Economics 215
Intermediate Macroeconomics
Sample Midterm 2005
Multiple Choice (6 points each)
1. In 1950, a country begins with real (constant dollar) GDP per capita of $2,000. The
average growth rate of real GDP is 14% and the population growth rate is 7%. In
what year, will GDP per capita be equal to $16,000?
a. 1960
b. 1970
c. 1990
d. 2010
_______C______
2. An economy progresses from its transition phase to its balanced growth phase. In
general
a. the productivity of capital is greater during the transition phase than the balanced
growth phase while the growth rate of labor productivity is greater during the
transition phase than the balanced growth phase.
b. the productivity of capital is less during the transition phase than the balanced
growth phase while the growth rate of labor productivity is greater during the
transition phase than the balanced growth phase.
c. the productivity of capital is greater during the transition phase than the balanced
growth phase while the growth rate of labor productivity is less during the
transition phase than the balanced growth phase.
d. the productivity of capital is less during the transition phase than the balanced
growth phase while the growth rate of labor productivity is less during the
transition phase than the balanced growth phase
_____A________
3. We observe a pattern that developing economies experience real exchange rate
appreciations as they grow. Assuming uncovered interest parity is true in the long
run, we should see that for developing economies with fixed exchange rates.
a. PPP-converted GDP grows faster than exchange rate-converted GDP and
inflation will be lower than in the USA.
b. PPP-converted GDP grows faster than exchange rate-converted GDP and
inflation will be higher than in the USA.
c. PPP-converted GDP grows slower than exchange rate-converted GDP and
inflation will be lower than in the USA.
d. PPP-converted GDP grows slower than exchange rate-converted GDP and
inflation will be higher than in the USA.
______D_______
4. Nominal GDP in year 2000 was HK$1.288 Trillion; nominal GDP in 2001 was
HK$1.278 trillion. Real GDP in 2001 was HK$1.297 Trillion (measured in year 2000
dollars). If we measure nominal prices with the GDP deflator, we can say that:
a. The inflation rate in year 2001 is positive and the ex post real interest rate
of year 2000 is greater than the nominal interest rate in year 2000.
b. The inflation rate is year 2001 is negative and the ex post real interest rate
of year 2000 is greater than the nominal interest rate in year 2000.
c. The inflation rate in year 2001 is positive and the ex post real interest rate
of year 2000 is less than the nominal interest rate in year 2000.
d. The inflation rate is year 2001 is negative and the ex post real interest rate
of year 2000 is less than the nominal interest rate in year 2000.dsd
_____B________
5. We see that around the year 2000,
a. Hong Kong has a higher GDP per capita than South Korea and Hong Kong has a
more evenly distributed income than South Korea.
b. Hong Kong has a higher GDP per capita than South Korea and Hong Kong has a
less evenly distributed income than South Korea.
c. Hong Kong has a lower GDP per capita than South Korea and Hong Kong has a
more evenly distributed income than South Korea.
d. Hong Kong has a lower GDP per capita than South Korea and Hong Kong has a
less evenly distributed income than South Korea.
______B_______
Short Answer
6. (10 points) An economy consistently has $2.00 in current dollar GDP for every $1.00
in labor compensation. The rate of capital deepening is 8% (i.e. the growth rate of the
capital-labor ratio) and the growth rate of labor productivity is 6%. What is the growth
rate of total factor productivity?
The real wage rate is the marginal product of labor which is proportional to the average
product which implies that the ratio of labor compensation to nominal GDP is a. In this
case, a = .5.
W
GDP
WL
a

a
P
L
PGDP
We can say that labor productivity is a function of capital productivity and technology.
This means that labor productivity growth is a weighted average of the capital deepening
rate and the technology growth rate. We can calculate the weighted technology growth
rate.
GDPt  Kta ( Z t Lt )1a  gdpt 
GDPt
 kta ( Z t )1a  gtgdp  a  gtk  (1  a )  gtZ
Lt
(1  a)  gtZ  gtgdp  a  gtk  .06  1 2 .08  .02
In the Cobb-Douglas set-up, TFP is equal to technology raised to a power 1-a.
a
1a
GDPt  TFPK
 TFPt  (Zt )1a  gtTFP  1  a  gtZ  .02
t t ( Lt )
7. (10 points) An economy has a Cobb-Douglas production function with a = .5.
Technology is equal to Z =1. The capital stock is equal to K = 100. What is the
demand for labor when the real wage is 2?
The marginal product of labor is
1
a
W
K
MPL  (1  a)   Z 1 a 
2
P
L
100
L
 6.25
16
1
2
100
 100 
 16
2
 
L
 L 
8. (15 points) In Brazil, capital productivity in the balanced growth phase is .6. In the
US, capital productivity in the balanced growth phase is .4. If these two economies
have the same Cobb-Douglass production function with a = 1/3 and the level of
technology, Zt, is always the same in each country, what is the ratio of labor
productivity in Brazil to labor productivity in the USA.
We can write labor productivity as a ratio of capital productivity and technology
a
gdpt 
gdpt  gdpta  gdpt1 a  kta ( Z t )1 a  gdpt1 a  
( Z t )1 a 
kt 

1
a
gdpt  a1
 2 (Z )
1  gdp   gdpt
gdpt  
(
Z
),
a


3
t
t
t
kt 
kt 


Given that two countries have the same technology, we can find the ratio of their labor
productivities as a function of the ratio of their capital productivities:
1
gdptBZ
gdptUSA
 gdptBZ
 2
1

.6  2
ktBZ 





1
1
 gdptUSA
 2 .4  2

ktUSA 

2
3
9. (10 points) An economy has a technology growth rate of 5% and a Cobb-Douglas
production function. With zero population growth rate and a depreciation rate of 10%,
what savings rate would be consistent with a steady state capital productivity equal to
1?
The steady state capital productivity sets the growth rate of capital deepening equal to
the growth rate of technology.
(n  d  g Z ) .15
 gdp 
z
gk  s 

(
n

d
)

g

s


 .15

1
 gdp 
 k  ss
k  ss

10. [10 points] In South Korea, real GDP in 2000 is Y 2000 = 780 billion. The nominal
interest rate is 6.25% (i.e. I = .0625). Money demand is given by. Money supply is
given by 510 trillion. Assume that the real exchange rate between the US and Korea
is re = 1.5. Normalize the US price level equal to PUS = 1. Calculate the Korean
price level, P, and the Korea-US exchange rate, e.
At equilibrium, money demand equals money supply so
1
510000
M t S  510000 
Pt  780  M t D  Pt  4 .0625 
 653.8461538
780
4 .0625
ePUS
1
1.5  re 

 e  980.7692308
P
653.8461538
11. [10 points] There are two countries, country A and country B. Country A and B have
the same Cobb-Douglas production function, the same level of technology, Z which is
constant over time. These two countries have the exact same savings rate, s, and the
exact same population growth rate, n. However, the weather is better in country B
than in country A, and the former has a lower capital depreciation rate. Demonstrate
using a single graph and explain in a single paragraph which country will have a
higher steady-state labor productivity level.
(n+dA)k
(n+dB) k
gdp
B
y
yA
s gdp
An economy with high capital depreciation such as country A will have high replacement
investment needs. Thus, it will reach the level of capital per labor at which its investment
capacity is equal to its replacement investment needs relatively quickly. By contrast, a
country with a relatively low capital depreciation rate could countine to accumulate
capital, since relatively little investment needs to be allocated to replacing depreciated
capital. The higher capital-labor ratio implies a higher level of labor productivity.
12. [5 points] Why might the efficiency wage and unemployment rate in Hong Kong be
lower than the efficiency wage and unemployment rate in Western Europe. Explain in
one paragraph.
In Europe, labor unions and regulations make it costly to fire workers. High social
welfare benefits may also make unemployment less unattractive than in Hong Kong.
Therefore, in Europe, employers may have to offer a high wage premium to motivate
workers and minimize turnover. With higher labor costs, the demand for labor is likely to
be lower.