Instructor: Marco Del Negro
Economia V, Spring 2000

PROBLEM SET 2, SOLUTIONS

3) México. U.S.
Px=10 pesos P= Px/Py= 1/5
Py= 1 peso Px=5py
e=10 pesos Px/5=0.2
x= gold Y= haircuts Px=1 U.S. (tradable good)

$$\alpha=0.3 \mbox{ } Z=10_US\$$$

$$\hat{Z}=\frac{Z_M}{p_XM}=100p/10p=10 \mbox{ } \hat{Z}=\frac{Z_US}{P_US}=10/1=10$$

$$P=1/10 \mbox{ } p=1/5$$

$$U(x,y)=\frac{\hat{z}}{P^{1-\alpha}} \mbox{ } U(x,y)= \frac{10}{(\frac{1}{5})^{0.7}}=30.85$$

U(x,y)=50.11

4)

W=20 Y₁=90 Y₂=110 C=0.1

$$a) PV= W+Y_1+\frac{Y_2}{1+r}=20+90+\frac{110}{1.1}=210$$

(1+r)(Y₁+W-C₁)=C₂-Y₂

(1.1)(90+20+C₁9=C₂-110

(99+22-(1.1)C₁)=C₂-110

121-(1.1)C₁=C₂-110

place for graph

$$c) \beta=1$$

$$C_1=\frac{1}{1+\beta}(W+Y_1+\frac{Y_2}{1+r})=\frac{1}{1+1}(210)=105$$

$$C_2=\frac{(1+r)\beta}{1+\beta}(W+Y_1+\frac{Y_2}{1+r})(\frac{(1.1)1}{1+1}(210)=115.5$$

SAVE S
d) d1)

$$W=20 \mbox{ } Y_1=101 \mbox{ } Y_2=110 \mbox{ } r=0.1$$

$$C_1=\frac{1}{1+\beta}(W+Y_1+\frac{Y_2}{1+r})=\frac{1}{1+1}(20+101+\frac{110}{1.1})=110.5$$

S=W+Y₁-C₁=20+101-110.5010.5

d2)

$$W=20 \mbox{ } Y_1=90 \mbox{ } Y_2=121 \mbox{ } r=0.1$$

$$C_1=\frac{1}{1+\beta}(W+Y_1+\frac{Y_2}{1+r}=\frac{1}{2}(20+90+\frac{121}{1.1}=110$$

S=w+Y₁-C₁=20+90-110=0

d3)

$$W=31 \mbox{ } Y_1=90 \mbox{ } Y_2=110 \mbox{ } r=0.1$$

$$C_1=\frac{1}{2}(30+90+\frac{110}{1.1})= \frac{1}{2}(221)=110.5$$

S=10.5

5)
a) CC goes up savings go down
b) C=
c) CC=goes down, s goes up
d) if Y₂ goes down: CC goes down, S goes up
if Y₂=, CC=, S=
e) C= (permanent income does not change)
f) CC goes down, S goes up