Question

country a and country b start with the same gdp per capita of $50,000. country a's gdp per capita grows at a constant rate of 2.8% and country b's gdp per capita grows at a constant rate of 1.4%. compute the difference in gdp per capita for these two countries after 100 years, in thousands of dollars.

Answer 1

To compute the difference in GDP per capita after 100 years, we use the formula for compound growth. Country A's GDP per capita will be $160,246.63 and country B's GDP per capita will be $98,470.93. The difference in GDP per capita is $61,775.70 thousand dollars.

Step-by-step explanation:

To compute the difference in GDP per capita for country A and country B after 100 years, we need to calculate the future GDP per capita for each country. Country A's GDP per capita grows at a rate of 2.8% annually, while country B's GDP per capita grows at a rate of 1.4% annually.

Country A's future GDP per capita can be calculated using the formula:

GDP per capita (A) = Initial GDP per capita * (1 + growth rate)^number of years

Substituting the values, we get:
GDP per capita (A) = $50,000 * (1 + 0.028)^100 = $160,246.63

Similarly, country B's future GDP per capita can be calculated:

GDP per capita (B) = $50,000 * (1 + 0.014)^100 = $98,470.93

The difference in GDP per capita after 100 years is:
Difference = GDP per capita (A) - GDP per capita (B) = $160,246.63 - $98,470.93 = $61,775.70 thousand dollars.