Download Homework Assignment 2

Homework Assignment 2
Economics 215
Intermediate Macroeconomics
Assigned: Thursday, March 10, 2005
Due: Thursday, March 17, 2005
1. Compare two countries. Each country has a population growth rate of 2% (i.e. n =
.02) and a depreciation rate of 10% (i.e. d = .10). Both countries have the same
Cobb-Douglas production function Yt = Kta(QLt)1-a with constant technology level
Qt = 1. Country A has an investment rate of s = .3 while Country B has an
investment rate of .18. Calculate the ratio of steady state labor productivity in
Country A to steady state labor productivity in Country B, when a = ⅓, ⅔, ½, and
⅞. If capital intensity is strong enough, can differences in capital fundamentals
explain differences in labor productivity seen in different areas of the world?
2. An economy is closed so that output is either used for household consumption, Ct
; capital investment, It; or government spending, Gt. The government collects a
constant share of output for its spending on output, Gt = τYt. The household
consumes a constant fraction of its after-tax income, Ct = c(1-τ)Yt, and invests the
rest, It = (1-c)(1-τ)Yt. Assume zero population growth, n = 0, and a realistic
depreciation rate of 8%, d = .08. The average rate of household consumption as a
share of GDP not spent by government over the last 10 years in Hong Kong is
66.4% , so set c = ⅔. The average of government spending as a share of GDP in
Hong Kong over the last 10 years is 9% .
a. Assume that production in country H is given by the Cobb-Douglas
function Yt = Kt⅓ (Lt) ⅔ with a = ⅓. Calculate steady state labor
productivity levels when government spending share is τ = .09. Calculate
steady state labor productivity levels when government spending share is τ
= .18.
b. Now assume a production function with nondiminishing returns to capital,
Yt = Kt. Calculate the rate of growth of output when τ = .09 and is τ = .18.
3. Examine an economy in which the production function is quadratic so
1
Yt  a  Lt  Lt 2 which implies a linear marginal product of labor curve,
2
Y
MPL  L  a  Lt . In this economy,
a. Assume that a = 100. What is the demand for labor in this economy if the
market real wage W = 10.
P
b. Calculate the equilibrium real wage in this economy when a = 100 and the
labor supply is unaffected by the real wage and is fixed at LS = 100.if the
labor market is perfectly competitive and firms have no labor management
costs.
Now assume that firms must pay the labor management costs per labor unit so
E2
W
that are a linear function of the real wage c(
)
P W
P
c. The marginal cost of hiring an extra unit of labor is now,
2
W  c(W )  W  E . Calculate the demand for labor when E = 10,
P
P
P W
P
a = 100 and the real wage rate is W = 10. Calculate the demand for
P
labor when E = 10 and the real wage rate is W = 20.
P
Given the cost function, so that the marginal benefit of increasing real wages is
c
E2
per labor unit while the marginal cost per labor unit of raising


2
W
W
P
P
the real wage is 1.
 
d. If the efficiency wage minimizes total costs of hiring a worker by
equalizing the marginal benefit of increasing the wage level with the extra
cost, solve for the efficiency wage if E = 10. Calculate the demand for
labor at the efficiency wage. If the labor supply is LS = 100, what is the
level of unemployment (i.e. the difference between labor demand at the
efficiency wage and labor supply). What is the unemployment rate (i.e. the
level of unemployment divided by the labor supply)?
e. Now assume that a negative technology shock reduces the productivity of
labor and decreases a from a = 100 to a = 90. If the efficiency wage rate
is unchanged, what is the new demand for labor and what is the new
unemployment rate?
4. Internet Question
Reported below are series for Current Dollar Gross Domestic Product and
Population for 10 East Asian Economies. Use the PPP and X-Rate conversion
factors for 2002 calculated by the World Bank (to be obtained from
http://siteresources.worldbank.org/ICPINT/Resources/Table5_7.pdf) to convert
the GDP of one of these into US dollars. Choose the country whose number
corresponds with the last digit of your student ID. For comparison, divide by the
population to get US dollar GDP per capita for both PPP converted GDP and XRate converted GDP. As an example, I have already completed the results for
China.
Last Digit
Student
Country
ID Number Name
Dave
China
0
Bangladesh
1
Hong Kong
2
India
3
Indonesia
4
Japan
5
Korea
6
Malaysia
7
Philippines
8
Singapore
9
Thailand
Currency
Unit
Millions of
Renminbi
Taka
HK Dollar
Rupee
Rupiah
Yen
Won
Ringgit
Peso
Sing Dollar
Baht
Current Price
GDP
10517230
3005801
1247381
24633240
1863274700
497897000
684263500
361624
3959648
158064
5446043
Population
(Millions)
1284.53
133.4
6.787
1055
211.06
127.377
47.615
24.526
79.503
4.185
63.437
Example
Dave
China
xp
1.8
e
8.28
US Dollars
PPP GDP
XRATE GDP
$5,842,905.56 $1,270,196.86
US Dollars
PPP GDP
XRATE GDP
per Capita
per Capita
$4,548.67
$988.84