Question

multiple choice 1 point suppose that over the last twenty - five years a country’s nominal gdp grew to three times its former size. in the meantime, population grew by 40 percent and prices rose by 100 percent. what happened to real gdp per person? it more than doubled. it increased, but it less than doubled. it was unchanged. it decreased.

Explanation:

1. Let the initial nominal GDP be \( N_0 \), initial population be \( P_0 \), and initial price level be \( P_{L0} \). So initial real GDP per person \( R_0=\frac{N_0/(P_{L0})}{P_0}=\frac{N_0}{P_{L0}P_0} \).
2. After changes: Nominal GDP \( N_1 = 3N_0 \) (grew to 3 times), population \( P_1=1.4P_0 \) (grew by 40%), price level \( P_{L1}=2P_{L0} \) (rose by 100% means doubled).
3. New real GDP per person \( R_1=\frac{N_1/(P_{L1})}{P_1}=\frac{3N_0/(2P_{L0})}{1.4P_0}=\frac{3N_0}{2\times1.4\times P_{L0}P_0}=\frac{3}{2.8}R_0\approx1.071R_0 \).
4. So real GDP per person increased (since \( 1.071> 1 \)) but less than doubled (as \( 1.071<2 \)).

Answer:

It increased, but it less than doubled.