7. We studied in the class endogenous growth models where human capital plays an important role in economic growth. We consider knowledge (quality of human capital) is one of the essential factors of production function. Assume the firm's production function as follows: Y, = (EL, ) K, ) which is accumulated in proportion to capital accumulation. E = ak (2) where a is a positive constant. Answer the following questions regarding this model. (19 points) (1) Explain how the technological progress measured in terms of efficiency of labor is determined within the model. (4 points)(2) Using mathematics, show that the marginal product of capital, (or the returns to capital, in other words) is constant under a certain condition. (4 points) (3) Discuss the implication of the constant marginal product of capital, and demonstrate it on a diagram. Also, discuss how the outcome is different from that of the Solow model. (4 points) (4) Discuss in what case the marginal product of capital does not become constant in the endogenous growth model. (4 points) (5) Discuss what will happen to the outcome of (3), if the population growth rate increases. Assume that population growth is exogenous, and does not affect the accumulation of knowledge. (3 points)