firm equates the expected return with the expected cost of borrowing we have
Et[1 + Rk,t+1] = Et[Θt+1(1 + Rt+1)]
(42)
where Θt = k μ-N-) -λ (43)
Qt-1Kt
is our chosen functional form. In (43), Nt is net worth and Qt-1Kt -Nt is the external
financing requirement. Thus Qt- 1Kt-Nt is the leverage ratio and thus (42) and (43) state
that the cost of capital is an increasing function of this ratio. Bernanke et al. (1999), in a
costly verification model, show that the optimal financial contract between a risk-neutral
intermediary and entrepreneur takes the form of a risk premium given by (43). Thus the
risk premium is an increasing function of leverage of the firm. Following these authors, in
the general equilibrium we ignore monitoring costs.
We now introduce entrepreneurs who own the capital of wholesale firms and who exit
with a given probability 1 - ξe . Then the net worth accumulates according to
Nt+1 =ξeVt+(1-ξe)Dte
(44)
where Dte are transfers from exiting to newly entering entrepreneurs continuing, and Vt , the
net value carried over from the previous period, is given by
Vt = (1 + Rk,t)Qt-1Kt - Θt(1 + Rt)(Qt-1Kt -Nt) (45)
where Rk,t is the ex post return given by
WW
(1 - αI ) -pr- ~Kr + (1 - δ ) Qt
(46)
1 + Rk∙t = ---------Q-l----------
Demand for capital is then given by
Et [1 + Rk,t+1 ]
Et h(1 - α)
PW YW
Pt+1 Yt+1
Pt+1 Kt+1
+ (1 - δ)Qt+1i
Qt
(47)
Finally, exiting entrepreneurs consume the residual equity so that their consumption
(48)
Ct = ^ Nt
ξe
must be added to total consumption. The full model is summarized in Appendix A with
the previous model as a special case.
15