Consider the endogenous growth model, where output is determined by the production function y = zuH^d. In this model, the stock of human capital accumulate as follows:

H'= b(1 - u)H

1. Solve for the growth rate of human capital, and make sure to show your work. If b(1 - u) = 1, will there be growth in aggregate output? Explain your answer
2. In equilibrium, the representative firm demands an efficiency units of labor that maximizes profits, and the representative consumer receives a real wage, w, for each efficiency unit of labor supplied. Write down the representative firm's profit maximization problem, and show that the equilibrium real wage equals the marginal product of efficiency units of labor.
3. The Canadian government subsidized 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.