Assume that between 1940 and 2010:

- The amount of physical capital per worker grows at 2% per year.
- Each 1% rise in physical capital per worker (holding human capital and technology constant) raises output per worker by 0.5%.
- There is no growth in human capital.
- Real GDP per capita rises from $30,000 to $60,000.

Growing physical capital per worker is responsible for how much productivity growth per year? Show your calculation.

To determine how much the growth in physical capital per worker is responsible for productivity growth between 1940 and 2010, we can utilize the given information: The physical capital per worker grew at 2% annually, and every 1% increase in physical capital per worker (holding human capital and technology constant) raises output per worker by 0.5%. There was no growth in human capital during this time, and Real GDP per capita rose from $30,000 to $60,000. We are to ignore growth in other areas and focus solely on the effect of physical capital growth on productivity.

The formula for productivity growth due to an increase in physical capital is:

Productivity Growth = Growth in Physical Capital per Worker * Increase in Output per Worker due to Capital

Here, the growth in physical capital per worker is 2%, and the increase in output per worker due to each percent growth in physical capital is 0.5%. Therefore, the productivity growth per year attributable to physical capital is:

Productivity Growth = 2% * 0.5% = 1%

Thus, the growth in physical capital per worker is responsible for an annual increase in productivity by 1%.