Change in Income Flashcards
How do you find the Engel Curve, given Demand Function x* (p1, p2, m)?
Plot x* against m
What is Engel Curve?
Shows Relationship between Income + Quantity chosen of a particular Good
Suppose U(x1, x2) = x1^0.5 x2^0.5, p1 = 1 & p2 = 4 What are the Engel Curves?
Good 1 => m = 2x1*
Good 2 => m = 8x2*
Suppose U(x1, x2) = x1 + x2 , p1 = 3 & p2 = 4 What are the Engel Curves?
Perfect Substitutes
Good 1 => m = 3x1*
Good 2 => x2* = 0
- No point buying if More Expensive + Perfect Sub.
Suppose U(x1, x2) = min {x1, x2} , p1 = 2 & p2 = 4
What are the Engel Curves?Perfect Complements
Good 1 => m = 6x1*
Good 2 => m = 6x2*
- Consumed in Fixed Proportions –> Same Engel Curve
What are the 4 possible cases for Engel Curves?
Normal Goods
Luxury Goods
Necessary Goods
Inferior Goods
What do Engel Curves of Normal Goods show?
Increased Income –> Increased Consumption
What do Engel Curves of Luxury Goods show?
Increased Demand by GREATER Proportion than Income
What do Engel Curves of Necessary Goods show?
Increased Demand by SMALLER Proportion than Income
What do Engel Curves of Inferior Goods show?
Increased Income –> Decreased Consumption
- Downward-sloping Engel Curve
How is Income Elasticity of Demand calculated?
n = %Change in Demand / %Change in Income
If Initial Income = m0, Initial Demand = x0
New Income = m1 & New Demand = x1
What is the Income Elasticity of Demand?
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
If n > 0, what type of Good is it?
Positive n –> Increased Income –> Increased Demand or Vice Versa
- NORMAL GOOD
If n < 0, what type of Good is it?
Negative n –> Increased Income –> Decreased Demand or Vice Versa
- INFERIOR GOOD
If n > 1, what type of Elasticity is it?
Income ELASTIC
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?
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)
If p1 Decreases, what happens to I.C?
Move to Higher Utility Curve
B.C rotates to Right about x2- Intercept
- Increased x1* –> x1**
- x2-intercept Unchanged
What is Substitution Effect?
Change in Demand due to Change in Rate of Exchange (-p1/p2) between 2 Goods
- i.e. Change in Slope of B.C
What is Income Effect?
Change in Demand due to Change in Consumer’s Purchasing Power
- i.e. Change in one of Intercepts of B.C
If x1 becomes Cheaper, why do SE + IE happen?
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
How is TE calculated?
TE = SE + IE
Suppose we know: x1 ( p1, p2, m ) & Price of x1: p1 –> p’1
How do you find the SE + IE?
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’)
Why is SE ALWAYS Negative?
SE is Opposite to Price Change
- Increased Price –> Decreased Demand - sub. for more x2
- Decreased Price –> Increased Demand - sub. for less x2
For a Normal Good, when is IE Positive?
Increased Income –> Increased Demand
Decreased Income –> Decreased Demand
For an Inferior Good, when is IE Negative?
Increased Income –> Decreased Demand
Decreased Income –> Increased Demand
For a Normal Good, what are SE + IE of Price Increase?
SE => Decreased Demand - Sub. for more x2
IE => Decreased Demand - Decreased Real Income
For an Inferior Good, what are SE + IE of Price Increase?
SE => Decrease Demand - Sub. for more x2
IE => Increased Demand - Decreased Real Income
What are the directions of SE + IE for Normal Good?
Move in SAME Direction
What are the directions of SE + IE for Inferior Good?
Move in OPPOSITE Direction
Regarding SE + IE, when is there a Negative relationship between P + Q.?
If SE > IE
Regarding SE + IE, when is there a Positive relationship between P + Q.?
If IE > SE
What type of Good is it If there is a Positive Relationship when Price Increases?
Increased Price –> Increased Demand
- GIFFEN GOOD
What does Slutsky SE do?
Adjust Income so Original Bundle is Affordable
- Pivot B.C around Initial Bundle
What does Hick’s SE do?
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
Which Demand Curve is Compensated Demand?
Hick’s Demand - holding Utility Fixed
- Compensated for Price Change to keep Utility Constant
What is the Slope of Ordinary Demand Curve for Normal, Inferior + Giffen Goods?
Normal + Inferior - DOWNWARD-sloping – SE > IE
Giffen - UPWARD-sloping – IE > SE
