The name is absent

CfFcrtuneandN ature Ifthedegreecfinheritabilitycftheinetdencyis
low, the dynamics ofwealth accumulation is ergodic and long-run distribu-
tiCn dCes nCtdepend Cn initialcCnditiCns. On the cCntrary, the higherthe
genetic cCmpCnent, the mCre the dynamics is nCn-ergCdic and may depend
CrnCtCn initialcCnditiCns. Theremayexistmultipleequilibria.

1 ASSUMPTIONS

L et’s cCnsideraclCsedecCnCmy, with twCgCCds: theCutputgCCdwhich can
beeithercCnsumed Crinvested and thecapitalgCCd, which can beused Cnly
in the prCductiCn Cfthe CutputgCCd.

T here exist cvenlappi ng generations cfa ccuntab ein..nity cftwc- peri cd
lived agents. P CpulatiCn is cCnstantCvertime. Y Cung agents are endCwed
Wthcneuniitcf Iabcurand di^π erex-ante frcm cneanctherin thei rdegreecf
technical inet dency (°t) and wealth (b_t), that is the bequest received frcm
their fathers. The cumulative distributicn functicn cfprcgenitcrs’ wealth
G (b) is excgencusly given. G (b) represents thesharecfthepcpulaticn hav-
ing initial wealth lcwer cr equal tc b. I assume that wealth is unifcrmly
distributed amcngprcgenitcrs cn the suppcrt(0; 1) :

T he prcgenitcrs' technical inetdency is randcmy assigned by N ature
acccrding tc a uniform distributicn cn (0; 1). T he degree cftechnical inet -
ciencyistransmittedfrcm ageneraticntcthectheracccrdingtcthefcllcwing
lawcfmcticn:

°t+ι = ½°t + (1 i ½) ut+ι

with 0 < ½ < 1 and ut+ 1~U (0; 1) . A cccrding tc (1) each agents' degree cf
inet dency is a Hnearccmbinaticn cfhis father’s technical inet dency and cf
a randcm ccmpcnentwhcse realizaticns are extracted frcm a time-invariant
unifcrm distributicn. ½ measures the degree cfinheritability cftechnicalin-
net dency.T his impies that, cnyiftechnical inetdencywereapure randcm
quality (½ =0) cra pure genetic quality (½ =1), each generaticn wculd be
characterizedbythesamedistributicn cfabilities. T hestcchasticccmpcnent
cftechnical inet dency ccud be interpreted as thee³ectcfccngenita∣ ski Il
randcmly chcsen byN ature acccrdingtca time-invariantdistributicn.

1. Ncte that

E (°t+i) = ½^t+1E ⁽°0 ) ^{+ 1 +} ½ ⁺ ::: ⁺ ^ ^{i E} ^t+^

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