where kLu is the capital demand of a lender who is unconstrained and nLu is the
corresponding demand for labor. On the other hand, an entrepreneur who is also
unconstrained but has assets in excess of his needs, will be a depositor and the
corresponding capital to labor ratio will be
D _ kDu (z) μ α ∖ w L
q ≡ nDu(z) = ∖i-α)rd >q.
For these financially unconstrained agents, independent of whether they are bor-
rowers or depositors, their input decisions only depend upon their productivity
signal. However, because of the gap between RL and RD , there may be agents
who would like to be borrowers at the high capital to labor ratio qD and deposi-
tors at the low capital to labor ratio qL . In such a case, these entrepreneurs are
constrained to have kA = a.7
3.4 Outside the stationary equilibrium
As pointed out above, proportional changes in the government liabilities are neu-
tral. Also, changes in government liabilities that permanently move the ratio of
liquid to illiquid liabilities (h/b) are associated with different steady states. In this
section, we look at how the economy moves between these stationary situations.
In particular, assume the economy is at the stationary equilibrium characterized
by the number h. Then, the central bank announces unexpectedly a permanent
change in this number, say, an increase to h>h. In the period of the announce-
ment, the total amount of liabilities (X) is fixed, so, this change could be achieved
by increasing liquid liabilities to H = hX > H and reducing illiquid liabilities to
B =(1- h)X < B through an open market operation. After that, the liabilities
of the central bank are permanently split between liquid and illiquid liabilities in
order to match the new values of h and b satisfying h + b =1.
The unexpected nature of the announcement means that in the first period of
the transition, the population starts with the distribution of assets and productiv-
ities of the old steady state, λ. With the new supplies of government liabilities,
the conditions to be satisfied in the first period of the transition are the market
7 The nature of this constraint is different from the financial restriction men-
tioned before and it is just a consequence of the gap between borrowing and lend-
ing rates imposed by the reserve requirement. Nevertheless, in the simulations we
run in the following section it turns out that agents for which k = a represent a
very small fraction of entrepreneurs (less than 1 percent of all entrepreneurs).
19