Now, let's continue our discussion.
And here, we will recall
that the maximum expected cash flow is not only the criterion of making choices.
Well, in financial economics,
as an economist in general,
there are some other fundamental things like supply and demand.
So, we will analyze the following situation here.
We will see at what face value supply for loans equals
demand and at what face value of a bank maximizes its cash flow.
And if that would be the same face value, everything would be great.
But as you can imagine,
it will be so great.
So, we will see something there.
Well, the first observation is that we know that demand
here falls not smoothly because when some borrowers drop out, then demand falls.
We will assume here,
and this is a normal assumption,
that supply actually does not change with this thing.
So, basically, how does this work?
The supply of money comes from depositors.
So, if the bank offers them a higher rate on their deposits,
then people bring more money.
That's all we will need here.
The numbers for supply will be
arbitrary in the model that I'll put up on this flip chart,
while, in order to come up with the numbers for demand,
we will assume that there are
10 borrowers of each kind.
That means there are 10 black borrowers of number one,
then 10 blue of number two, and then 10 red.
So, a total of 30.
So we can see that the maximum demand,
let me recall you that each company borrows $8 million, is 240.
But we know that when we go over 12 in face value,
them the number of borrowers immediately drops to 20.
So, let's put a table here.
The table will be like this.
This is the face value versus supply,
and this is the demand.
Well, what we know is that for face value,
we have five potential face values that are rolling just this.
This is 12 minus this epsilon.
Now, this is 12 + ε,
and then 18 - ε. I put this in blue because here,
black borrowers no longer borrow.
And then, finally, this is 18 + ε,
and then 20 - ε.
This is the maximum possible amount that the bank can
charge only to borrowers number three.
Well, we'll start with demand.
We know that first the 12 - ε,
everyone borrows, and we can see 240 like we said.
30 borrowers at each, all of them stay.
Immediately, as we jumped toward 12,
we see that borrowers number one disappear,
and now we have only 160.
Then at 18 - ε,
we have the same 160.
But immediately, after we jump over 18,
we drop to 80.
And then, clearly at the lowest 180 stays.
So, we analyze the demand.
Now, for supply, like I said,
I'll put some arbitrary numbers.
The only thing we know that supply will grow.
So, the higher is the interest that the bank charges to his borrowers,
then clearly, it can afford to offer high interest rate to its depositors too.
So, let's say that here it will be 40.
Now, at 12 + ε is the same 40.
So, I'll have to use a blue marker, so, it's 40 here.
At 18, it's 60,
and let's say at 20, it's 80.
Let's look at this table and ask them a couple of big questions.
Question number one, what is the face value at which supply equals demand?
Well, we'll look at the table and see that this is here.
So, in order to avoid market failure, so,
to find the point that which supply equals demand,
and this is a market clearing point we can see that this is 20 - ε.
So, this is the situation back to the previous chart.
Then the bank makes loans only to the riskiest borrowers and at
such a high face value that
the remaining cash flow to the borrower is just this infinitesimal epsilon.
So, this is really a fundamentally risky situation.
And as we all know, unfortunately,
at this face value of the bank does not maximize its cash flow.
Let's go back for a moment here.
So, we're talking about this point.
So, this is the point at which supply is equal to demand.
And the point at which the bank maximizes its cash flow is this.
Let me use proper color.
Back to this table.
That happens here.
What do we see?
At this point, the bank does maximize its expected cash flow,
but the demand is 160 and supply is only 60.
So, we can see a huge disbalance,
and that is called credit rationing.
So, I have only $60 million.
So, I can give loans to just a few people.
So, if everyone takes eight,
then I can give it to how many?
I cannot give loans to eight people,
I can give only to seven because it's 56,
or I can say to each and everyone,
I can give just a fraction,
60 to 160, which is,
out of eight, I will give you just a small amount.
So, this is a problem.
We can see that the bank,
as the only provider of cash in this situation,
sticks to this face value.
And at this face value,
supply is much smaller than demand and we see credit rationing.
So, that is a problem.
That clearly is an inefficient behavior of capital markets,
but this is not only eight.
Unfortunately, we will see that adverse selection as a result of
forcing face value to grow brings back our old good friend more hazard.
And in the next final episode of this week,
we will see what happens if these borrowers had not one project but two projects.
We will see. And by now,
you already have an idea with what will happen.
We'll see that as long as the bank pushes the face value up,
not only does it push out of the market good borrowers,
but it also will produce incentives for
the borrowers in their choice of projects within the company to switch
from nice riskless projects to
riskier projects in the hope of pushing part of the risk on the bank.
That's exactly what we will see it in the next final episode.
