Price Consumption Curve

1. Ch 4. Consumers in the Marketplace
•Consumption choices change as a function of
price and/or income
•Price increases
–Lead to decreases in quantity demanded
–Lead to pivoting budget line and consumers
choosing new consumption point

2. Contents
1.Income Change
a.Income-Consumption Curve
b.Normal/Inferior good
2.Price Change
a.Price-Consumption Curve
b.Substitution Effect / Income Effect
c.Normal/Inferior/Giffen Good
3.Elasticity
a.Point/Arc Elasticity
b.Elasticity and Total Revenue

3. Changes in Income
•Composite good convention
•Income changes
–Result in a parallel shift of the budget line
•Increase in income
–Cause consumption increase if normal good
–Cause consumption decrease if inferior good

4. Suppose the price of X is $2 and the price of Y is $3. Given the following
indifference curve mapping, draw an Engel curve graph for X.

Y 6


4



2



1 3 4 6 9

5. EXHIBIT 4.3 Normal and Inferior Goods

6. Income-Consumption Curve
•Assumption that prices fixed
•Relationship between income and quantity of good
consumed
–prices of goods consuming and indifference curves are
constant
•Shape of Income-Consumption Curve
–Upward-sloping if good X is normal
•If consumer income rises, consumes more of good X
–Downward-sloping if good X is inferior
•If consumer income rises, consumes less of good X
•From this, we can get an Engel Curve
–showing the relationship between Income and
quantity demanded

7. EXHIBIT 4.4 Constructing the Engel Curve

8. Changes in Price
•Income and price of good Y remain fixed
•Y-intercept of budget line unchanged by
change in price of X
•Budget line pivots around y-intercept
–Pivots inward if rise in price of X
–Pivots outward if fall in price of X
•Changes in optimum point
–Located anywhere along new budget line

9. Suppose the price of Y is $4 and your income is $30. Given the following
indifference curve mapping, generate a demand curve for X.
Y









4 6 7 9 10 15 X

10. Price-Consumption Curve
•Locus of optimal
bundles when the
price of the good on
the x-axis changes.
•This is not a demand
curve but the
information for a
demand curve is
here

11. The Demand Curve
•Engel curve vs demand curve
–Engel curve: relationship between income and
consumption
•Plots income on horizontal axis and consumption on
the vertical axis
–Demand curve: relationship between price and
consumption
•Plots price on the vertical axis and consumption on the
horizontal axis

12. Constructing the Demand Curve
•Derived from indifference curves
–Find price of X
–Draw budget line given income and prices
–Find tangency between budget line and
indifference curve
–Read off quantity of X
–Plot point on demand curve relating price to
quantity
–Repeat the process for additional points on the
demand curve

13. Constructing the Demand Curve (P falls)
•From this we can get a
demand schedule and curve.
•Assuming Income is constant.
Price Q
d
250 C1
200 C2
150 C3

14. Shape of Demand Curve
•Slopes downward
•If Giffen good, slopes upward
•Demand and indifference curves cannot be
drawn on same graph
–Require different axes

15. Giffen Goods
•If price of X increases, quantity demanded decreases
–Follows law of demand
–Then, non-Giffen goods
•If price of X increases, quantity demanded increases
–Violates law of demand
–Then, Giffen goods
•Giffen goods rare or nonexistent
–Using theory of indifference curves indicates exception to
law of demand

16. Non-Giffen Goods and Giffen Goods

17. Income and Substitution Effects
•When the price of a good changes, consumers
choose a new bundle.
•Economists decompose this shift from one bundle to
another into two parts: the substitution effect and
the income effect.
–Substitution effect
•Price rises
•Adjust consumption of goods whose price above marginal value
–Income effect
•Price rises
•Can no longer afford previous basket
•Decrease (increase) consumption if normal (inferior) good

18. Income and Substitution Effects
•Substitution Effect: The change in Qd resulting from
a change in the relative price of a good, and
assuming the original level of utility is maintained.
–Substitution effects are always the opposite (negative) of
the price change.
•Income Effect: The effect on the quantity demanded
that results from the change in the purchasing
power of a given income when the price of a good
changes.
–Income effects can go either way.

19. Y







6


3 U1
2
U0

8 9 10 14 15 20 X
Suppose Jane has an income of $40 and the price of Y is $4.
(1) Price of X = $2: She consumes 14 X & 3 Y. What is her MV of X?
(2) Price of X = $4: She decides to consume 8 X & 2 Y. What is her MV of X?
(3) With (9X, 6Y), her MV of X = 1 & she will be as happy as with (14X, 3Y)

20. Income and Substitution Effects
•The substitution effect
is the change in “X”
caused by the move
from A to C (X
A
to X
C
).
•The income effect is the
change in “X” caused by
the move from C to B (X
B
to X
C
).
A: original bundle (with X = X
A
)
C: compensated bundle (with X = X
C
)
B: new optimal bundle (with X = X
B
)

21. Isolating the Substitution Effect
•Suppose given just enough money to offset income
effect (Compensated: same indifference curve
originally on)
–If Px increases, the compensated budget constraint must
always be steeper than the original budget constraint. (a
negative effect on the consumption of X)
–If Px were to decrease, the compensated budget
constraint must always be flatter than the original
budget constraint. (a positive effect on the consumption
of X)

22. the Income Effects
•If know how substitution effect changes consumption
–Can deduce impact of income effect
•Substitution effects are always the opposite (negative) of the price
change.
•Income effects can go either way.
•Ordinary Inferior/ Giffen Inferior can be determined by the relative
size of Income effect to Substitution effect
Price change Income Effect Therefore…
Price increase Negative income effect Normal Good
Price increase Positive income effectInferior Good
Price decrease Negative income effect Inferior Good
Price decrease Positive income effectNormal Good

23. Inferior Good (Ordinary & Giffen)
Ordinary: Substitution Effect > Income EffectGiffen: Substitution Effect < Income Effect

24. Total effect
Income and Substitution Effects of a Fall in
Price of Good X (Normal Good)
0
Quantity of
X per
week
Quantity
of Y per
week
Old budget constraint
U
1
X
A
Y
A
New budget
constraint after lower
price of X
U
2
X
B
Y
B
X
C
A
Substitution
effect
Income effect
B
C
Compensated Budget
after subtracting
income to put
consumer on original
indifference curve
Created by Dr. Michael Nieswiadomy
Y
C

25. Total effect
Income and Substitution Effects of a Fall in
Price of Good X (Inferior Good)
0
Quantity of
X per
week
Quantity
of Y per
week
Old budget constraint
U
1
X
A
Y
A
New budget
constraint after lower
price of X
U
2
X
B
Y
B
X
C
A
Substitution
effect
Income effect
B
C
Compensated Budget
after subtracting
income to put
consumer on original
indifference curve
Created by Dr. Michael Nieswiadomy
Y
C

26. Total effect
Income and Substitution Effects of a Fall in
Price of Good X (Giffen Good)
0
Quantity of
X per
week
Quantity
of Y per
week
Old budget constraint
U
1
X
A
Y
A
New budget
constraint after lower
price of X
U
2
X
B
Y
B
X
C
A
Substitution
effect
Income effect
B
C
Compensated Budget
after subtracting
income to put
consumer on original
indifference curve
Created by Dr. Michael Nieswiadomy
Y
C

27. Total effect
Income and Substitution Effects of a Rise in
Price of Good X (Normal Good)
0
Quantity of
X per
week
Quantity
of Y per
week
Old budget constraint
U
2
X
B
Y
B
New budget
constraint after higher
price of X
U
1
X
A
Y
A
X
C
A
Substitution
effect
Income effect
B
C
Compensated Budget
after adding income
to put consumer on
original indifference
curve
Created by Dr. Michael Nieswiadomy
Y
C

28. Total effect
Income and Substitution Effects of a Rise in
Price of Good X (Inferior Good)
0
Quantity of
X per
week
Quantity
of Y per
week
Old budget constraint
U
2
X
B
Y
B
New budget
constraint after higher
price of X
U
1
X
A
Y
A
X
C
A
Substitution
effect
Income effect
B
C
Compensated Budget
after adding income
to put consumer on
original indifference
curve
Created by Dr. Michael Nieswiadomy
Y
C

29. Total effect
Income and Substitution Effects of a Rise in
Price of Good X (Giffen Good)
0
Quantity of
X per
week
Quantity
of Y per
week
Old budget constraint
U
2
X
B
Y
B
New budget
constraint after higher
price of X
U
1
X
A
Y
A
X
C
A
Substitution
effect
Income effect
B
C
Compensated Budget
after adding income
to put consumer on
original indifference
curve
Created by Dr. Michael Nieswiadomy
Y
C

30. the relative size of Income effect to Substitution effect
for a good on X axis
Price of X rises
Normal
B C A
Inferior (Ordinary)
C B A
Inferior (Giffen)
C A B
Price of X falls


Income Effect
Substitution Effect
Normal
A C B
Inferior (Ordinary)
A B C
Inferior (Giffen)
B A C
I.E.
S.E.
S.E.
I.E.
S.E. I.E.
S.E.
S.E.
I.E.
I.E.

31. the relative size of Income effect to Substitution effect
for a good on Y axis
Price of X rises
Normal
C
B
A
Inferior (Ordinary)
B
C
A
Price of X falls


I.
E.
S.
E.

I.
E.

S.
E.
Normal
A
B
C
Inferior (Ordinary)
A
C
B
S.
E.

S.
E.

I.
E.
I.
E.

32. Why Demand Curves Slope Downward:
Normal Goods
•Geometric Observations
–Increases in price, substitution effect means less
consumption
–Move from compensated line to new line, income
falls, consume less of good if normal
•Demand curve for normal good
–Both effects move consumer leftward
–Normal goods are not Giffen goods

33. Why Demand Curves Slope Downward:
Inferior Goods
•Demand curve for inferior goods
–Effects move in opposite directions and not as easily analyzed as
normal good
–Inferior good non-Giffen is substitution effect exceeds income effect
–Inferior good Giffen if income effect exceeds substitution effect
•Size of income effect
–Income effect of price change large if good large fraction of consumer
expenditures
•Giffen goods revisited
–Giffen goods are inferior
–Giffen goods account for a large portion of consumer expenditures
–However, goods that make up a large portion of your budget are
generally normal.
–Conditions above explain why so rare (or nonexistent)

34. Example)
Beatrice has a monthly income of $100 and buys gasoline (Pg =
$2) and a composite commodity Y (Py = $2). Say Beatrice
consumes 20 gallons of gas and 30 units of Y each month (let’s
call that bundle “A”).
In order to reduce our use of foreign oil, the government places
a tax on gasoline resulting in a new price for gas of Pg = $4. But
to eliminate the hardship of extra taxes, the government decides
to give citizens like Beatrice $40 per month. They call this the
Gas Tax and Gift Policy (GaTGiP).
Will Beatrice be better or worse off after the GaTGiP, Tax and
Gift policy? Verbally and using the above graph, explain how you
know.
Will the tax raise enough revenue to pay for the $40 gift?
Explain.

35. Substitutes/Complements
When P
X
↑Q
Y
↓(Complements),
1.True/False: Y could not possibly be an inferior
good for you.
2.True/False: X could not possibly be an inferior
good for you.

36. Compensated Demand Curve
•Curve showing, for each price, what the
quantity demanded would be if the consumer
were income-compensated for all price
changes (if there were no income effect.)
•Allows for isolation of substitution effect
•Confirms that compensated demand curve
downward sloping

37. EXHIBIT 4.12 Compensated and Uncompensated
Demand Curve
Price Qd
P
1
=$1 7
P
2
=$3 1

38. Summing Individual Demands to Obtain Market Demand

39. Elasticity
•Anticipate changes in consumer buying habits
•Prediction about direction of change
–If income increases or price falls, consumer buys more
•No predictions about magnitude of change
–Consumption and expenditures change by how much
•An elasticity can be calculated for any
relationships between two variables
–the price elasticity of demand
–the income elasticity of demand
–the cross-price elasticity.

40. Price Elasticity
•If price of the good decreased by one dollar,
by how many units would you increase your
consumption of X?
•If price of the good decreased by 1%, by what
percent would you increase your consumption
of X?
•Slope = e =
%
%
Q
P
D
D
Q
P
D
D

41. Price Elasticity of Demand
Arc Price elasticity:
Point Price elasticity:

2 1
2 1
2 1
2 1
( )
( )
% 100 /
2
( )% 100 /
( )
2
Q Q
Q QQ
Q Q Q Q
P P PP P P
P P P
-
+D
D ·D
= = =
D -D ·D
+
Q
P
P
Q
PP
QQ
P
Q
·
D
D
=
D·
D·
=
D
D
/100
/100
%
%
The coefficient on Price of demand function.

Ex) Q=22-2P: 2-=
D
D
P
Q

42. More about Price Elasticity
•Demand highly elastic when price elasticity of
demand has large absolute value
•Why one good is more elastic?
–Availability of substitutes

43. More about Price Elasticity
Elasticity Demand is
considered…
If P increases, then
total expenditure...
e = 0 perfectly inelasticQd completely
insensitive to D in P
increases
0 < e < 1 inelastic Qd highly
insensitive to D in P
increases
e = 1 unit elastic % D in Qd exactly
the same as the % D
in P
does not change
1 < e < ¥ elastic Qd highly sensitive
to D in P
decreases
e = ¥ perfectly elasticQd extremely
sensitive to D in P
decreases

44. REVENUE/EXPENDITURE AND ELASTICITY
Demand Curve: Qd = 22-2P (or P = 11-.5Qd)
Price Quantity Point
Elasticity
Total
Revenue
Elastic?
10 2 20
9 4 36
8 6 48
7 8 56
6 10 60
5 12 60
4 14 56
3 16 48
2 18 36
1 20 20

45. Income Elasticity
Income elasticity
=
Q
I
I
Q
QI
IQ
II
QQ
I
Q
·
D
D
=
·D
·D
=
D·
D·
=
D
D
/100
/100
%
%
Elasticity Goods are considered…
e
Y
< 0 Inferior good
0 ≤ e
Y
≤1 Normal, Necessity
e
Y
> 1 Normal, Luxury
The coefficient on INCOME of
demand function.
Ex) Q=1200-16*P+0.2*I :
2.0=
D
D
I
Q

46. Relationship between Income and Price
Elasticity of Demand
•Determinants of value of price elasticity of demand
–Size of substitution effect
–Size and direction of income effect
•Larger for goods that take up large fraction of income
•Larger for goods with high income elasticity of demand
•Income effect depends on whether good normal or inferior
–Normal: larger income effect means larger price elasticity of demand
–Inferior: larger income effect means smaller price elasticity of
demand

47. Cross Elasticity of Demand
•Demand for good X affected by change in price of some other
good Y
–Use cross elasticity of demand to measure size of effect
–Percent change in consumption of good X divided by the percent
change in the price of good Y
•Used to determine level and amount of monopoly power held
by certain firms in antitrust cases
Elasticity Goods are considered…
e
Qa,Pb
> 0 Substitutes
e
Qa,Pb
= 0 Independent goods
e
Qa,Pb
< 0 Complements