An economy of 25 million people has twenty percent of them engaged in research and development,where their productivity is 0.0056.The economy is on a balanced growth path,when suddenly a wave of immigration raises the population to 27 million.Assume that the new workers are immediately "on the job," and that the fraction engaged in R&D remains twenty percent.For the one period that begins with this population increase,the growth rate of output per person is ________.[Refer to the instruction above.]

Question

Quizplus · Accepted Answer

Before the immigration wave, the economy had 25 million people and 20% of them (5 million people) were engaged in R&D, with a productivity level of 0.0056. This means that the total productivity of the R&D sector was 5 million * 0.0056 = 28,000. 
After the immigration wave, the economy has 27 million people and 20% of them (5.4 million people) are engaged in R&D. The total productivity of the R&D sector is now 5.4 million * 0.0056 = 30,240. 
Therefore, the growth rate of output per person is (30,240/28,000)^(1/27) - 1 = 0.018 or 1.8%.

An Economy of 25 Million People Has Twenty Percent of Them