Labor Productivity and Economic Growth

Problems

An economy starts off with a GDP per capita of $5,000. How large will the GDP per capita 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?

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?

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?

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?