3.2 ... WHENTECHNICAL IN EFFICIEN CY ISEX-
CLUSIVELY STOCHASTIC (½=0)
I fthe degree cfteclhnical ineΦ ciency is stochastic; wealth accumulation is a
M arkov P rocess. Thesetofstates can be decomposed in a setoftransient
states and in an irreducible and closed set of persistent states. Once the
M arkovChainvisitsonepersistentstate, itremains inthatclassofstates and
doesnotabandonitanymore. Inthelong-runtransientstatesdisappears and
the state space coincides with the closed and irreducible setofstates. Each
dynasty visits each ofthe persistent state with a positive probability. All
the long-run states are therefore non-nullpersistentstates and the long-run
distribution ofwealth is unique, stationary and ergodic, independent from
initial conditions. Each dynasty may move among wealth classes without
implyingany change in the mean wealth.
The long-run distribution of wealth for each scenario is represented in
...cμιre3. T his is the resultcfa numericsimuIaticn based cn theparameters
said above. I have plotted the distribution ofwealth of1500 dynasties after
200 pericds.
The suppcrtand the.rstmcmentcfthe distributicns, when parameters
cive rise tc the II and IV scenarics, dc nctchance relatively tc the perfect
genetic case; T hecn ydiπ erence is that i n the One- run there exists occupa
ticnalmcbility. Each family dces nctccnverce tca unique steady state, but
mcves amcnc states. The absence cfthe familiardeterminant cfintercen-
eraticnalcccupaticnaland inccme persistence determines an extreme sccial
≠uιclιty
Summincup:
w when the transmission Oftechnical ire¢ ciency is stochastic, the Icng
run distribution ofwealth is ergodic. Each dynastyvisitswith a posi-
tive probability each steady state. The long-run distribution is unique
and stationary, buteach family moves among occupationaland wealth
classes;
in scenarios II and IV,when, in the genetic transmission case, the
long-run distribution ofwealth does notdependon initialcondition, the
hypcthesis Ofstochastic transmission Oftechnical i∏e3 ciency dees not
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