clearing condition for deposits
-H = P1 I aλ (da × dz) + P1 ∣ max[0,α — k1 (a, z)] λ (da × dz) , (7)
ρ W1 E1
and the market clearing condition for loans
with
Lb = P1
/
E1
max [0, k1 (a, z)
— a] λ (da × dz ) ,
(8)
Hb + Bb = X = H + B.
In these expressions, the subscript 1 denotes that these are variables for the first
period of the transition and Lb is the new supply of loans to entrepreneurs computed
from the balance sheet of commercial banks
1
(ρ - 1) h = b + Bb.
Notice the split between entrepreneurs and workers (the indices W1 and E1) may
change also in response to the different composition of government liabilities.
Equations (7) and (8) are the market clearing conditions to find the price level
P1 and the interest rate R1 for the new values of reserves (H) and government
debt (B ). Remember from section 3.2 that a proportional change in government
liabilities is necessary for monetary policy to be neutral. In the current case,
financial intermediaries learn that the supply of reserves have increased which gives
them the possibility of expanding credit. However, the government is borrowing
less through debt so banks will have to give these credits to entrepreneurs. Given
that the interest rate is a cost to entrepreneurs borrowing credits, the only way
to convince them to borrow more is by reducing the lending rate. This change
produces several effects. First, some of the idle assets that were not used before
are now available to finance productive capital. Also, lower interest rates make
entrepreneurs borrow more assets, use more capital and produce more. With the
larger use of capital the demand for labor moves up and wages rise. Given the
concavity of the production function, how much the marginal productivity of labor,
and therefore wages, increases depends on how labor is allocated between highly
productive, constrained firms and low productive, unconstrained firms. Finally,
there is a reduction in the gap between borrowing and lending rates which, by
itself, enhances efficiency further.
As a consequence of these movements, the distribution of assets after the first
period changes because prices and allocations have been altered. From that point
20