Midterm Examination
Economics 215
Intermediate Macroeconomics
Date: March 22, 2001
Start Time 7:00 PM End Time – 9:00
1. As a financial analyst, you observe that the average ratio of stock prices to
dividend payments is currently 20. Assume that the interest rate of 8% per
year will remain constant through the future. Assume that the price of stocks is
equal to the present value of future dividends (not including the current
dividend payment). Assume that the growth rate of dividends will be constant
through the future. What would the growth rate be? We can write the sum of
dividends as
1 g
2
N
1

g
1

g
1

g




1 i D  1 g D
P EQ 
D
D

....

D

.....


 1 i 
1 g
1 i
ig
 1 i 


1
1 i
EQ
P
1 g
.6
 20 
g
 .0286
D
.08  g
21
2. Hong Kong’s (nominal) GDP was 5.5 trillion Hong Kong Dollars in 1997. In
base year 1996 dollars, Real GDP was Q97 = 5 trillion dollars. The nominal
interest rate offered by Hong Kong banks in 1996 was 15%. What was the
goods interest rate in 1996? The price deflator in 1997 is the ratio of the nominal
GDP to real GDP P97 = 1.1. Since 1996 is the base year, the price deflator in 1996 is P96 =
1. This implies the inflation rate in 1997 is
1  Pˆ97  1.1  1  r96 
1  i96 1.15

 1.0454
1.1
1  Pˆ97
3. You pick up the newspaper, and see that the spot exchange rate between the
Hong Kong dollar and the Japanese Yen is .10 (i.e. .1 Hong Kong Dollars are
necessary to buy 1 Japanese Yen). The 1-year forward rate is .11 (i.e. if you
promise to deliver .11 HK dollars in 1 year, a counter party will promise to
deliver 1 yen). The 1-year interest rate on an Exchange Fund bond is 15%. The
yield to market on a 2-year yen bond issued by the Japanese government is
5%. If the Uncovered Interest Parity AND the Covered Interest Parity Theory
AND the Expectations Theory of the Term Structure are true, what does the
market expect the Hong Kong dollar/Yen spot exchange rate and the 1-year
interest rate on Yen bonds to be next year? Covered interest parity implies
F
JPN
JPN
1  iHK
 (1  iJPN
0 ,1 
0 ,1 )  1.15  1.1  (1  i  0 ,1 )  (1  i  0 ,1 )  1.0454 . The
E
expectations theory of the term structure implies that
JPN
iJPN
0 ,1  i 1,1
JPN
JPN
i 0, 2 
 .1  .0454  iJPN
1,1  i 1,1  .0546 . Uncovered interest
2
parity implies
1 i
HK
 0,1
E E1
E

 (1  iJPN
0 ,1 )  F  E 1  .11
E
4. In 1999, the Philippines had a (nominal) GDP valued at 2,996,371million
pesos. In 1999, Hong Kong had a (nominal) GDP valued at 1,233,133 million
HK dollars. In 1999, the exchange rate was E = .2, i.e. you needed .2 HK$ to
buy 1 Philippine Pesos.
a. Convert the Philippines GDP into HK dollars using the exchange rate
HK $
 .2  2996371 =599274.2 million
method. XRGDPPhil
b. Divide Philippines goods into two categories: tradable goods (such as
manufacturing goods) and non-tradable goods (such as personal
services). The ratio of prices of Philippines tradable goods (in terms of
pesos) to the prices of Hong Kong tradable goods (in terms of dollars)
is 5. The ratio of prices of Philippines non-tradable goods (in terms of
pesos) to the prices of Hong Kong non-tradable goods (in terms of HK
dollars) is 2. Calculate a PPP conversion factor as a weighted average
of the relative prices of tradable and non-tradable goods, with a weight
of .5 on each type of good. Use that to convert the Philippines GDP to
HK dollars using the PPP method.
$
HK $
  PTHK

 PNT

, HK
, HK



  .5.2   .5.5  .35
PPP   w1 P
 w2 P
P

P

 NT , PHIL 
  T , PHIL 
PPPGDP  .35  2996371
PPPGDP
 .35 * 2,996,371million  1048729million
c. The population of the Philippines in 1999 was 75.2 million. The
population of Hong Kong in 1999 was 6.7 million. Calculate per capita
(PPP converted) output of Hong Kong and the Philippines
PC PPPGDPPhil = 1,048,729/75.2 = 13,945
PC RGDPHK = 1,233,133/6.7 = 184049
HK $
Phil
Longer Answers
I
=.
Q
2). The country has a depreciation rate of 10% (d=. 10) and a population
growth rate of 2% (n = .02). Assume the country has a Cobb-Douglas
I. GROWTH (30 points) A country has an investment rate of 20% (s =
1
1
production function Q  K 2 (XL) 2 where K = physical capital, X =
technology, and L = labor.
A. What is the growth rate of the capital per labor ratio when the returns
to investing in physical capital are 5% (i.e. (1-d)+MPK = 1.05)? [Hint:
A Cobb-Douglas production function implies that the average
q
productivity of capital, , is proportional to the marginal product of
k
capital, MPK].
The marginal productivity of capital is proportional to the average
(1  d )  MPK  1.05  MPK  .15
productivity of capital
We can write
q
q
MPK  12   .3
k
k
the accumulation of physical capital as
K
k K
k 

n
L
k
K
K
I
sQ
sq
K 1  (1  d ) K  I  K  I  dK 
 d 
d 
d
K
K
K
k
k
q
 s  (d  n)  .2 * .3  (.1  .02)  .06
We can then derive
k
k
B. The growth rate of X factor technology is 2% (i.e. gX =.02). What is
the average productivity of capital along the mature growth path? What
is the marginal product of capital along the mature growth path? What
is the growth rate of the average productivity of labor on the mature
growth path? Along the mature growth path, the growth rate of the
capital labor ratio is equal to the growth rate of technology. We
can then write
k
q
q
q
 s  (d  n)  g X  .2 *  (.1  .02)  .02   .7
k
k
k
k
q
q
MPK  12  MPK  .35 . If is constant, the numerator must be
k
k
growing at the same rate as the denominator, so gq = gk = gX.
C. On the mature growth path, it is possible to solve for the average
productivity of labor as a function of the X factor technology level.
That is, on the mature growth path q=AX. Solve for
1
1
Q K 2  XL  2  K  2   XL   2
q 
  
  k  2 X 2 
L
L
L  L 
1
1
1
1
1
q k  2 X 2
1
 k  2 X 2  .7 
A. 
k
k
1
1
1
 1  2  2 1 1
1
k    X  q    X  X 2 
.7
 .7 
 .7  
2
II. INVESTMENT (30 points) We analyze capital investment in Finland. We
assume that in Finland, the X factor of technology is constant at a level of
X = 1. Finland has a Cobb-Douglas production function.
 
1
1
   
1
1
Q  K F 2 [ LF ] 2  MPK  12 K F 2 LF 2 .
The depreciation rate in Finland is 5% (d = .05) and the goods
interest rate is 5% (r = .05).
A. Solve for the capital-labor ratio in Finland when the rate of return on
physical capital is equal to the interest rate. Solve for the average
productivity of labor implied by that target capital stock. As we saw in
class 1+ik = 1+i implies MPK=r+d
=.05+.05=,10
MPK 
1
2
K  L 
1
F 2
F
1
2
 12 k
 12
 .1  k  25,
1
q k2 5
B. Explain in 1 graph and 1 paragraph why an increase in the goods
interest rate would lead to a decline in the capital labor ratio and a
decline in the average productivity of labor.
If firms choose an amount of physical capital to maximize their total return, they
will shift funds away from physical capital and toward bank deposits whenever
the returns on bank deposits are above those on physical capital. A rise in the
goods interest rate will increase the returns on bank deposits. This will lead firms
to reduce their capital stock (in other words to disinvest), and shift funds to bank
deposits. As firms reduce their capital stock, the remaining capital stock will be
used by more workers and will produce higher returns. Capital will drop until the
returns on capital rise to equal the new interest rate. Thus, the capital per worker
will drop and the output per worker will also drop as each worker has less capital
available.