The name is absent

where b^o_t , the individualwealth when old, is equalto b_t ifthe agenthas not
investedin education;tob_t 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 (L_q) and unskilled
labour (L_nq) 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 +
b_t+1  ∙ yt₊1 it is immediate to conclude thateach agent bequeaths his sen

with a share (1 j °) ofhis second-period income (y_t+1), whi le the residual
is consumed: b_t+1 = (1 j °) y_t+1 ; c_t+₁ = °y_t+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 = ib_t + w 4.
A nalccously a cμali...ed worker’s income is: yW;1 = i (b_t 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 b_t + h). A non-cuιaii...ed entrepreneur’s income

⁴Wstandsforworker; nqstandsfo:rnor-c|uaii...ed. Symmetrycaly, qstandsfo:rc|uaii...ec|
e stands forentrepreneur.

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