2. Output in the economy of Erewhon has grown 3% per year over the past 30 years. The labor force has grown at 1% per year, and the quantity of physical capital has grown at 4% per year. The average education level hasn’t changed. Estimates by economists say that each 1% increase in physical capital per worker, other things equal, raises productivity by 0.3%. (Hint: % change in (X/Y) = % change in X − % change in Y.)
How fast has productivity in Erewhon grown?
If output has grown 3% per year and the labor force has grown 1% per year, then productivity—output per person—has grown at approximately 3% − 1% = 2% per year.
How fast has physical capital per worker grown?
If physical capital has grown 4% per year and the labor force has grown 1% per year, then physical capital per worker has grown at approximately 4% − 1% = 3% per year.
How much has growing physical capital per worker contributed to productivity growth? What percentage of productivity growth is that?
According to estimates, each 1% rise in physical capital, other things equal, increases productivity by 0.3%. So, as physical capital per worker has increased by 3%, productivity growth that can be attributed to an increase in physical capital per worker is 0.3 × 3% = 0.9%. As a percentage of total productivity growth, this is 0.9%/2% × 100% = 45%.
How much has technological progress contributed to productivity growth? What percentage of productivity growth is that?
If the rest of productivity growth is due to technological progress, then technological progress has contributed 2% − 0.9% = 1.1% to productivity growth. As a percentage of total productivity growth, this is 1.1%/2% × 100% = 55%.