Final answer:
After applying the compound growth formula, Mexico surpasses the U.S. in worker productivity after 25 years due to its higher annual growth rate.
Step-by-step explanation:
The question asks whether the average worker in the U.S., being eight times as productive as an average worker in Mexico, will maintain a higher level of productivity after 25 years of differing growth rates. To answer this, we need to calculate the growth of productivity in each country over the given time period.
If the U.S. workers' productivity grows at 2% per year for 25 years, the increase in productivity can be calculated using the formula for compound interest: P_final = P_initial x (1 + r)^n. For the U.S., P_initial is 8 times that of Mexico's P_initial, with r being 2% or 0.02, and n being 25.
Similarly, for Mexico, with a productivity growth rate of 6%, the same formula is used but with r being 6% or 0.06.
After performing these calculations, Mexico's productivity outgrows that of the U.S. due to the higher percentage increase per year over the 25-year period. Thus, despite the U.S. starting at a higher productivity level, Mexico will have higher worker productivity at the end of 25 years.