I would like some help with this question:

Take a simple intertemporal model of consumption. The consumer lives for two periods; you can think of these as her working life and her retirement. The consumer earns income when she is young, y, which she does not choose. She chooses to save some amount of her income, 5, and consumes the rest while she is young, (:1 . Her savings attract the after-tax rate of return, r(1 t). When she retires, her consumption, (:2, will equal her savings and any after-tax return that has accrued. The consumer '3 utility maximization problem is therefore: mach[c1,cz)=2c}/2+2c;/Z s.t. y=c1+s c1:2 C2 = 5(1+r(1t))- (a) Let's start by simplifying the problem. Use the constraints to substitute for c1 and (:2 in the utility function, recasting the consumer 's constrained optimization problem in which she chooses c1 and C2 into an unconstrained problem in which she chooses s, as in: msax 11(3)... (b) The idea is that because income is given, any choice about how much to save is implicitly a choice about how to divide consumption between working life and retirement. So let's determine the consumer 's optimal saving decision by differentiating the consumer's utility function, deriving the consumer 's first-order condition. Don't simplify the expression yet. du_ a_...=o