A So dynasties descending from cu∣ali...ed workers and cu∣ali...ed entrepre-
neurs donctexperienceoccupaticnal mcb>i lity D escendants from a cu∣aii...∈d
worker converge to (bw;q)* = (1 ∣ )(w ' ±h), 'h) = 2:25. D escendants from a
cuali.ed entrepreneurconverge to a steady state which is parametrized to
. .........r∣..b.∙...∣∙>.⅜ ~____ fuo V (l °) |qKx(1 °i +h )-i(x+h )]
the dynasty s degree oftechnιcaι11 neX αency (be,q) =-----l—1-(1-7)i-------i.
T he ∈ss ineXdentthedynasty thehicherthesteadystatewealth: (be;q)* 2
(2:2 5;9:83].
The dynamics of the dynasty coming from non-cuali.ed entrepreneur
are a little bit more complex. In this case dynasties characterized by a
level of ineX dency lower than e = 1 ∣ i(x-b)(1-7)-h = о,23233 succeed in
q 1 qK (1-7)
accumulating enough wealth in order to invest in human capital. T hey
become cuali.ed entrepreneurs, whereas dynasties characterized by a de-
græ of technical ineCdencye ∙ ° ∙ °e;nq accumulate wealth converg-
■__. ∕7en0V (1-7)[qκ(1-°i)-iχ∣ ._____ ɪ- ■ ɪ. ■
ing to (be;nq) = -----1-(1-7)i----i and remain ndn-euaii,,,ed. Even in this
case, the higher the degree of ineX dency, the lower steady state wealth:
(be>nq)* 2 [0,69; 0,7).
Theevolution ofthe occupationalstructure ofthe population is summa-
rized in table 2-3: in the long-run 54% ofthe population do not invest in
education. 53.66% ofthe population consists ofunskilled workers. The re-
maining46% ofthe population is cuali.ed. The majorshare ofthe cuali.ed
populationismadeofentrepreneurs: theyare38.26% ofthepopulation. Only
entrepreneurs experimentoccupationalmobility: 16.26% ofnon-cuali.eden-
trepreneurs become cuali.ed entrepreneurs.
|
N Q |
Q |
marg. distr. | ||
|
W |
0,5366 |
0,5366 |
0,08 ! 0,08 |
0,6166 ! 0,6166 |
|
E |
0,1633 |
0,0007 |
0,22 ! 0,382633 |
0,3833 ! 0,3833 |
|
marg, distr. |
0,7 ! |
0,5373 |
0,3 ! 0,462633 |
1 |
|
G IN I = |
0,263 |
! 0,367 | ||
T able 3: evolution of occupational distribution in scenario I (progenitors !long-run) .
A verage wealth increases, from 0.5 to 2.8 6, thanks tothe increase ofthe
cuali.ed entrepreneurialshare ofthe population6.
6A verage wealth is also an indicatorofaggregate utility. A ctually, given preferences,
aggregate utility is an increasingfunction ofaggregate income. Ifpopulation is constant,
aggregate utility is alsoan increasingfunction ofaverage income and wealth.