In the endogenous economic growth model, suppose the government decides to encourage education via various programs that leads to an increase in time spend accumulating human capital. Those programs are not free and cost taxpayers (consumers) t fraction of their income every period. At the same time, firms in the economy become more productive (z, efficiency units of labor increases). Determine what happens to the path of consumption and output in this model. Show your results both analytically as well as graphically.