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Chapter 7: Problem 35

Say that the average worker in the U.S. economy is eight times as productive as an average worker in Mexico. If the productivity of U.S. workers grows at \(2 \%\) for 25 years and the productivity of Mexico's workers grows at \(6 \%\) for 25 years, which country will have higher worker productivity at that point?

Short Answer

Expert verified
After 25 years, the US will still have higher worker productivity than Mexico, given the initial productivity levels and growth rates provided. The future productivity of US workers is approximately 13.25P, while the future productivity of Mexico workers is approximately 4.29P.

Step by step solution

01

Identify the given values

We have the given values: - Initial ratio of productivity: US workers are 8 times more productive than Mexico workers - Productivity growth rates: US workers = 2%, Mexico workers = 6% - Time period: 25 years
02

Calculate the future productivity of US workers

We will use the compound interest formula to calculate the future productivity of US workers: \[Future\,Productivity = Initial\,Productivity \times (1 + Growth\,Rate)^{Time\,Period}\] Let P represent the productivity of Mexico workers, then the initial productivity of US workers is 8P. \[Future\,Productivity_{US} = 8P \times (1 + 0.02)^{25}\]
03

Calculate the future productivity of Mexico workers

Using the same compound interest formula, we can calculate the future productivity of Mexico workers: \[Future\,Productivity_{Mexico} = P \times (1 + 0.06)^{25}\]
04

Compare the future productivity levels

We will now compare the future productivity levels of both countries to determine which country has higher worker productivity after 25 years. If \(Future\,Productivity_{US} > Future\,Productivity_{Mexico}\), then US workers will have higher productivity. If \(Future\,Productivity_{Mexico} > Future\,Productivity_{US}\), then Mexico workers will have higher productivity.
05

Finding the result

Calculate the future productivity levels for both countries: \[Future\,Productivity_{US} = 8P \times (1 + 0.02)^{25} ≈ 13.25P\] \[Future\,Productivity_{Mexico} = P \times (1 + 0.06)^{25} ≈ 4.29P\] Comparing the values, we see that \(13.25P > 4.29P\), which implies that the future productivity of US workers is greater than that of Mexico workers.
06

Conclusion

After 25 years, the US will still have higher worker productivity than Mexico, given the initial productivity levels and growth rates provided.

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Most popular questions from this chapter

An economy starts off with a GDP per capita of 12,000 euros. How large will the GDP per capita be if it grows at an annual rate of \(3 \%\) for 10 years? \(3 \%\) for 30 years? \(6 \%\) for 30 years?

Would the following events usually lead to capital deepening? Why or why not? a. A weak economy in which businesses become reluctant to make long-term investments in physical capital. b. A rise in international trade. c. A trend in which many more adults participate in continuing education courses through their employers and at colleges and universities.

Assume there are two countries: South Korea and the United States. South Korea grows at 4\% and the United States grows at \(1 \% .\) For the sake of simplicity, assume they both start from the same fictional income level, \(\$ 10,000\). What will the incomes of the United States and South Korea be in 20 years? By how many multiples will each country's income grow in 20 years?

Say that the average worker in Canada has a productivity level of \(\$ 30\) per hour while the average worker in the United Kingdom has a productivity level of \(\$ 25\) per hour (both measured in U.S. dollars). Over the next five years, say that worker productivity in Canada grows at \(1 \%\) per year while worker productivity in the UK grows \(3 \%\) per year. After five years, who will have the higher productivity level, and by how much?

Why does productivity growth in high-income economies not slow down as it runs into diminishing returns from additional investments in physical capital and human capital? Does this show one area where the theory of diminishing returns fails to apply? Why or why not?
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