Life-cycle saving. (Modigliani and Bromberg, 1954.) Consider an individual who lives from 0 to T, and whose lifetime utility is given by u(C(t))dt, where u (•) > 0, u(•) < 0.=”” the=”” individual’s=”” income=”” is=”” y0=”” +=”” gt=”” for=”” 0=”” ≤=”” t=””>< r,=”” and=”” 0=”” for=”” r=”” ≤=”” t=”” ≤=”” t.=”” the=”” retirement=”” age,=”” r,=”” satisfies=”” 0=””>< r=””>< t.=”” the=”” interest=”” rate=”” is=”” zero,=”” the=”” individual=”” has=”” no=”” initial=”” wealth,=”” and=”” there=”” is=”” no=””> a) What is the individual’s lifetime budget constraint? (b) What is the individual’s utility-maximizing path of consumption, C(t)? (c) What is the path of the individual’s wealth as a function of t ?

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