The interest rate on loans
The interest rate on loans can easily be obtained substituting the solution (44) for the quantity of
loans in the demand condition:
Lt+j = a - brL + drB+ j + ηt+j,
(88)
For simplicity we use the solution of (26), but the result is general.
1 1 [(1 - i)(γγβ - h) + (1 - q)κH∖rB+ j+■+ κ(rR+ jq - rD+ j)
Lt+j+1 = τγβLt+j + γγβ nw γγβα
(βγY - 1) [z - a ] - κu
γγ βα
1 - b )( γγβ -1)+ (1 - q )κ
-■------j------------------------COV
γγ βα
+ ' COV ( Ld ,1 ),(89)
βγγ α αβ
rL+ j = â{ a + drB+ j + ηt+j--Lt++j--NW +
+j b I + j γγ β γγ β
[(1 - d )(γγβ - h)+ (1 - q) κH] rB+ j+ι+ κ (rR+ j q- rD+ j ) (βγγ -1) [z - a] - κu
γγβα γγβα
(1 - τ)(γγβ-1)+ (1 -q)κ
b----j------------------COV
γγ βα
(rB,1 ) - γxβ~1 COV(Ld,1 )};
∖ α/ βγγ α αβ J
(90)
focusing just on the relationship with the rate on bonds, we obtain:
L -ɪ{d,в + K1 -β(γγβ-h)+(1 -’)κβrB+ j+■ +c
t+j = b∖drt+j+ γ-βα + g
(91)
where
g = a + ηt+j - Lt+j - NW +
κ(rR+ j q - rD+ j)
γγ βα
(βγγ - 1) [z - a ] - κu
γγ βα
(1 - τ)( γγβ - 1)+ (1 - q )κ
b----j------------------C^V
γγ βα
(rB,1 ) - γγβ-1 COV(Ld,1 )};
∖ α/ βγγ α α/ J
(92)
It is useful to study in first instance the result when the bank has no market power and the rate on
loans is taken as exogenous. Considering the bank as representative of the sector and aggregating
we would obtain:
l [-( γγ β - h ) rL+ j+■+ (1 - q ) κH∖rB+ j+■ y, rt+j = γγφv + g Γ |
(93) | |
and |
rL + γγβ - H rL = (1 - q) κrB+ j + G t+j γγ βv t + j + 1 γγ βv |
(94) |
Finally, |
rL = 1 - γγβv rL . (1 - q)κ rB + vG rt+j +1 = 7γ β rt+j + 7γ β rt+j + , |
(95) |
where |
, 1 1 κ(rR+ jq - rD+ j - u) g = - γγβLt+j - γγβ nw + γγβv + + (1-q)κCOV(rB,1 ) - γγβ-1 COV(Ld,1 )}; |
(96) |
28