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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 PX PX1 Io 1 PX X

X0

3

5) You observe a consumer in two different market situations: (i) earning $100 and spending it on 5 units of x at the price of $10 each and 10 units of y at the price of $5 each; (ii) earning $175 and buying 3 units of x at the price of $15 and 13 units of y at the price of $10. Is the consumer rational ?

Q(6) Io = 100, Px0 = 10, Py0 = 5. Choose A(5X,10Y) I1 = 175, Px1 = 15, Py1 = 10. Choose B(3X,13Y). Is he rational? Y

1) He choose A when B is feasible.
I0 =20 0 PY 17.5

2) He chose B when A is still feasible. Not rational.
B • •A

13

10

3

5

Io/ Px =10

0

11.67

X

We begin at point A where the following budget line applies: Px Xo + Py Yo = Io. 10 ∗ 5 + 5 ∗ 10 = 100 Now, we have a new budget line and a new choice B: Px X1 + Py Y1 = I1 15 ∗ 3 + 10 ∗ 13 = 175 Is A(5X, 10Y) is on the new budget line? Px 5 + Py 10 = 15 ∗ 5 + 10 ∗ 10 = 175 Hence A is on the new BL. 1 1 1 1 0 0

Yes

4

6) When the price of X is 3 and price of Y is 3, an individual consumes a bundle of X=4, Y=4. When the price of X has become 1 and the price of Y is 5, the individual chooses a bundle of X=3, Y=5. Therefore the consumer prefers (3,5) over (4,4). True or false, explain. Y I0 0 PY 8 I1 28 1 PY 5 5 B

• A •

4

U0

CU • 2

3

4

8 I0 0 Px

28 X I1 1 Px

This is a question about choice and could be analysed by the use of ‘revealed preference approach’. 0 0 At A(4,4), I0 = Px X0 + Py Y0 = 3(4) + 3(4) = 24 1 1 At B(3,5), I1 = Px X1 + Py Y1 = 1(3) + 5(5) = 28 Using indifference curve analysis, it is easy to see that the individual behaves irrationally by choosing B.

5

7) A good is a normal good whenever the substitution and income effects work in the same direction. True or false? Explain. Y I0 0 PY A • 1 PX X 0 PY

X normal X inferior

↓Px

C •

Uo

BN •

U1

X2 X0

X1

X I0 0 PX

X

When an individual receives income in kind of units of X, the SE and IE can move in the...
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