Question

Suppose a country's population grows by 2% a year and at the same time its real GDP shrinks by 1% a year. Real GDP per person is increasing by- a year. a. -3% b. 2% c. 1% d.190 3%

Answer 1

Real GDP per person is given by dividing total real GDP by the number of persons comprising country's population.

$RGDPP = \frac{RGDP}{N}$

Let initial RGDP_i be R₀ and initial population be N₀.

Intial RGDP per person

$= RGDPP_i = \frac{RGDP_i}{N_i} = \frac{R_0}{N_0}$

After a year, New RGDP = RGDP_f = R₀ + %change in R₀

= R₀ - 1% of R₀ = R₀ - 0.01R₀ = 0.99R₀

New population = N_f = N₀ + %change in N₀

= N_{0 +} 2% of N₀ = N_{0 +} 0.02N₀ = 1.02N₀

Thus, new real GDP per person

$= RGDPP_f = \frac{RGDP_f}{N_f} = \frac{0.99R_0}{1.02N_0} = 0.97\frac{R_0}{N_0}$

Therefore % change in RGDPP =

$\frac{RGDPP_f - RGDPP_i }{RGDPP_i} = \frac{0.97\frac{R_0}{N_0} - \frac{R_0}{N_0}}{\frac{R_0}{N_0}}$$= -0.03 = -3\%$

Thus real GDP per person is increasing by -3% per year (i.e. it is actually shrinking by 3% per year).