Notice q is independent of the individual state of the agent. Also, implicit here is
the fact that because the agent is unconstrained, the choice of capital and labor do
not depend on the asset level of the agent and only change with the productivity
signal, z. However, it may occur that the financial constraint (6) does not hold for
this choice of inputs, that is,
wnu (z) + Rku (z) > (1 — δ + R) a + zf [ku (z) , nu (z)].
In this case, it is still optimal to keep the same capital to labor ratio q and the
constrained level of labor (and, implicitly, the level of capital) is determined from
the expression
wnc (a) + Rqnc (a) = (1 — δ + R) a + zf [qnc (a) , nc (a)].
The skill and asset levels of an individual affect both his occupational decision
and the financial constraints he faces if he becomes an entrepreneur. Giving a skill
level, z , the larger the asset position of an agent the more benefits he has from
becoming an entrepreneur. So, for each value of the signal z there is a critical
level of assets, call it as (z), such that for a>as (z) the agent decides to be an
entrepreneur and for a<as (z) the agent decides to be a worker. Furthermore,
for a given skill level, the financial constraint is more likely to bind as the assets
of the agent are lower. So, there is another level of assets, call it ac(z), such
that, if the agent is an entrepreneur, for a > ac(z) he is financially unconstrained
and for a<ac (z ) the agent is financially constrained. Thus, entrepreneurs with
skill z and assets in the interval [as (z) ,ac (z)] are constrained and their demands
of inputs are an increasing function of accumulated assets. Entrepreneurs with
assets a > ac(z) have demands of inputs which are independent of the level of
wealth and only depend on the productivity signal z . By the same intuition, given
the level of assets, as the productivity signal gets larger, it is more profitable to
become an entrepreneur and it is more likely that entrepreneurs are financially
constrained. This means that any shock making financial markets more liquid or
credit cheaper will reallocate assets towards constrained entrepreneurs and will, in
general, increase the aggregate level of productivity of the economy.
The second distortion is the spread between borrowing and lending rates due
to the reserve requirement. For an unconstrained entrepreneur who is borrowing,
the relevant opportunity cost of capital is RL . This means that his optimal capital
to labor ratio is
L _ kLu (z) α α \ w
q nLu (z) y 1 — α J RL
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