Answer to Question #281683 in Macroeconomics for Tenn

Question

1. The population of the world in 2003 was 6.314 billion. It grew between 1975 and 2003 at an annual rate of 1.6%. Assume that it continues to grow at this rate. a. Compute the doubling time. b. Estimate the world population in 2048 and 2093 (assuming all other things remain unchanged). 2. With a world population in 2003 of 6.314 billion and a projected population growth rate of 1.1% instead (which is the United Nations’ projection for the period 2003 to 2015). a. Compute the doubling time. b. State the year in which the world’s population would be 12.628 billion. 3. Suppose a country’s population grows at the rate of 2% per year and its output grows at the rate of 3% per year. a. Calculate its rate of growth of per capita output. b. If instead its population grows at 3% per year and its output grows at 2% per year, calculate its rate of growth of per capita output. 

Answer 1

1a. The doubling time using the rule of 70 is:$t = \frac{70}{1.6} = 43.75$ years.

b. The world population in 2048 will be:

$6.314×1.016^{45 }= 12.898$ billion.

The world population in 2093 will be:

$6.314×1.016^{90} = 26.347$ billion.

2.a) Using the rule of 70 for getting the doubling time ;

$=\frac{70}{Rate of growth }$

, where r is the rate of growth.

$=\frac{70}{1.1}$ $=63.63 yrs$

Hence it will have a doubling time of 64 years

b)

$\frac{12.628}{6.314}=2$

This shows that its the doubling time .Hence;

=2003+64 yrs =2067

=2067

3.Population growth rate $→ p.g.r=2\%$

output growth rate$\rightarrow o.g.r=3\%$

rate of growth of per capita output=$o.g.r-p.g.r$

$=3\%-2\%=1\%$