Answers  Homework Assignment #2  ECON 423/823  Fall, 2008
1.
Using equation (310), or
∆
Y/Y
= g
Y
=
σ
/
γ
,
a. 10% / 2 = 5%.
b. 10% / 4 = 2.5%.
c. 20% / 2 = 10%.
d. 20% / 4 =
5%.
Clearly, the growth rate is higher, the higher the rate of saving and the lower the capitaloutput ratio.
2.
The
population function
that Malthus
described is illustrated in Figure 42.
Population growth, which is the change in
population P over the level of P, or
∆
P/P,
is given on the vertical axis.
Note that the
symbol “
∆
” signifies “the change in.”
Real per capita income, y = Y/P, is shown
on the horizontal axis.
If real per capita
income is above y
2
, say at y
3
, the death
rate is less than the birth rate and the
population grows.
If real per capita
income is below y
2
, such as at y
1
, the
death rate is greater than the birth rate and
the population shrinks.
At real per capita income y
2
, the death rate is exactly equal to the birth rate
and the result is “zero population growth” or
ZPG
.
Figure 43 illustrates diminishing returns and constant returns to scale graphically.
The
lower curve in Figure 43 represents the production function in the case of a fixed quantity of 100
acres of land, the higher curve the case of 200 acres of land. There are clearly diminishing returns
to labor: the production functions
always slope upward, but their
slopes become less steep the more
labor
is
added
to
production.
Average output per worker depends
on the ratio of output to labor.
In
Figure 43, output per worker is
represented by the slope of the
dashed lines that connect the origin
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 Spring '08
 VanDenBerg,H
 Economics, Demography, per capita, Demographic economics, capita income

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