Question

Growth and development: In 2017, Ethiopia had a per capita income of $1,600, about $4 per day. Compute per capita income in Ethiopia for the year 2050 assuming average annual growth is

1. 1% per year.
2. 2% per year.
3. 4% per year.
4. 6% per year. (
5. For comparison, per capita income in Mexico in the year 2017 was nearly $17,000, about 30 percent of the U.S. level.)

Answer 1

Data given:

• Per capita income of Euthopia in 2017 = $1600
• We have to find per capita income in 2050, therefore number of years between 2050 & 2017 = 2050 – 2017 = 33 years.

(a) average annual growth rate = 1 % per year

• Per capita income in 2050 = Per capita income in 2017 × [1 + (growth rate ÷ 100) ]^{(number of years)}

• = 1600 × [1 + (1/100)]³³
• = 1600 × (101/100)³³
• = 1600 × (1.01)³³
• = 1600 × 1.3887
• = $ 2222

(b) average annual growth rate = 2 % per year

• Per capita income in 2050 = Per capita income in 2017 × [1 + (growth rate ÷ 100) ](number of years)

• = 1600 × [1 + (2/100)]³³
• = 1600 × (102/100)³³
• = 1600 × (1.02)³³
• = 1600 × 1.92223
• = $ 3076

(c) average annual growth rate = 4 % per year

• Per capita income in 2050 = Per capita income in 2017 × [1 + (growth rate ÷ 100) ]^{(number of years)}

• = 1600 × [1 + (4/100)]³³
• = 1600 × (104/100)³³
• = 1600 × (1.04)³³
• = 1600 × 3.6484
• = $ 5837

(d) average annual growth rate = 6 % per year

• Per capita income in 2050 = Per capita income in 2017 × [1 + (growth rate ÷ 100) ]^{(number of years)}

• = 1600 × [1 + (6/100)]³³
• = 1600 × (106/100)³³
• = 1600 × (1.06)³³
• = 1600 × 6.8406
• = $ 10945

(e) Comparing the per capita income of Euthopia in 2050 with assuming growth rate of 6 % per year, with that of Mexico and USA, the per capita income of Euthopia at 2050 level will still be about $ 6000 less tham Mexico's per capita income at 2017 level.