Change in Income

Question 1

How do you find the Engel Curve, given Demand Function x* (p1, p2, m)?

Answer 1

Plot x* against m

Question 2

What is Engel Curve?

Answer 2

Shows Relationship between Income + Quantity chosen of a particular Good

Question 3

Suppose U(x1, x2) = x1^0.5 x2^0.5, p1 = 1 & p2 = 4
What are the Engel Curves?

Answer 3

Good 1 => m = 2x1*

Good 2 => m = 8x2*

Question 4

Suppose U(x1, x2) = x1 + x2 , p1 = 3 & p2 = 4
What are the Engel Curves?

Answer 4

Perfect Substitutes
Good 1 => m = 3x1*
Good 2 => x2* = 0
- No point buying if More Expensive + Perfect Sub.

Question 5

Suppose U(x1, x2) = min {x1, x2} , p1 = 2 & p2 = 4
What are the Engel Curves?

Answer 5

Perfect Complements
Good 1 => m = 6x1*
Good 2 => m = 6x2*
- Consumed in Fixed Proportions –> Same Engel Curve

Question 6

What are the 4 possible cases for Engel Curves?

Answer 6

Normal Goods
Luxury Goods
Necessary Goods
Inferior Goods

Question 7

What do Engel Curves of Normal Goods show?

Answer 7

Increased Income –> Increased Consumption

Question 8

What do Engel Curves of Luxury Goods show?

Answer 8

Increased Demand by GREATER Proportion than Income

Question 9

What do Engel Curves of Necessary Goods show?

Answer 9

Increased Demand by SMALLER Proportion than Income

Question 10

What do Engel Curves of Inferior Goods show?

Answer 10

Increased Income –> Decreased Consumption

- Downward-sloping Engel Curve

Question 11

How is Income Elasticity of Demand calculated?

Answer 11

n = %Change in Demand / %Change in Income

Question 12

If Initial Income = m0, Initial Demand = x0
New Income = m1 & New Demand = x1
What is the Income Elasticity of Demand?

Answer 12

n = [(x1(m1) - x0(m0)) / x0(m0)] / [(m1 - m0) / m0]
= [dx / x(m0))] / (dm / m0)
= (dx / dm) (m0 / x0)
i.e. (New - Old) / Old for both Demand + Income

Question 13

If n > 0, what type of Good is it?

Answer 13

Positive n –> Increased Income –> Increased Demand or Vice Versa
- NORMAL GOOD

Question 14

If n < 0, what type of Good is it?

Answer 14

Negative n –> Increased Income –> Decreased Demand or Vice Versa
- INFERIOR GOOD

Question 15

If n > 1, what type of Elasticity is it?

Answer 15

Income ELASTIC

Question 16

Suppose we know x1(p1, p2, m) & x2(p1, p2, m)
Price p1 Increases: p1 –> p’1
Price p2: Unchanged
Income m: Unchanged
What is the TE of Price change on each good?

Answer 16

New Optimal Bundle: x1(p’1, p2, m) & x2(p’1, p2, m)
TE: dx1 = x1(p’1, p2, m) - x1(p1, p2, m)
dx2 = x2**(p’1, p2, m) - x2(p1, p2, m)

Question 17

If p1 Decreases, what happens to I.C?

Answer 17

Move to Higher Utility Curve
B.C rotates to Right about x2- Intercept
- Increased x1* –> x1**
- x2-intercept Unchanged

Question 18

What is Substitution Effect?

Answer 18

Change in Demand due to Change in Rate of Exchange (-p1/p2) between 2 Goods
- i.e. Change in Slope of B.C

Question 19

What is Income Effect?

Answer 19

Change in Demand due to Change in Consumer’s Purchasing Power
- i.e. Change in one of Intercepts of B.C

Question 20

If x1 becomes Cheaper, why do SE + IE happen?

Answer 20

Cheaper x1 –> Consumer must Give up LESS x2 to buy More x1

• Incentive to SUBSTITUTE x2 for More x1 - SE
• • Consumer’s Real Income Increases: m/p1 –> m/p’1 - IE

Question 21

How is TE calculated?

Answer 21

TE = SE + IE

Question 22

Suppose we know: x1 ( p1, p2, m ) & Price of x1: p1 –> p’1
How do you find the SE + IE?

Answer 22

SE: Compute New Q. of x1 at p’1 - But Adjust Income to level that Affords Original Bundle - denote m’
SE = dx1s = x1 (p’1 , p2, m’) - x1 (p1, p2, m)
IE = dx1n = x1 (p’1, p2, m) - x1 (p’1, p2, m’)

Question 23

Why is SE ALWAYS Negative?

Answer 23

SE is Opposite to Price Change

• Increased Price –> Decreased Demand - sub. for more x2
• Decreased Price –> Increased Demand - sub. for less x2

Question 24

For a Normal Good, when is IE Positive?

Answer 24

Increased Income –> Increased Demand

Decreased Income –> Decreased Demand

Question 25

For an Inferior Good, when is IE Negative?

Answer 25

Increased Income –> Decreased Demand

Decreased Income –> Increased Demand

Question 26

For a Normal Good, what are SE + IE of Price Increase?

Answer 26

SE => Decreased Demand - Sub. for more x2

IE => Decreased Demand - Decreased Real Income

Question 27

For an Inferior Good, what are SE + IE of Price Increase?

Answer 27

SE => Decrease Demand - Sub. for more x2

IE => Increased Demand - Decreased Real Income

Question 28

What are the directions of SE + IE for Normal Good?

Answer 28

Move in SAME Direction

Question 29

What are the directions of SE + IE for Inferior Good?

Answer 29

Move in OPPOSITE Direction

Question 30

Regarding SE + IE, when is there a Negative relationship between P + Q.?

Answer 30

If SE > IE

Question 31

Regarding SE + IE, when is there a Positive relationship between P + Q.?

Answer 31

If IE > SE

Question 32

What type of Good is it If there is a Positive Relationship when Price Increases?

Answer 32

Increased Price –> Increased Demand

- GIFFEN GOOD

Question 33

What does Slutsky SE do?

Answer 33

Adjust Income so Original Bundle is Affordable

- Pivot B.C around Initial Bundle

Question 34

What does Hick’s SE do?

Answer 34

Adjust Income so Original Utility Level remains Same w/ New Relative Prices
- Roll B.C around I.C of Initial Choice
- Keeps Utility Constant instead of Maintaining Purchasing Power Constant
Also NEGATIVE

Question 35

Which Demand Curve is Compensated Demand?

Answer 35

Hick’s Demand - holding Utility Fixed

- Compensated for Price Change to keep Utility Constant

Question 36

What is the Slope of Ordinary Demand Curve for Normal, Inferior + Giffen Goods?

Answer 36

Normal + Inferior - DOWNWARD-sloping – SE > IE

Giffen - UPWARD-sloping – IE > SE