Plz provide detailed answers thank u;-)

2. Consider an economy where each household has preferences over leisure L and consumption C given by U(C,L) : C + blogL Nonlabor income equals Y0 T and the real wage to. The time on dowment is h, : 1, and the only uses of time are leisure and labor, N. Households spend all their household income on consumption each pe riod. (a) Show that the marginal rate of susbtitution between consumption and leisure does not depend on consumption. (b) Derive the budget line for the household and use it to show how consumption depends on leisure. (c) Suppose the household leisure falls slightly, which increases income. How will this affect household utility? Under what condition does utility increase? (d) The household chooses leisure to maximize utility U(C, L). Under what condtion will the household choose not to work (N = 0)? (e) For a given real wage 11; what is the optimal labor supply? Suppose TFP grows at a constant rate 9 > 0. Will this economy have a blanaccd-growth path? (f) The government decides to \"stimulate\" the economy by building a costly new project, paid for by a rise AT in the lump-sum tax T Will this strategy succeed in raising labor supply? How is this different than the case with log preferences