Question

3- Suppose 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

Answer 1

Let the original population be $x$

and the original total output be $y$

Then,

the original per capita output will be $\frac{y}{x}$

According to question ,

New population $= x+\frac{2x}{100} = \frac{102x}{100}$

Then,

New Total Output $= y+ \frac{3y}{100} = \frac{103x}{100}$

So,

New per capita output $=\frac{103y}{102x}$

Then,

Change in per capita output $\frac{103y}{102x} - \frac{y}{x} = \frac{103y-102y}{102x} = \frac{y}{102x}$

Percentage change in per capita output $= \frac{\frac{y}{102x}}{\frac{y}{x}} \times 100$ $= \frac{100}{102} = 0.98039216\%$