An economy of 82 million people has twenty percent of them engaged in research and development,where their productivity is 0.003.The economy is on a balanced growth path,when suddenly the productiveness of R&D rises to 0.004.For the one period that begins with this productivity increase,the growth rate of output is ________.[Refer to the instruction above.]

Question

Quizplus · Accepted Answer

The growth rate of output due to the increase in productivity in R&D can be calculated by the formula for the growth rate of technology, which is given by the change in productivity times the fraction of the population engaged in R&D. Initially, the productivity is 0.003, and it increases to 0.004, which is an increase of 0.001. With 20% of 82 million people, or 16.4 million people, engaged in R&D, the growth rate of output is 0.001 * 16.4 million / 82 million = 0.001 * 0.2 = 0.0002, or 0.02. To convert this to a percentage, we multiply by 100, resulting in a 2% increase. However, this calculation does not directly apply to the options provided, indicating a misunderstanding in the calculation process.The correct approach involves understanding that the productivity increase from 0.003 to 0.004 represents a 33.33% increase in productivity (since 0.001/0.003 = 1/3 or 33.33%). This productivity increase applies to the 20% of the population engaged in R&D. Therefore, the overall impact on the economy's growth rate is more significant than the simple calculation above suggests, and it should reflect the proportional increase in productivity for the portion of the economy engaged in R&D. The correct answer, considering the proportional impact and the options provided, aligns with the understanding that the growth rate of output significantly increases due to the productivity jump in R&D, leading to a higher growth rate than the initial miscalculation. The correct calculation involves understanding the broader economic impact of R&D productivity on growth, which is not directly calculated through the initial formula provided.

An Economy of 82 Million People Has Twenty Percent of Them