Three countries have different levels of gross domestic product (GDP)per capita and different growth rates of GDP per capita,as identified in the table. If these countries continue to grow at the rates indicated in the table,then,over the next few years,________ will have the highest level of GDP per capita and,in the long run,________ will have the highest level of GDP per capita.
A) Andover; Bohemia
B) Andover; Andover
C) Bohemia; Bohemia
D) Bohemia; Andover
E) Bohemia; Catalonia

Question

Three countries have different levels of gross domestic product (GDP)per capita and different growth rates of GDP per capita,as identified in the table.  If these countries continue to grow at the rates indicated in the table,then,over the next few years,________ will have the highest level of GDP per capita and,in the long run,________ will have the highest level of GDP per capita.
A) Andover; Bohemia 
B) Andover; Andover 
C) Bohemia; Bohemia 
D) Bohemia; Andover 
E) Bohemia; Catalonia

Quizplus · Accepted Answer

From the table, we can see that Bohemia has the highest initial GDP per capita of $35,000, followed by Andover with $30,000, and then Catalonia with $25,000.

Over the next few years, we need to calculate the expected GDP per capita of each country by multiplying the current GDP per capita by the growth rate (in decimal form) for each year, and adding the result to the current GDP per capita.

For example, for Andover, the expected GDP per capita for year 1 would be:
$30,000 x 1.03 = $30,900

And for year 2:
$30,900 x 1.04 = $32,136

And for year 3:
$32,136 x 1.05 = $33,743

Doing these calculations for each country yields the following expected GDP per capita values:

Andover: 
Year 1 = $30,900 
Year 2 = $32,136 
Year 3 = $33,743

Bohemia: 
Year 1 = $35,700 
Year 2 = $37,416 
Year 3 = $39,287

Catalonia: 
Year 1 = $26,250 
Year 2 = $27,563 
Year 3 = $28,941

Therefore, in the next few years, Bohemia will have the highest level of GDP per capita.

In the long run, we need to find the limit of each country's expected GDP per capita as the number of years approaches infinity. This can be done by using the formula for the sum of an infinite geometric series:

limit = a / (1 - r)

Where a is the initial value and r is the growth rate.

For Andover, the limit would be:
$30,000 / (1 - 0.03) = $30,927

For Bohemia, the limit would be:
$35,000 / (1 - 0.02) = $35,714

For Catalonia, the limit would be:
$25,000 / (1 - 0.06) = $26,596

Therefore, in the long run, Bohemia will still have the highest level of GDP per capita.

Thus, the best choice is D.

Three Countries Have Different Levels of Gross Domestic Product (GDP)per