Consider the infinite horizon RBC model with uncertainty developed in class where the representative consumer and firm are assumed to have rational expectations. The consumer has following expected lifetime utility: Eost {log (C₂) + 1 log(lt)} ŋ>0, and ß € (0,1), t=0 wher C, is consumption and 1, is leisure. The consumer's lifetime budget constraint looks like: Ct II 0(1+rs) ² • wƒ (h − 1;) + II; − Tt II(1+rs) + So where h> 0 denotes total hours available for either work or leisure; w, is the wage rate; II. denotes the dividend/profit payments: T. denotes lump-sum taxes: r. is the interest rate

Consider the infinite horizon RBC model with uncertainty developed in class where the representative consumer and firm are assumed to have rational expectations. The consumer has following expected lifetime utility: Eost {log (C₂) + 1 log(lt)} ŋ>0, and ß € (0,1), t=0 wher C, is consumption and 1, is leisure. The consumer's lifetime budget constraint looks like: Ct II 0(1+rs) ² • wƒ (h − 1;) + II; − Tt II(1+rs) + So where h> 0 denotes total hours available for either work or leisure; w, is the wage rate; II. denotes the dividend/profit payments: T. denotes lump-sum taxes: r. is the interest rate

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider the infinite horizon RBC model with uncertainty developed in class where the
representative consumer and firm are assumed to have rational expectations. The consumer
has following expected lifetime utility:
Eo B¹ {log (C₂) +nlog(1)} ŋ>0, and ß € (0,1),
t=0
wher C, is consumption and 1, is leisure. The consumer's lifetime budget constraint looks
like:
Ct
› wt (h − lt) + IIt − It
==0(1+rs) t=0 II's=0(1+rs)
Σ
+ So
where h> 0 denotes total hours available for either work or leisure; w, is the wage rate;
II, denotes the dividend/profit payments; T, denotes lump-sum taxes; r is the interest rate
and So 20 denotes the initial savings.
Show that the consumer's Euler equation-i.e., the optimal choice of consumption today
versus consumption tomorrow-takes the following from:
} = BE: {C+7(1+7+4+1)}.
(Hint: take the F.O.C. w.r.t. C, and isolate E,{A}. Next, take the F.O.C. w.r.t. C++1 and isolate
Et+1{A} then take the expectation of this expression at time t and note that E+E++1{A} =
E{A} by the law of iterative expectations.)

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