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Exponential inter-temporal utility function question




Exponential inter-temporal utility function question;I have this function;U(C0, C1,C2) = ln(C_0) + (?)*lnln(C_1) + (?^2)*(ln(C_2);where? =0.8;Suppose I have $60 in period 0 (C_0). How much should they consume in each period?;Show your math. (Set the discounted marginal utility of consumption between period 0 and 1 equal, and also the discounted marginal utility of consumption between period 1 and 2 equal. That gives you 2 equations and 3 unknowns. The third equation comes from the constraint. Recall that the derivative of ln x is 1/x.);HELPFUL INFO;Constraint;C_0 + C_1 + C_2 = 60;A SOLUTION OF A SIMILAR PROBLEM;Suppose you 7 hours of leisure spend over 3 periods (days).;U(L_0, L_2,L_2) = ln(C_0) + (?)*lnln(C_1) + (?^2)*(ln(C_2);where? = 1/2;MU_0 = (1/2) MU_1;(1/2) MU_1=(1/4) MU_1;Constraint;L_0 + L_1 + L_2 = 7;MU_n= 1/L_n = (du/dL);(1/L_0)= (1/2)(1/L_1);and;(1/2)(1/L_1)=(1/4)(1/L_2);s.t.;L_0 + L_1 + L_2 = 7;So, this simplifies to;L_0=2*L_1;and;L_1=2*L_1;So our lifetime consumption plan is;L_0= 4;L_1= 2;L_2= 1;NOTES;I'm having trouble figuring out where the 4 came from in the example problem. I'm not sure how to translate that to the problem where I have 60, instead of 7. The delta is also different and I'm not sure how to divide the 60 into three periods based on the utility function.;Additional Requirements;Min Pages: 1;Level of Detail: Show all work


Paper#15217 | Written in 18-Jul-2015

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