Download Homework Assignment 1

Homework Assignment 1
Intermediate Macroeconomics
Assigned: Thursday, February 24, 2005
Due: Thursday, March 4, 2005
Data Analysis
1. You are given a time series of annual real GDP data for Australia beginning in
1970 from the OECD website
(http://www.oecd.org/document/28/0,2340,en_2825_495684_2750044_1_1_1_1,00.html ). See the
table on the next page for the data.
a. Calculate the average annual growth rate of Australian data from 1971 to
2003. There are two ways to do this.
i. First, calculate the average discrete growth rate. For each period,
(Y  Y )
calculate the growth rate gtY  t t 1
. Take the average by
Yt 1
summing and dividing by the number of observations
Y
Y
Y
g Y  g Y  g1973
 ....g 2003
.
g  1971 1972
33
ii. Calculate the average continuous growth rate. The continuous
growth rate is t Y  ln Yt  ln Yt 1 . Take an average of this over the
period. We can see there is a simplified formula for the average, so
we can calculate the average continuous growth rate of a series
using just the natural logs of the beginning and the end.
Y
Y
Y
Y
Y
1971
 1972
 1973
 ....2003
 
33


 ln Y
2003
 ln Y2002    ln Y2002  ln Y2001   ...   ln Y1972  ln Y1971    ln Y1971  ln Y1970 
33
ln Y2003  ln Y1970 
33
b. Calculate a trend growth path. Use your estimate of the average
continuous growth rate and the initial income level to calculate the trend at
Y
every period: TREND1970 j  (1   ) j  Y1970 . Calculate the output gap in
2003 as the % deviation of output from that trend. Is Australia currently in
a recession or a boom according to your findings.?
Table I- Australian Real GDP Data in 2000 Australian Dollars
2000 Australian
Dollars
Y
1970
259970
1971
270195
1972
278233
1973
290291
1974
293161
1975
301432
1976
311815
1977
314872
1978
328309
1979
338903
1980
349968
1981
360838
1982
352348
1983
369163
1984
388694
1985
405378
1986
414902
1987
437149
1988
454826
1989
471833
1990
471282
1991
472474
1992
489718
1993
508800
1994
530222
1995
552848
1996
573802
1997
599393
1998
631221
1999
654955
2000
668426
2001
694359
2002
716641
2003
743681
2. Based on the final digit of your student ID, you are asked to compare the TFP
level and average TFP growth rate of one European country with the TFP level of
the United States.
a. Assume that we have a Cobb Douglas production function of the form
1
2
1
2
Yt  3  Yt  3

3
3
Yt  K t (Qt Lt )  TFPt  
 
 . Calculate TFP levels for
 K t   Lt 
your country for year t = 1980 and year t = 2001 using data from the
Groningen Growth and Development Centre (www.ggdc.net). You can get
data on output and the capital stock for each country by downloading the
spreadsheet found on http://www.ggdc.net/dseries/growthaccounting.shtml (the series on capital is on the sheet titled GFCS {under
Total} and the series on output is on the sheet title Basics). You can find
data on output per hour worked for each country in 1980 and 2001 by
downloading the spreadsheet on OECD countries measured in 2002 US
dollars found on (http://www.ggdc.net/dseries/gdph.shtml#top). As an
example, I calculate TFP for the USA by the same method.
USA
1980
Output
4,268,900
Capital
6,949,866
Capital
Productivity 0.614242
Labor
Productivity
29.12
Total Factor
Productivity 8.045123
2001
8,183,492
13,571,187
1995 US $
1995 US $
0.60300487
40.28
2002 US$ per Hour
9.926734118
b. Calculate the average continuous growth rates of TFP for your country by
TFP
ln TFP2001  ln TFP1980
 
. For the USA, the average growth rate is
21

TFP
 0.010007882 .
Country ID # Last Digit
Austria
Belgium
Denmark
Finland
France
0
1
2
3
4
Country
Greece
Ireland
Italy
Netherlands
Spain
ID # Last
Digit
5
6
7
8
9
Algebra Problems
3. Assume a Cobb-Douglas production function of the form Yt  Kt 2 Lt
1
1
average product of labor is given by the function
marginal product of labor is given by MPL = ½
1
1
2
so that the
1
Yt Kt 2 Lt 2 K 2
 1 1  1 and the
Lt Lt 2 Lt 2
Lt 2
Yt
Lt
. Assume a constant capital
stock, K = 1000.
a. What would be the average and marginal productivity if L = 2?
b. Calculate the demand for labor, if the real wage rate were 5. Calculate the
demand for labor if the real wage rate were 10.
4. You find that in Korea, the wage bill as a share of GDP is .59. What is the capital
intensity parameter of the Cobb-Douglas production function, a? You have
information on the growth rate of real GDP, capital, and labor. Calculate the
growth rate of capital productivity, labor productivity, and TFP.
Variable
Output (Y)
Growth Rates
gY = .06
Capital (K)
gK = .08
Labor (L)
gL = .03
5.
Variable
Capital Productivity
Y
K
Labor Productivity
Y
L
TFP
Growth Rates
Assume a Cobb-Douglas production function with a constant level of technology,
1
1
Q = 1and gQ = 0: Yt  Kt 2 Lt 2 . The economy is closed and output is either used
for consumption, Ct, and investment, It, Ct + It = Yt. The investment ratio is
constant, so It = s Yt and Ct = (1-s)Yt. Assume a depreciation rate of 8%, d = .08
and a population growth rate of 2%, n = .02. Calculate the steady state capitallabor ratio implied by these capital fundamentals when s = .2, .4, and .8. Calculate
the labor productivity at the steady. Assume that the number of hours worked per
person was L
 600. Calculate output and consumption per person when s =
POP
.2, .4, and .8. Which investment rate generates the highest per capita GDP and
consumption? Explain.
6. Assuming a Cobb-Douglas production function with a capital intensity parameter,
a = .4; an investment rate of 25%, s = .25; a population growth rate of 1%, n =
.01; a depreciation rate of 10%, d = .10; and a constant growth rate of technology
of 1.5%, gQ = .015.
a. Capital productivity in an economy is
Yt
=1. What is the growth rate of
Kt
the capital-labor ratio? What is the growth rate of labor productivity?
b. Calculate the steady-state capital productivity along the balanced growth
path.
c. Assume the economy is on its balanced growth path. We observe that the
real wage rate is equal to 25. What is the level of TFP? (Hint: TFP is the
weighted geometric average of capital productivity and labor productivity
with a as the exponential weight on capital productivity and 1-a on labor
productivity. You calculated steady state capital productivity in b. You
also know the marginal product of labor and the real wage are a fraction,
a, of labor productivity.)