For project one, well we know that the bank does

not have all the money because here it loses something.

But lets say that the bank charges F, as always.

Now, first of all,

how much money is left to the borrower?

And we can see that for Project one its 1/2 (18 -

F) because basically you

know that we assume that F is higher than three and here you have zero.

But for Project two,

you have just 15 - F,

because in both cases well we assume that F is less than 15 for now.

Well, so far the question is,

at what F does the project owners switch from project two to project one?

Well, it's very simple to find,

we can say that happens when this is greater than that.

So when F/ 18 - F is greater than 15 - F,

t hat gives us the answer that happens that when F is greater than 12.

So you can see that until the bank charges less than 12,

I stick to my nice project two.

However, as soon as the bank jumps over 12 then,

I switch to one.

Now lets see what happens to the expected cash flow to the bank.

Now here F is less or equal to 12 and here F is greater than 12.

We can see that expected cash flow to the bank in the first case is equal to F

while the expected cash flow to the bank in

the second phase is equal to (1.5 + F) / 2.

So you can see that here when F is less than 12,

this is 12, we jump over 12, we see 7.5.

Well, it's strange but let's again summarize that in a chart.

So the chart will be very much like the one we had before but somewhat different.

So this is F, this is expected cash flow to the bank.

Now we put some benchmark point here as we did before.

This is just to show the scale,

and now we start pointing out something.

First of all, this is 12.

We know that this is an important point.

Why this is important?

We know that, here

we have project two.

Here we have Project one.

This is the choice of the borrower.

Here is that we put all blue mark.

Now, let's show what happens to the expected cash flow to bank.

Well, we know that this part that goes here as F like this up to 12.

So here we have also we have 12,

this is expected cash flow to the bank.

And now, as we jump over 12 it goes down to seven and a half here.

And then can be maximized back at the point of 18.

18 and then we will have here at the point of 18,

is (1.5 + 18) /2 which is 10.5.

Right, somewhere here.

So that is what is the expected cash flow to the bank.

And we can see now that before it had this point as a maximum one.

I specifically, going back to these projects,

I specifically put the maximum cash flow for Project one at 18.

So basically, the bank cannot go over 18,

because clearly in this case there is no way that they borrower takes a loan.

Now we can see that if the bank keeps pushing and keeps raising the F,

then it produces incentives for the borrower to switch

from nice riskless projects like two to a risky projects like one.

Why? Because if the,

by the way it's important that the borrower could actually take loans for project two,

not up to the point 12 but two point 15.

Because here still there is something left,

but in between, the borrower will switch to project one.

Because the borrower says, "Why bother?

All the benefit accrues to the bank."

So in this case I switch to a riskier project in which the benefit is divided.

In some cases, I have a greater expected cash flow.

So you can see that the behavior of that is based only on

greed and on ignoring the adverse incentives that occur in this case,

it results in the break up of efficiency.

So we're wrapping up this week by stating the following.

Throughout this week, we not only

declared that problems caused by private information exist,

namely moral hazard and reverse selection.

We also have built models for them and we have

demonstrated how the existence of these problems result in damage.

And although sometimes this damage looked like based on

some examples or simple calculations.

But I said that that is all done only for the sake of

simplicity and the articles that were written in this area,

they actually took a problem in a much more generalized way.

It just unfortunately employs advanced math that goes beyond the scope of the scores.

Now, we have arrived at the end of the first week and we see a big question that arises.

What do we have to do with that?

How can we find some instruments or

weapons if you will to alleviate the problems caused by private information?

Starting next week, we will first analyze

some other more egregious cases and then we will start

to somehow formulate these weapons and they will lead us to the understanding

of how one of the most widespread and most well known financial institutions

emerges, namely a bank.

Now I wish you good luck with your assignments and I'll see you next week.