Solutions
Homework I
Economic Growth
1) The number of people worldwide living on less than one dollar per day can be calculated using
either market exchange rates or purchasing power exchange rates. Which will be larger? Explain
why.
Answer
: The number of people living on less than a dollar a day will be larger if we calculate it
using market exchange rates instead of purchasing power exchange rates because market
exchange rates only take into account the relative value of traded goods, which are relatively
more expensive in poorer countries. Individuals in these countries will have low purchasing
power for traded goods.
By using the market exchange rate, we are assuming that traded goods
and non-traded goods are the same price, and therefore individuals in poor countries will have
low purchasing power for non-traded goods as well, which will make they appear poorer than
they actually are.
2)
Between 1970 and 2005, China’s GDP per capita grew at an average rate of 7.3% per year
while GDP per capita in the United States grew at an average rate of 2.2%. In 2005, U.S. GDP
per capita was $36,806 and Chinese GDP per capita was $5,955. Assuming that the two countries
continue to grow at these rates, in what year will China overtake the United States in terms of
GDP per capita?
Answer:
In order to calculate the year in which income per capita in China will overtake the
income per capita in the United States, we first need to find
t
, the number of years it will take for
the income per capita in both countries will be equal.
That is,
(
Y
US
, 2005
) * (1+
.022
)
t
= (
Y
China
, 2005
) * (1+
.075
)
t
.
Since
Y
US
, 2005
=$36,806,
Y
China
, 2005
= $5,955, we then substitute in these values and solve for
t
.
(1+0.075/1+.022)
t
=( $36,806 /$5,955)
Taking the Natural Log of both sides, and noting that
ln(x
y
) = y ln (x)
, we get
t
ln
(1.05) =
ln
( $36,806 /$5,955)
t
= 37.33
That is, in 37.33 years, assuming they grow at the current growth rates, the income per capita of
China will surpass that of the United States.
This year will roughly be 2005+