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Chapter 20: Problem 32

An economy starts off with a GDP per capital of \(\$ 5,000 .\) How large will the GDP per capital be if it grows at an annual rate of \(2 \%\) for 20 years? \(2 \%\) for 40 years? 4\% for 40 years? 6\% for 40 years?

Short Answer

Expert verified
The final GDP per capita for each scenario is: 1. 2% annual growth for 20 years: \( \$7,372.74 \) 2. 2% annual growth for 40 years: \( \$10,837.54 \) 3. 4% annual growth for 40 years: \( \$29,234.07 \) 4. 6% annual growth for 40 years: \( \$79,670.56 \)

Step by step solution

01

1. 2% annual growth for 20 years

The formula for the final GDP per capita is: Final GDP per capita = Initial GDP per capita × (1 + Growth rate) ^ Years Plugging in the values provided in the exercise, we get: Final GDP per capita = $5,000 × (1 + 0.02) ^ 20 Calculating the result, we get: Final GDP per capita = $7,372.74
02

2. 2% annual growth for 40 years

Using the same formula, now with 40 years: Final GDP per capita = $5,000 × (1 + 0.02) ^ 40 Calculating the result, we get: Final GDP per capita = $10,837.54
03

3. 4% annual growth for 40 years

With a 4% annual growth rate for 40 years: Final GDP per capita = $5,000 × (1 + 0.04) ^ 40 Calculating the result, we get: Final GDP per capita = $29,234.07
04

4. 6% annual growth for 40 years

Finally, with a 6% annual growth rate for 40 years: Final GDP per capita = $5,000 × (1 + 0.06) ^ 40 Calculating the result, we get: Final GDP per capita = $79,670.56 In summary, the final GDP per capita for each scenario is as follows: 1. 2% annual growth for 20 years: $7,372.74 2. 2% annual growth for 40 years: $10,837.54 3. 4% annual growth for 40 years: $29,234.07 4. 6% annual growth for 40 years: $79,670.56

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Most popular questions from this chapter

Over the past 50 years, many countries have experienced an annual growth rate in real GDP per capital greater than that of the United States. Some examples are China, Japan, South Korea, and Taiwan. Does that mean the United States is regressing relative to other countries? Does that mean these countries will eventually overtake the United States in terms of the growth rate of real GDP per capital? Explain.

Are there other ways in which we can measure productivity besides the amount produced per hour of work?

As technological change makes us more sedentary and food costs increase, obesity is likely. What factors do you think may limit obesity?

List the areas where government policy can help economic growth.

For a high-income economy like the United States, what aggregate production function elements are most important in bringing about growth in GDP per capital? What about a middle-income country such as Brazil? A low-income country such as Niger?
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