In the previous episode,

we saw that the existence of

an observability produces some very inefficient and potentially damaging outcomes.

Namely, the owner of the project is induced to take

the riskier project instead of a riskless one with positive NPV.

Now, in this episode,

we will study the special case that is entitled 'Co-insurance'.

This is a market way to overcome the problem of moral hazard.

Well, let's go back to the set-up that we had before.

So again, we have the same high and low state.

20 and 0 for project one,

and then we have 12 and 12 for project two.

But now, let's assume that from this $10 million that we need for investment,

we now have seven will be own funds.

So, we will have to borrow just three. I will put it in red.

Borrow three.

See what happens.

Again we go back to,

and let's assume that now the bank again gives

a riskless or let's say interest free loan.

So, F is three as well.

Let's see what happens.

In this case for project one,

I pay three and then the remainder is 17 that goes to me.

Here I have three and nine,

three and nine.

Here clearly zeros.

And now the new calculation NPV shows that NPV 1 is

here I have +8.5 but then I have to subtract seven.

So I'll put 8.5 less 7, which is +1.5.

Well, for project two nothing changes.

So then you have to,

how much do we have here?

Nine is the remainder.

So I have 4.5.

No, it's actually 4.5 from here plus 4.5 from there.

And then I subtract my 7 because in

both cases here I did that because probability is one half.

So, this is +2.

So, see what happens.

Now the bank doesn't observe my choice,

but because the bank expects me to behave as a rational individual.

And we made this assumption before,

we see that now I will indeed take project two because it gives me a higher NPV.

Now see what happened.

We did not restore observability,

but my choice has changed.

And now seeing these calculations,

the bank is positive that I will take project two and in this case,

in both cases, these three arrive at the bank's accounts so everyone is happy.

So, we can take

a little bit more advanced approach and see that there is a certain threshold.

So, if, for example,

we have six our own money,

then NPV 1 becomes equal to +2 and then I become indifferent.

So in this case that we started,

with these high and low stage,

where probability is one half and these cash flow profiles,

we can say that, until I have six or more money of my own,

the bank will give me an interest free loan and I will take a project two.

If for example I ask for more money,

then unfortunately the bank charges me more and I am forced to

take one and projects two are driven out of the market.

So, that is the way to alleviate the moral hazard problem with the use of co-insurance.