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Scenario: Productivity
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.
-(Scenario: Productivity) Look at the scenario Productivity. How much has growing physical capital per worker contributed as a percentage of total productivity growth?

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Quizplus · Accepted Answer

The total annual growth rate of the economy (4%) can be expressed as the sum of the growth rate of labor (1%), physical capital (5%), and productivity (X%). X% can be calculated as 4% - 1% - 5% = -2%. This negative value for productivity growth indicates that productivity has decreased over the past 30 years. However, we are asked to find the contribution of physical capital to total productivity growth, not the change in productivity itself. 
Each 1% increase in physical capital per worker increases productivity by 0.4%, so a 5% increase in physical capital per worker would increase productivity by 2%. Therefore, the contribution of physical capital to total productivity growth is 2% / -2% = -0.53, or 53%.

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