Please show work (answer chosen is incorrect) Consider the table that identifies

Question

Please show work (answer chosen is incorrect)

Consider the table that identifies the annual growth rate of real GDP per capita and the current level of real GDP per capita in four countries. Current Growth Rate Country of RGDP per Level of RGDP per capita capita 4% $1,200 2% $23,000 3% $5,900 196 $16,700 Assuming the annual growth rates remain the same over time, which countries will be able to "catch up" to country B in that at some future time they will have the same level of RGDP per capita as country B? Countries A and C will catch up Country B will always have the highest level of RGDP per capita Country D will catch up All countries (A, C, and D) will eventually have a level of per capita real GDP that is equal to country B

Explanation / Answer

Correct Answer:

Countries A & C will catch up.

Since country A and C has the higher growth rate than that of the country B, hence the country A & C can catchup country B in the future. Though, it is not possible for the country D as the RDGP growth rate of country D is less than the RGDP growth rate of country B.

For example for the country A and B

Let, in n years the RGDP per capita becomes equal.

Then

1200*(1+4%)^n = 23000*(1+2%)^n

(1.04/1.02)^n = 23000/1200

1.0196^n = 19.167

n = log (19.167)/log (1.0196)

n = 152.08 years

For the case of Country B and C

5900*(1+3%)^n = 23000*(1+2%)^n

(1.03/1.02)^n = 23000/5900

1.0098^n = 3.8983

n = log(3.8983)/log(1.0098)

n= 139.45 years

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