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Belgium's real GDP per person is $33,000 and Austria's is $34,700. The population growth rate in Belgium is 0.13 percent and the growth rate of real GDP is 3.0 percent. The population growth rate in Austria is 0.08 percent and the growth rate of real GDP is 3.3 percent. If these growth rates continue, how many years will it take for Belgium's real GDP per person to equal Austria's real GDP per person?

A) Belgium's standard of living will never equal Austria's.
B) just over 23 years
C) just over 24 years
D) just over 21 years
E) over 230 years

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pedrocarratore

Answer:

A) Belgium's standard of living will never equal Austria's.

Explanation:

The rates of change in the GDP per person for both Austria and Belgium are, respectively:

[tex]R=\frac{GDP_1}{Population_1} -\frac{GDP_0}{Population_0}\\R_A = \frac{1+0.033}{1+0.0008}-1=0.03217\\R_B = \frac{1+0.03}{1+0.0013}-1=0.02866[/tex]

Comparing both rates of change, it can be observed that Austria's GDP per person is increasing at a higher rate than Belgium's, and since Austria initially had a higher GDP per person,  Belgium's standard of living will never equal Austria's.