Why Doesn’t Capital Flow from Rich to Poor Countries?Human Capital: Our textbook points out that human capital is not included in thesimple model of production but that it could be an important factor in explaining whythe marginal product of capital differs among countries.1. Consider a Cobb-Douglas production function with three inputs:Y = K13L13H13; (1)where K is capital, L is labor, and H is human capital. What is the marginalproduct of capital (MPK) implied by this production function?Answer: MPK =K2=3(2) 13L1=3H1=32. Is MPK increasing in human capital or decreasing?Answer: The MPK is increasing in human capital. This is because H appears inthe numerator.3. Use this model to explain why capital may flow from poor to rich countries.Answer: In the absence of human capital in the model, the marginal product ofcapital is strictly decreasing as the amount of capital increases. Therefore, capitalrich countries should have low returns to capital. However, when human capitalis considered, the MPK can rise as human capital rises. Therefore, high levels ofhuman capital may offset high levels of physical capital resulting in higher returnsin rich countries and lower in poor countries.4. Is the return to education higher or lower in countries with scarce capital?1Answer: The return is lower. This question requires the MPH in order to answer.This is given by MP H =H2=3 :(3) 13K1=3L1=3Note that MPH is an increasing function of K. Therefore, the returns to educationare higher in countries with abundant capital compared to countries with very littlecapital for any given level of H.Note that we are assuming perfect competition for all of our analysis here. Returnsonly match the marginal productivity of the factors of production under perfectcompetition.2
