all levels of the signal z there is either none or at most one level of accumulated
assets as (z) above which agents become entrepreneurs.
3.3 Entrepreneurial decisions and financial intermediation
As mentioned above, entrepreneurs have to decide on the size of their firms before
they know their productivity levels for the period. Given the assumed properties
of the utility function and the assumptions of full information and no possibility of
default, any entrepreneur will choose productive capital, k, and labor, n, so that
consumption levels are nonnegative for all possible realizations of shocks. This
means that entrepreneurial decisions are taken so that
wn + RL max [0, k — a] ≤ (1 — δ) a + zf (k, n) + RD max [0, a — k]. (6)
This constraint implies that entrepreneurs with a low level of accumulated assets
may be constrained and run their firms below their optimal size. Nevertheless,
because of the properties assumed for Q, becoming an entrepreneur has a future
value. That is, an entrepreneur is willing to sacrifice current consumption for
having the possibility of starting a career that increases the firm’s return over
time. The way to obtain this return profile is by investing a large share of his
income and wealth so as to relax the credit constraint in order to run the firm at
its optimal size.
There are two frictions that affect the production decisions of entrepreneurs.
The first distortion is characterized by the financial constraint (6) which makes
some entrepreneurs run projects with size lower than what it is efficient. To under-
stand the role of the financial constraint, let R be the opportunity cost of capital
which could be equal to RL or RD depending on whether the entrepreneur is a
borrower or a depositor. For an unconstrained agent, the first order conditions
with respect to inputs are given by
u0(c)[z0fk (k, n) — R] Q(z, dz0)=0
and
u0(c)[z0fn (k, n) — w] Q(z, dz0)=0.
These two expressions produce the optimal capital to output ratio, q .Forthe
production function (1), the optimal capital to output ratio is given by
_ ku (z) α α \ w
q nu (z) y 1 — α) R
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