Economics 215
Intermediate Macroeconomics
Homework Assignment 3
Assigned: Monday, April 23 2001
Due: Thursday, May 4, 2001
1.
Permanent Income and Consumption
Consider three households each of which will live for two periods. These households each
begin with zero wealth, but will earn a certain amount of income in terms of goods in each
period. The following table lists the income earned by households in each period
Income in Period 1
Income in Period 2
Household #1
150
220
Household #2
200
220
Household #3
250
220
Assume all households can borrow and lend at a goods interest rate of 10% (1+r = 1.10).
Solve for the permanent income level for each household. Assuming that each household
consumes permanent income in period 1, what is the period 1 saving level for each
household? Now, solve for permanent income and period 1 saving for each household under
an interest rate of 15% (1+r = 1.15). Why does household 3, which had positive saving under
the original interest rate, have a lower saving level under the higher interest rate? Why does
household 2, which had negative saving under the original interest rate, have a higher saving
level under the higher interest rate?
The formula for permanent income of a consumer
is C 
Q
Q
C
1 r
 Q1  2  C 
[Q1  2 ] . The formula for savings would then
1 r
1 r
2r
1 r
be S = Q1 – C. Calculating this for each household under each interest rate
C
r = .1
r = .15
Household #1
C = 183.33
S = -33.33
C = 182.56
S = -32.56
Household #2
C = 209.52
S = -9.52
C = 209.30
S = -9.30
Household #3
C = 235.71
S = 14.29
C = 236.05
S = 13.95
The rise in the interest rate reduces the lifetime income of the borrowing household – they
have to pay higher interest rates. Thus, the rise in interest rates from r = .1 to r = .15 reduces
their consumption in both periods, while increasing initial savings. The rise in the interest
rate has an opposite effect on the saving household. For them, the rise in interest rates is an
increase in income. They increase consumption in both periods and reduce savings.
2.
World Interest Rate and the Current Account
Imagine the world financial market is made up of 2 large economies and one small economy.
Each economy has a downward sloping investment schedule (in the interest rate) and an
upward sloping saving schedule. The first large economy, Europe, has an investment and
saving schedule
SEU = 14500 + 10000r
IEU = 15500 – 20000r
The second large economy, Japan, has an investment and saving schedule
SJPN = 12000 + 20000r
IJPN = 17900 – 10000r
The third economy, Hong Kong, has an investment and saving schedule
.
SHK = 500 + 5000r
IHK = 600 – 5000r
If each country were closed, then the interest rate that prevailed in that economy would set
savings equal to investment in each economy. Solve for the closed economy interest rate in
each economy. Now, assume that each economy is part of the world financial market. What is
the world interest rate that sets the sum of world savings equal to world investment? Solve for
the level of savings, investment and the current account for each economy at the world
interest rate. Assume some event happened which shifted out the investment schedule of the
EU. Show, graphically, how that would change the world interest rate and the current account
in Hong Kong. Assume that the new EU investment schedule is
IEU = 19000 – 20000r
Solve for the new world interest rate and the new level of the current account in Hong Kong.
The closed economy interest rate for each economy sets savings equal to investment:
SEU = 14500 + 10000r = IEU = 15500 – 20000r  rEU = 1/30 =
.033
SJPN = 12000 + 20000r = IJPN = 17900 – 10000r  rJPN = .197
SHK = 500 + 5000r = IHK = 600 – 5000r
 rHK = .01
The world interest rate sets world savings = world investment
SEU + SJPN + SHK = IEU + IJPN + IHK = 27000 +35000r = 34000 – 35000r  rW =
.1
SEU = 15500; IEU = 13500  CAEU = SEU – IEU = 2000
SJPN = 14000; IJPN = 16900  CAJPN = -2900
SHK = 1000; IHK = 100
 CAHK = 900
An increase in investment spending by the EU implies
SEU + SJPN + SHK =IEU + IJPN + IHK = 30500 +35000r = 34000 – 35000r  rW =
.15
SHK = 1250; IHK = -150 CAHK = 1400
3.
Assume that Malaysia has a net international investment position of B 0 = -50 billion ringgit
worth of goods. Assume a constant real interest rate of 5% per year and a constant trade
surplus in periods 1 through infinity NX1 = NX2 = NX3 = ……NX = NX. Solve for NX.
NX 3
NX N
NX 2

 .... 
 ......
2
1 r
(1  r )
(1  r ) N 1
NX
NX
NX
 1.05 * 50  52.5  NX 

 .... 
 ....
2
1.05 (1.05)
(1.05) N 1
1
1
 NX  1.05 NX  NX
 NX  .05 * 50  2.5
1
.05
1
1.05
1.05

 (1  r ) B0  NX 1 