Question

QUESTION-3: Suppose that L two period-lived individuals (1.2) (young, old) are born in period t and that 1: = (1+n)Le-1- Let utility be logarithmic: u(C1,0, C2,4+1) = In(1.c) + In(C2.6+1). Each individual born at timetis endowed with A units of the economy's single good. The good can be either consumed or stored. Each unit stored yields x>0 units of the good in the following period. Also that in the initial period, period t=0, in addition to the LO young individuals each endowed with A units of the good, there are [1/(1+n)]/L individuals who are alive only in period 0. Each of the "old" individuals is endowed with some amount Z of the good; their utility is simply their consumption in the initial period, C20- a) Describe the decentralized equilibrium of this economy i.e. given the overlapping-generations structure, will the members of any generation engage in transactions with members of another generation?

Answer 1

Answers in the decentralized equilibrium , thou will be no inter genarational trade, even if the young would like to trade, good this ferial for goods next feriod, the only peoples around to trade with are the old infortunelly; the old will be dead- and thus in no forution to Comfbeat the fale noot ferial. the individual's vtilly faction is gee bay ' in ce, t t in Catt . The contracts one lli, cit+FtA, and il 6.4+/- xFt, where Ft is the ascon- stored eley the individual Subbaleta equillibráty in wito yeild the sentert y cat + Cz, ++/4 = A. the inchideals frollenes in the mimate likelime utilbyr as grees by equation ) Subogels to wintergausational lecket. who trained af, given the equi (iv), set up the borgen v) t= Ancie t + Inc2,t+1+7 (A-Gyt-(2,4+ [2] The frit oder Conditions are given by IL den t=%e15-Y = 03 yei, tTI and (vi) de 1862,t+1=Y6 215+1-S2=0=7%27t+1=4\x(vii) Conebrowt

Subalidale equa (u) unto (wit) and Seconogo. Io allen (ur) •62, ++ = 261, to Substibil cgu (vii) with the winter towel heelgeta Contract equ (iv) to alitan (x) < £+ *C1, 6/4 = 1 (x) a t= Ale To altaine an exfrecenion for Seconds - heriod Constructions, Suitabilute equ (x) eruto equilibrium (vi) (2C2, -+1=xW2 where young reach widicidecal Conawses that of here cudowanit and stores the other half, that is, fl=% this allows her to Corcumue t A/2 where old note that with log-utilly the fraction of het. Eulautant that lhe interidiel Stecked does not defend up on the action to storage.