where bot , the individualwealth when old, is equalto bt ifthe agenthas not
investedin education;tobt jh if hehas invested in education.
G iven the hypotheses on wages and on pro..t- the marginal return from
education is Constantand equal to ± forworkers and it is equal to qK for
entrepreneurs. Capital depreciates completely in each period. T herefore,
in each period, aggregate capitalis the sum ofallthe undertaken projects.
Inputs in the production ofthe output good are skilled (Lq) and unskilled
labour (Lnq) and capital (K) . G iven the hypotheses on factors rewards,
aggregate outputis
Y = wLnq + (w + ±h) Lq + qK (3)
2 HUMANCAPITAL INVESTMENTAND
OCCUPATIONAL CHOICE
From the maximization ofutility (2) subjecttothe budgetconstraint ct+1 +
bt+1 ∙ yt+1 it is immediate to conclude thateach agent bequeaths his sen
with a share (1 j °) ofhis second-period income (yt+1), whi le the residual
is consumed: bt+1 = (1 j °) yt+1 ; ct+1 = °yt+1. T he indirectuti ity function
therefore is linearin income:
u = °(°) (1 j °)(1 °) yt+ι
Indirectutilitymaximization is thereforeequivalenttoincomemaximiza-
tion.
Ifa non-quali.ed agentchooses tobecome worker, his income is the sum
ofthe unskilled labourwage and the return on investmentofhis savings in
the capital marketatthe gross interestratei. T heιefcreyW;nq = ibt + w 4.
A nalccously a cμali...ed worker’s income is: yW;1 = i (bt j h) + w + ±h. N et
return from education is therefore (± j i) h, that is the college premium ±h
ess the cpportunitycostcfeducaticn ih:
If a quali.ed agent chooses to become entrepreneur, his second-period
income is equalto the gross return on investmentless the debtburden, i.e.
ye+q1 = 1IK (1 j ° + h) j i (x j bt + h). A non-cuιaii...ed entrepreneur’s income
4Wstandsforworker; nqstandsfo:rnor-c|uaii...ed. Symmetrycaly, qstandsfo:rc|uaii...ec|
e stands forentrepreneur.