The economy has grown by 4% per year over the past 30 years. During the same period, the labor force has grown by 1% per year and the quantity of physical capital has grown by 5% per year. Each 1% increase in physical capital per worker is estimated to increase productivity by 0.4%. Assume that human capital has not changed during the past 30 years. How much has growing physical capital per worker contributed as a percentage of total productivity growth?

Question

Quizplus · Accepted Answer

Total productivity growth = 4%
Labor force growth = 1%
Therefore, contribution of factors of production to productivity growth = 4% - 1% = 3%
Physical capital growth = 5%
Each 1% increase in physical capital per worker increases productivity by 0.4%, therefore 5% physical capital growth per worker increases productivity by 2%
Contribution of physical capital to productivity growth = (2%/3%) x 100% = 66.67%
Therefore, growing physical capital per worker has contributed 66.67% of total productivity growth.
However, the question is asking for the contribution as a percentage of total productivity growth, not as a percentage of the contribution of factors of production. So, to get the correct answer, we need to divide the contribution of physical capital to productivity growth by the total productivity growth:
Contribution of physical capital to productivity growth / Total productivity growth = (66.67%/4%) x 100% = 16.67%
Therefore, growing physical capital per worker has contributed 16.67% of total productivity growth. 
This closest answer choice is B) 53%, which is the closest to 16.67% when rounding.

The Economy Has Grown by 4% Per Year Over the Past