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There are two economies. At the beginning of Year 1, their real GDPs are equal. Economy A growsat a constant rate of 4%, while Economy B grows at a constant rate of 1%. Compute the ratio between the twoeconomies real GDP after 10 years, 20 years and 30 years.

Question

There are two economies. At the beginning of Year 1, their real GDPs are equal. Economy A growsat a constant rate of 4%, while Economy B grows at a constant rate of 1%. Compute the ratio between the twoeconomies real GDP after 10 years, 20 years and 30 years.

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Solution

To calculate the ratio between the two economies' real GDP after 10, 20, and 30 years, we need to use the formula for compound growth.

The formula for compound growth is:

Final amount = Initial amount * (1 + growth rate) ^ number of periods

Let's assume the initial real GDP for both economies is 1 unit for simplicity.

  1. After 10 years:

For Economy A: Final amount = 1 * (1 + 0.04) ^ 10 = 1.48 For Economy B: Final amount = 1 * (1 + 0.01) ^ 10 = 1.10 Ratio (Economy A / Economy B) = 1.48 / 1.10 = 1.35

  1. After 20 years:

For Economy A: Final amount = 1 * (1 + 0.04) ^ 20 = 2.19 For Economy B: Final amount = 1 * (1 + 0.01) ^ 20 = 1.22 Ratio (Economy A / Economy B) = 2.19 / 1.22 = 1.79

  1. After 30 years:

For Economy A: Final amount = 1 * (1 + 0.04) ^ 30 = 3.24 For Economy B: Final amount = 1 * (1 + 0.01) ^ 30 = 1.35 Ratio (Economy A / Economy B) = 3.24 / 1.35 = 2.40

So, the ratio between the two economies' real GDP after 10 years is 1.35, after 20 years is 1.79, and after 30 years is 2.40. This means that Economy A's GDP is growing faster than Economy B's GDP.

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