Consider the endogenous growth model, where output is determined by the production function y = ZUhD In this model, there is one unit of time, which is divided between work and human capital accumulation, and u denotes the fraction of time devoted to working. Hence the efficiency units of labour demanded by the representative firm is uHd, where Hd is the level of human capital. The future stock of human capital is a function of the current stock of human capital, the fraction of time devoted to human capital accumulation in the current period (1-u), and the efficiency of the human capital, the fraction of time devoted to human capital accumulation in the current period (1-u), and the efficiency of the human accumulation technology (b).

a) Solve for the growth rate of human capital and be sure to show your work. If b (1-u) > 1, will there be growth in aggregate output? Explain your answer.

b) The Canadian government subsidizes the cost of education for domestic students in an effort to increase (1-u). Within the context of this model, explain why this education subsidy reflects a trade-off to consumers