Download Homework Assignment 1

Homework Assignment 1
Economics 514
Macroeconomic Analysis
Due: October 18th, 2013
1. European Leisure
We hope to explain the level of household leisure adopted in Italy vs. Hong Kong by
differences in tax rates.

First, get data on labor hours and productivity in the two countries from the
Groningen Growth Development Center Total Economy database. Go to Link.
Download the Excel file Total Economy Database™ - Output, Labor, and Labor Productivity,
1950 - 2012
Fill in the following table. Calculate the number of hours worked, L2012, as the hours
per person aged between 15-64 in Hong Kong. Assume each person has time equal to
TIME = 8,760 per year. What is the leisure time per person in Hong Kong if leisure
is ls = TIME - L.
Productivity – LP
Total Hours (Thousands)
Population (Thousands)
% Pop. 15-64
L2012
Italy
Hong Kong
65%
75%
Calculate the number of hours worked, L2012, as the hours per person aged between
15-64 in Hong Kong. Assume each person has time equal to TIME = 8,760 per year.
What is the leisure time per person in Hong Kong if leisure is ls = TIME - L.
Households have a general utility function dsd
Ut   Ct  1 lst 
1

 1
They will earn labor income, wtLt, and private non-labor income, Πt. They pay a
proportional tax rate, τ, on all private income and receive a subsidy S from the
government regardless of how much they work. The budget constraint is
C  (1   )  wt  TIME  lst    t   St
on all private income. The first order condition showing the ratio of leisure to
consumption as a function of the real wage and the tax rate. MUls  (1   )wt  MUC
a. Assume  = 0 so the elasticity of substitution between consumption and leisure
is 1. Assume that all taxes are paid back to the average household as a flat
subsidy, so there are two equations. C   wt  TIME  lst    t  and
w(1   ) 
 . Use the data from GGDC to solve for ls for Hong Kong. In Hong
C
ls
Kong, we could say the tax rate is 15%, τ=.15. Assume that w is ⅔ of labor
productivity. Assume that t is ¼ of wtLt. Solve for the parameter Γ that would
generate the level of leisure in HK.
b. Now assume that Italy has the same level, Γ, as solved for in Hong Kong. What
would the tax rate need to be in Italy, to lead to a level of labor.
2. Growth Accounting
Researchers at the University of Pennsylvania have assembled a database on
comparable levels of output and investment for a large number of countries. Use the
data from Penn-World Tables. Data can be obtained here: Link, Get data on
Real GDP at constant 2005 national prices (in mil. 2005US$) (Yt)
Capital stock at constant 2005 national prices (in mil. 2005US$) (Kt)
Number of persons engaged (in millions) (Lt)
Under Regions select China and India. Under Periods select 1960, 1970,
1980, 1990, 2000, and 2010.
a. Calculate the average compound growth rate γ for GDP, Capital, and Number of
Employees for each country for each decade.
b. Assume a Cobb-Douglas utility function with α = ⅓. Calculate the growth of TFP
in each country in each decade.
c. Calculate the share of growth due to each factor and TFP for each country.
3. Development Accounting
Compare the level of technology in Hong Kong with that in the USA. Assume a
production function in each country of the form:
Yt  Kt ( At Ht Lt )1

H t  e1
yearst
yt  kt ( At )1 e  yearst
where Ht is human capital which is a function of the number of years of schooling.
A. Data on output, labor and capital can be obtained here: Link
Expenditure-side real GDP at chained PPPs (in mil. 2005US$) , (Yt)
Capital stock at current PPPs (in mil. 2005US$) (Kt)
Labor can be calculated as the product of
Number of persons engaged (in millions)
Average annual hours worked by persons engaged
Under Regions select
Hong Kong
and
United States.
Under Periods select
B. Data on Human Capital can be obtained here Link
Select China, Hong Kong Special Administrative Region and USA for
Gender select Total; under Age group select 25+. Press
Average years of schooling for both economies.
2010.
2010; under
. Report
Under the assumption that α = ⅓ and  = .08, calculate the level of technology for
both economies in 2010.
Computational Problems
Macroeconomics often uses computer simulations to study theoretical models. Do a
couple of simulation exercises for an economy with a Cobb-Douglas production
function
1
2
1
2
Yt  Kt 3 ( At Lt ) 3
yt  kt 3 ( At ) 3
a depreciation rate of 8% (δ=.08), a population growth rate of 1% (n = .01),and an
annual technology growth rate of 2% (gA = .02).
1. Golden Rule
Assume that the economy was on its balanced growth path. Normalize technology at
L
time t to At = 1. Assume a constant labor hours per population of t
= 500.
POPt
Output is used for consumption and investment, Ct + It = Yt and investment is a
constant share of output. Calculate consumption per capita at different levels of invest
rates s = 1100 , 1 4 , 13 , and 1 2 . Which investment rate generates the highest steady
state labor productivity.
2. Convergence
Assume that the investment rate for the economy is at the level which generates
the highest level of consumption per capita. Examine the dynamics of the neoclassical model. Start in period 0. In that period, technology is A0 = 1 and k0 = 1.5.
Calculate labor productivity in period 0 and the labor productivity if the economy
were on its balanced growth path. What is the percentage gap between the actual
level of the economy and the balanced growth path (y0 and yBGP). Calculate the capital
productivity in period 0. Use this to calculate the growth rate of the capital labor ratio,
k  g k  kt 1  kt between period 0 and period 1. Use the growth rate of the capital
t 1
k
kt
A  At
labor ratio and the growth rate of technology A  gtA1  t 1
to calculate k1 and
A
At
A1. Use these numbers to calculate actual and balanced growth path labor productivity
and capital productivity in period 1. Use capital productivity to calculate the growth
rate of the capital-labor ratio in period 1. Calculate technology and the capital labor
ratio in period. 2. Repeat. Calculate the path of actual labor productivity as well as the
balanced growth path for periods 0 through 30. How large is the percentage gap at
period 30.