ECN 2001
MICROECONOMICS I
SLUTSKY EQUATION
Class Discussion 6 (Ch. 7) - Answer Key
TRUE-FALSE
Two people are flying in a hot air balloon and they realize they are
lost. They see a man on the ground, so they yell to him:
-Please help us sir. We are lost. Where are we now?
The man replies:
-You’re in a hot air balloon, about two fifty meters off the ground.
One of the men replies:
- Well then sir, you are an economist, aren’t you?
- Yes, how did you know?
- You gave us the true explanation, but it’s completely useless.
The economist on the ground then says:
- Well then, you are a politician, aren’t you?
- Yes, how did you know?
- You’re in the same situation you were in before you talked to me,
but now it’s my fault!
1. FALSE
Jimmy’s old consumption lies on his new budget line means that the new budget line cuts the old budget line at the
equilibrium point. This does not mean that Jimmy will still buy the same bundle, because the new budget line is not
tangent to the old indifference curve (I0). In the graph below, Jimmy can increase his utility by moving to a new
equilibrium at point E2 and increase his utility (I1).
2. FALSE
When preferences are homothetic, the change in demand that results from a price change may be due to the
income affect, as well as the substitution effect.
3. TRUE
Every Giffen good is an inferior good, but not every inferior good is a Giffen good.
4. FALSE
This only holds true for Giffen goods. When the price of a Giffen good increases, the quantity demand for it
increases as well. Yet for other inferior goods, an increase in price decreases quantity demanded.
5. TRUE
When the price of the Giffen good rises, the demand for it increases as well. So Ivan now has less money left to
spend on the other good.
MULTIPLE CHOICES
1. E - The substitution effect increases the quantity of x by 90.
In order for Walt to consider x and y to be perfect substitutes, the ratio of the marginal utilities of these two
goods has to be equal to one for him: “MUX / MUY = 1”. This means that the indifference curve’s slope is -1 at
every point on it; making it a non-convex, negatively sloped straight line. So Walt has non-convex preferences,
so we require a corner solution (boundary optimum).
Slope of budget curve = -(PX/PY)
Before the price change, slope of the budget curve is equal to -(10/9). After the price change, it is -(8/9).
At first, Walt is at equilibrium at point E1, according to the corner solution. After the price changes and the Budget
Line 1 rotates to take the shape of Budget Line 2, his new equilibrium is at E2.
In order to detect the substitution effect, we always draw a pivoted budget line which must
a) Be parallel to the final (new) budget line.
This condition confirms that the pivoted budget line reflects the price changes. (Remember that a budget
line’s slope is equal to the ratio of two prices.)
b) Intersect the old (first) equilibrium point.
This condition confirms that Charlie is set to be consuming the same bundle of goods, so his real income is
still the same as it was before prices changed.
Once we draw this new (pivoted) budget line, we find that it actually is the final budget line which reflects the price
change. The reason is that there can be only one line that is both parallel to the new budget line and intersects the
old equilibrium point, and it is the final budget line itself and no other. This only holds true for the perfect
substitutes case. As the change in demand reflected by the pivoted budget line is due to the substitution effect, we
decide that the hole change in demand that results from this price change is due to the substitution effect and
there is no income effect. ∆X= ∆XS
2. C
Normal Goods (income elasticity > 0)
PX
Income
Effect
(∆Xm)
↑
M
Inferior Goods (income elasticity < 0)
↓ Q dx ↓
PX
↑
M
↓ Q dx ↑
When price of a normal good INCREASES, real
income (M) of the consumer decreases. This
income effect causes the consumer to tend to
DECREASE his demand for the normal good.
When price of an inferior good INCREASE, real
income (M) of the consumer decreases. This
income effect causes the consumer to tend to
INCREASE his demand for the inferior good.
This means that income effect of a price
increase on demand is NEGATIVE for normal
goods. So the income effect results in a
NEGATIVE RELATIONSHIP between price and
demand for normal goods.
This means that income effect of a price
increase on demand is POSITIVE for inferior
goods. So the income effect results in a
POSITIVE RELATIONSHIP between price and
demand for inferior goods.
INTERPRETATION
As consumers’ income levels decrease, the income effect leads them to spend less on normal goods
and spend more on inferior goods, because inferior goods are cheaper than normal goods.
PX
Substitution
Effect
(∆Xs)
↑
P X / Py
↑ Q dx ↓
PX
↑
P X / Py
↑ Q dx ↓
When price of a normal good INCREASES, it
becomes more expensive in relation to its
substitute(s). This substitution effect causes
the consumer to DECREASE his demand for the
good whose price has risen, and increase his
demand for the substitute good(s).
When price of an inferior good INCREASES, it
becomes more expensive in relation to its
substitute(s). This substitution effect causes
the consumer to DECREASE his demand for
the good whose price has risen, and increase
his demand for the substitute good(s).
This means that substitution effect of a price
increase on demand is NEGATIVE for normal
goods. So the substitution effect results in a
NEGATIVE RELATIONSHIP between price and
demand for normal goods.
This means that substitution effect of a price
increase on demand is NEGATIVE for inferior
goods. So the substitution effect results in a
NEGATIVE RELATIONSHIP between price and
demand for inferior goods.
INTERPRETATION
As a good becomes more expensive in relation to its substitutes, consumers always tend to move
away from that good, regardless of whether it’s a normal good or an inferior good.
Normal goods
∆X = ∆Xs + ∆Xm
(-) (-)
(-)
Inferior goods
∆X = ∆Xs + ∆Xm
(-)
(-)
(+)
INTERPRETATION
Total Effect
(∆X)
NORMAL GOODS: Both income and substitution effects of a price increase on demand are negative
for normal goods, so the total effect is always negative. This means that when the price of a normal
good increases, the quantity demanded of it always decreases, therefore the demand curve has a
negative slope.
INFERIOR GOODS: The substitution effect of a price increase is always negative on demand for
inferior goods, just like normal goods. Yet, the income effect of a price increase is always negative on
demand. The total effect depends on which effect dominates the other. If the substitution effect
dominates, the inferior good has a negatively sloped demand curve. If the income effect dominates,
the inferior good is indeed a GIFFEN good and has a positively sloped demand curve, for the total
effect is positive (a price increase causes an increase in quantity demanded).
CAUTION: The negative signs above only mean that there is a negative relationship between price
and demand, or that price and demand move in opposite direction, in other words.
3. C
In the case of perfect substitutes, the entire change in demand that results from a price change is due to the
substitution effect, just like the case in question 1.
4. D
The Cobb-Douglas utility function shows that preferences are convex. In this case, both goods are normal goods, so
after the price of good 1 decreases the income effect causes the demand of both goods to increase. In the contrary,
the substitution effect causes the demand for good 1 to increase and the demand for good 2 to decrease. The only
suiting answer is D.
|X1Xs| = Increase in demand for X due to the substitution effect
|Y1Ys| = Decrease in demand for Y due to the substitution effect
|XsX2| = Increase in demand for X due to the income effect
|YsY2| = Increase in demand for Y due to the income effect
5. C
U(XA,XB)=XA*XB
PA =1 PB =2 M=40 PA’ =7 PB’ = 2
What is the substitution effect? In order to find that, first we need to find M’. In order to find M’, we need ∆M.
First, find Charlie’s utility maximization: ( MUxA / MUxB ) = ( PA / PB )
( XA / XB ) = - 1/2
XA = 2 * XB8
Budget constraint: 40 = (1 * XA) + (2 * XB) = 4 * XB
XB= 10 , XA= 20 This is Charlie’s old (first) bundle. Keep it in mind.
∆M= XA * ∆PA = 20 * (7-1) = 120
M’=M+∆M=40+120 = 160 This is the pivoted budget.
So in order to find the substitution effect, we’ll go for utility maximization with the pivoted budget and the new
prices.
M’=160 PA’=7 PB’=2
U(XA,XB)=XA’*XB’
160 = 7* XA’ + 2* Xb’
( MUxA / MUxB ) = ( PA’ / PB’ )
( XA’ / XB’ ) = - 7/2
2XA’ = 7 * XB’
160= 14* XA’ XA’=11,43 = XA(PA’ , M’)
Subs. Effect
= XA(PA’ , M’) - XA(PA , M)
= 11,43-20 = -8,57
SECOND WAY: Using the demand curve
XA= M/2P DEMAND CURVE FOR XA
XA(PA’ , M’)= 160/2*7=11,43
XA(PA , M)=40/2*1=20
Subs. Effect: 11,43-20 = 8,57
6. A
This question is all about finding the pivoted budget.
“IN ORDER TO BE ABLE TO JUST AFFORD HIS OLD BUNDLE, CHARLIE WOULD HAVE TO HAVE A DAILY INCOME OF…”
indeed means: “CALCULATE CHARLIE’S PIVOTED BUDGET.”
U(XA,XB)=XA*XB
PA =1 PB =2 M=40
PA’ =2 PB’ =1,75
∆M=? M’=?
Charlie’s utility maximization:
( MUxA / MUxB ) = ( PA / PB )
( XA / XB ) = - 1/2
XA = 2 * XB8
Budget constraint: 40 = (1 * XA) + (2 * XB) = 4 * XB
XB= 10 , XA= 20 This is Charlie’s old (first) bundle.
In order for Charlie to afford this bundle with the new prices, he would have to have a daily income of:
(2 * XA) + (1,75 * XB) = 2*20 + 1,75*10 = $ 57,50 is the answer, which is the M’.
In order to show this result graphically, we
need to draw the pivoted budget line. The
pivoted budget line, which is parallel to the
final (new) budget line and is intersecting the
old (first) equilibrium point.