substitution and Income Effects

C

BLd
B

U2
U1
BL1

XA

BL2
X

XB

XC

21

Food


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The Substitution and Income Effects

Chapter Five

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•

Initial Basket A

•

Final Basket C

Px1
Slope of BL1 = −
Py

Slope of BL1=

Px1
Py

Slope of BL2 =

•
A

Decomposition Basket B

C

BLd
B

BL1

BL2
X

XB

Slope of BL1 =

Px1
Py

Slope of BL2 =

Px 2
Py

Slope of BL d =

Px 2
Py

U2
U1

XA

Px 2
Py

XC

Food

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Clothing

Y

The Substitution and Income Effects

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The Substitution and Income Effects

Chapter Five

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Giffen Goods

If a good is so inferior that the net effect of a price decrease of good x, all else constant, is
a decrease in consumption of good x, good x is a Giffen good.

For Giffen goods, demand does not slope down.

When might an income effect be large enough to offset the substitution effect? The good
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would have to represent a very large proportion of the budget.

Chapter Five

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Giffen Goods – Income and Substitution Effects

Chapter Five

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