1.1 Brain-drain in the endogenous growth model As discussed in class, human capital externalities could explain why we observe the phenomenon known as brain drain. That is, skilled individuals (i.e., fast learners) from less developed countries migrating to more developed countries to benefit from higher levels of human capital. An implication of this brain drain is that the average skill of workers in developed countries is higher than it is in less developed countries. This idea can be easily introduced into the endogenous model of growth seen in class. Suppose there are two countries, one with a highly skilled population and one with a low-skilled population. Hence, human capital accumulation depends, not only on the amount of time each person spends at school, but also on his or her individual ability to learn, ?. Each country has a different ability to learn, given by ?d and ?` for the developed and less developed economies, respectively, where ?` < ?d, u < 1 ? 1 b?d and u > 1 ? 1 b?` , with u representing the fraction of time people decide to work and b > 0 is a parameter that represents the efficiency of the education system. a. Determine the law of motion for human capital in both the less developed country and more developed country. Graph both of them in the same plane and determine the growth rate of human capital in each country. b. Based on the laws of motion derived in part (a), is there a poverty trap for the less developed economy? That is, could the less developed country catch up with the more developed country? Explain intuitively.