Paperplane
Tutorial 3 Solutions 1) In a world of two goods, will the fact that one of the goods is normal have any implication regarding whether the two goods are gross substitutes or complements? Y Io 0 PY X normal
Yo
•
A
BN •
C S •BN
Complements ↓Px → Y↑ U0 U1 Gross substitutes ↓Px → Y↓
c
•
X0 X1
Io 0 PX
Io 1 PX
X
2) In a world of two goods, when the demand elasticity of good X is greater than unity, X and Y must be gross substitutes and X is more likely to be a normal good. True or false? Explain. X normal
Io 0 PY
Yo
•
A
Complements ↓Px → Y↑ c
•
U0 SE X0 X1 Io 0 PX
Gross substitutes ↓Px → Y↓
Io 1 PX
X
↓Px → demand is elastic → Total spending on X will rise. As nominal income is unchanged, total spending on Y must fall. As the price of Y remains unchanged, the quantity demanded of Y must fall. Y↓ Hence, X and Y must be gross substitutes. From the diagram, they lie on the right of C. Therefore, X is a normal good.
1
3) In a world of two goods, if the price of x decreases at the same time that the price of y increases in such a way that the real income under Slutsky’s definition remains unchanged, individuals will be worse off. True or false, explain. Y Io 0 PY Io 1 PY A • B •
U1 U0
Io 0 PX
Io 1 PX
X
As the individual ended up with a higher utility, he is now better off than before.
2
4) The Slutsky substitution effect is always greater than the Hicksian substitution effect if X is normal. True or false? Will your answer change if X is inferior?
X is normal. SEs > SEH T/F
Y Inf Normal
C I •S •CS
N
Px↑ IES > IEH N X is normal ⇒ SEH > SES X is inferior ⇒ SEH < SESI
Io 0 PY
CH• •B
•A
U1 U0 U2
SES
I N
SES
SEH
IES IEH Io 1 PX IH Is 1 PX PX1 Io 0 PX X
X1
Y Io PY0
Inf Normal
↓Px IEH > IES
X is normal ⇒ SEH < SES I X is inferior ⇒ SEH > SES
A •
N
CSI
•
CH C N S •
•
I SES
U1 U0
SES SEH
N
IEH IES X1 Io 0 PX IH Is 1
Yo
•
A
BN •
C S •BN
Complements ↓Px → Y↑ U0 U1 Gross substitutes ↓Px → Y↓
c
•
X0 X1
Io 0 PX
Io 1 PX
X
2) In a world of two goods, when the demand elasticity of good X is greater than unity, X and Y must be gross substitutes and X is more likely to be a normal good. True or false? Explain. X normal
Io 0 PY
Yo
•
A
Complements ↓Px → Y↑ c
•
U0 SE X0 X1 Io 0 PX
Gross substitutes ↓Px → Y↓
Io 1 PX
X
↓Px → demand is elastic → Total spending on X will rise. As nominal income is unchanged, total spending on Y must fall. As the price of Y remains unchanged, the quantity demanded of Y must fall. Y↓ Hence, X and Y must be gross substitutes. From the diagram, they lie on the right of C. Therefore, X is a normal good.
1
3) In a world of two goods, if the price of x decreases at the same time that the price of y increases in such a way that the real income under Slutsky’s definition remains unchanged, individuals will be worse off. True or false, explain. Y Io 0 PY Io 1 PY A • B •
U1 U0
Io 0 PX
Io 1 PX
X
As the individual ended up with a higher utility, he is now better off than before.
2
4) The Slutsky substitution effect is always greater than the Hicksian substitution effect if X is normal. True or false? Will your answer change if X is inferior?
X is normal. SEs > SEH T/F
Y Inf Normal
C I •S •CS
N
Px↑ IES > IEH N X is normal ⇒ SEH > SES X is inferior ⇒ SEH < SESI
Io 0 PY
CH• •B
•A
U1 U0 U2
SES
I N
SES
SEH
IES IEH Io 1 PX IH Is 1 PX PX1 Io 0 PX X
X1
Y Io PY0
Inf Normal
↓Px IEH > IES
X is normal ⇒ SEH < SES I X is inferior ⇒ SEH > SES
A •
N
CSI
•
CH C N S •
•
I SES
U1 U0
SES SEH
N
IEH IES X1 Io 0 PX IH Is 1