Download Due Date: Thursday, September 8th (at the beginning of class)

Problem Set 4
FE411 Fall 2017
Rahman
Date to be Completed: February 16th, 2017
The Malthusian Model
Consider the Malthusian model, as described by Weil in section 4.1 and in class.
1) Suppose that the economy is in steady state when suddenly there is a change in cultural
attitudes toward parenthood. For a given income, people now want to have more
children. Draw graphs showing the growth rates of population and income per capita
over time.
2) Let’s look at a Malthusian model with some actual functions. Suppose that the
^
relationship between income per capita (y) and the growth rate of the population
given by the equation:
L is
^
L = y − 100
Suppose that output is produced using labor and land, according to the equation:
Y = L1 / 2 X 1 / 2 ,
where X is the quantity of land. Assume that X = 1,000,000.
a) Derive the relationship between population L and income per capita y.
b) Use the equations you have derived to compute the steady-state values of L and y.
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Problem Set 4
FE411 Fall 2017
Rahman
3) Let’s look at a different Malthusian model. Let’s say that the growth rate of population
is given by:
^
L=
y − 100
100
Let X be the total quantity of land in the economy, which is fixed. Let x then be
the quantity of land per capita. The function that relates land per capita and
income per capita is simply
y = Ax
where A is just a measure of productivity.
a) Suppose that A is constant. What will the steady-state level of income per
capita be?
^
b) Now suppose that A grows at a rate of 10% per year (that is, A = 0.1). What
will be the steady-state level of income per capita? Explain what is going on.
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Problem Set 4
FE411 Fall 2017
Rahman
4) Composition Effects of Population Growth
Suppose that the world has only two countries. The following table gives data on their
populations and GDP per capita. It also shows the growth rates of population and GDP.
The growth rates of population and GDP per capita in each country never change.
Country
Population in
2000
GDP per
Capita in 2000
Country A
Country B
1,000,000
1,000,000
1000
1000
Growth Rate
of Population
(% per year)
0
2
Growth Rate of
GDP per Capita
(% per year)
2
0
a. What will the growth rate of world population be in the year 2000? Following
2000, will the growth rate of world population rise or fall? Explain why. Draw a
graph showing the growth rate of world population starting in 2000 and
continuing in to the future. Toward what growth rate does the world population
move in the long run?
b. Draw a similar graph showing the growth rate of total world GDP.
c. Draw a similar graph shoing the growth rate of average GDP per capita in the
world.
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