In Techland, from 1980 to 2010, holding technology and human capital fixed, increasing physical capital per worker from $25,000 to $100,000 would have led to a doubling of real GDP per worker, from $40,000 to $80,000. However, not only did physical capital per worker increase from $25,000 to $100,000, but technological progress shifted the productivity curve upward so that real GDP per worker actually increased from $40,000 to $320,000. What share of the annual growth rate of real GDP per capita was attributable to increasing physical capital per worker?

Question

Quizplus · Accepted Answer

2.0%Given that increasing physical capital per worker from $25,000 to $100,000 would have led to a doubling of real GDP per worker from $40,000 to $80,000, this increase represents the growth attributable solely to the increase in physical capital. The actual increase to $320,000 includes effects beyond just physical capital, such as technological progress. The growth from $40,000 to $80,000 represents a 100% increase in real GDP per worker due to physical capital alone. Since this doubling would have occurred over the same 30-year period that saw real GDP per worker actually increase to $320,000, we can calculate the annual growth rate attributable to physical capital using the formula for annual growth rate: $(\frac{Final\ Value}{Initial\ Value})^{\frac{1}{Number\ of\ Years}} - 1$. Applying this to the increase from $40,000 to $80,000 over 30 years gives an annual growth rate of approximately 2.0%, indicating that the contribution of increasing physical capital per worker to the annual growth rate of real GDP per capita is 2.0%.

In Techland, from 1980 to 2010, Holding Technology and Human