Question: Let Subscript[c, t]>= 0 be her consumption in period t,t=0,1,... The present value of the stream of consumption Subsuperscript[(Subscript[c, t]), t=0, [Infinity]] is Subscript[c, 0]

Let Subscript[c, t]>= 0 be her consumption in period t,t=0,1,... The present value of the stream of consumption Subsuperscript[(Subscript[c, t]), t=0, \[Infinity]] is Subscript[c, 0] Subscript[c, 1]/(1 Subscript[r, 1]) Subscript[c, 2]/((1 Subscript[r, 1])(1 Subscript[r, 2])) ... Subscript[c, t]/((1 Subscript[r, 1])(1 Subscript[r, 2])...(1 Subscript[r, t])) ... Let u[c] denote her utility in a period, when her consumption in that period is c. Suppose that \[Delta],0<\[Delta]<1, is the factor the consumer uses to discount her future utilities. The problem faced by the consumer is (1) Subscript[max, Subsuperscript[(Subscript[c, t]), t=0, \[Infinity]]] Subsuperscript[\[CapitalSigma], t=0, \[Infinity]] \[Delta]^t u[Subscript[c, t]] subject to the intertemporal budget constraint (2) Subscript[k, 0] Subscript[h, 0]=Subscript[c, 0] Subscript[c, 1]/(1 Subscript[r, 1]) Subscript[c, 2]/((1 Subscript[r, 1])(1 Subscript[r, 2])) ... Subscript[c, t]/((1 Subscript[r, 1])(1 Subscript[r, 2])...(1 Subscript[r, t]))

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