10. Financial Market Equilibrium Flashcards
What is r?
Real rate of interest
What is the saving function?
S(r) where S’(r)>0
What can we say about U(c0,c1)?
U(c0, c1)= u(c0) + c1, where u(.) is increasing and concave
What does the functional form of the savings function (supply of funds by households) do?
It preserves risk neutrality wrt returns while making the savings function perfectly elastic
What is the maximisation problem and solution to the savings function?
Max(u(c0) +c1)
Subject to
c0+ c1/(1+r)=y
Solution
u’(c0(r))=1+r
Why is period-0 consumption decreasing in r and hence savings S(r)=y-c0(r) increase in r?
Because u is concave
For the balance sheet channel: moral hazard, what assumptions do we make?
-continuum of risk neutral entrepreneurs
-fixed investment model
-Heterogeneity in A: cumulative distribution function G(A), density function g(A), support [A, Ā] where Ā<=I
-pHR>(1+r)I>pLR+B
What is a necessary and sufficient condition for an entrepreneur with assets A to receive financing in the balance sheet channel: moral hazard?
PH(R-B/delta p)>= (1+r)(I-A)
How do we define A*(r)?
Such that
PH(R-B/delta p)= (1+r)(I-A*(r))
What is the net demand for funds by investors given by?
I(r)= (1-G(A*(r)))I-A^e
What is true at market clearing?
I(r)=S(r)
What happens if the distribution of A shifts to the left?
Then the demand for funds will increase for those firms that can still obtain funds. But the proportion of firms that can obtain funds decreases
What assumptions do we make in the balance sheet channel: adverse selection model?
-Asymmetric info about private benefits.
-All borrowers have the same fixed investment technology and the same level of assets A<I
-heterogeneity: private benefit B is distributed on the interval [0,B top] according to the cumulative distribution function H(B); private info
What are the only feasible contracts in the balance sheet channel: adverse selection and why?
Pooling contracts. All borrowers make the same repayment R-Rb. Bad types (high B) can’t be screened out since their surplus from the lending relationship is higher to that of the entrepreneur with lower private benefits
When does the entrepreneur behave and misbehave?
Behaves if B<B(Rb)
Misbehaves if B>B(Rb)
Where (delta p)Rb= B*(Rb)
What does the cut off level of benefits depend on?
It’s endogenous and depends on the level of repayment
What is the lenders break even condition given by?
P hat(Rb)(R-Rb)=(1+r)(I-A)
What is the expected probability of success from a lenders perspective?
P hat(Rb)= pH x H(B(Rb))+ pL(1-H(B(R)))
What happens if the debt burden increases for a given p hat?
Rb decreases, and the entrepreneur is less likely to behave (B* decreases). As a result p hat decreases which in turn increases the debt burden
What does the lending channel focus on?
The impact of the strength of financial intermediaries’ balance sheets on firm’s activity. Weak firms depend on monitoring and certification by financial intermediaries to secure access to funds
What are the extensions to the fixed investment model added in the lending channel?
-heterogeneity in R and A
-three types of agents: Investors, Entrepreneurs and monitors
-monitors charge interest rate X>1+r and ensure the entrepreneur exerts effort (prob of success is pH)
-borrower can receive funds either from investors or monitors
Three possible equilibria in lending channel model
- If pH(R-B/delta p) >= (1+r)(I-A) the entrepreneur borrows from investors
- If pH(R-B/delta p)= (1+r)(I-A) and pHR>X(I-A) the entrepreneur borrows from monitors
- If pH(R-B/delta p) <(1+r)(I-A) and pHR < X(I-A) the entrepreneur can’t borrow
What are the three possible causes of economic slowdown we find?
- Decrease in savings (lower secular growth- neoclassical model)
- Decrease in average A: industrial recession (balance sheet channel)
- Decrease in bank funds: credit crunch
