So, let's think about what drives the value of audits in a simple context,
an everyday context, that you want to buy a new car and in particular,
you're keen on getting a 1999 Porsche 911 Turbo.
That's a nice looking vehicle in that picture.
And the problem is you're not really sure if the car that is in that picture is
exactly the car you're going to get, and so when
you start looking in the market for these 911s,
let's suppose that about 60% of these cars are of great quality,
of a quality you would expect,
and that'll satisfy you.
And if that's the case,
you should expect to pay $15,000 for that car,
and we're making this very very simple.
The other 40% are not reliable.
In fact, they are what you might call lemons.
Lemons is a phrase that you often see in the car market and in fact,
if you were to go to a car dealer, you would find that
sometimes even on the windows is when they're describing the options on that car,
you will even see an allusion to that state's lemon law.
It gives you a right as a purchaser of a car in states
to bring cars back if you can show that it truly is a lemon,
and that's if you're talking to a dealer on a lot.
But not everyone from whom you're buying cars is going to be a dealer.
Not that all dealers can be trusted either.
But most dealers have a substantial amount of money invested in
their reputation and so they're going to be guarding that, one hopes.
So, let's think about this a little bit and how would you
as someone who wants this car think about making an offer for the car?
So how much would the owner of a 1999 ask for it?
So you have your offering price, that you have, and then you have the owner of a
1999 Porsche Turbo 911
trying to figure out what the asking price is. And in this situation,
one very good question to ask is,
does the owner even know what kind of car that he or she has?
Is this a good,
excellent condition Porsche 911,
or is it a lemon?
The other thing you have to worry about is that even if the owner
of that car knew or thought it was a lemon,
would that owner be constrained by that knowledge?
Now you'd like to think, and most people in the world are worthy of trust,
you'd like to think you can trust owners.
But unfortunately, some owners would try to sell you
the car probably even with the knowledge that it is
a lemon and they'd like to sell you the car without
any returns possible for the price that you would expect to pay for a high quality car.
So, in a world in which you cannot really revise your beliefs very
much about the quality of the car based on the owner's asking price,
that's a world in which you don't pay $15,000 for a car, right?
How much would you pay?
So, if you cannot believe
the owner at all, when they represent that they have a high quality car,
then you would back away from
the owner's asking price and you would come to a calculation.
A calculation if you were risk neutral,
is that you would just take the expected value into consideration.
The expected value would be 60% times $15,000 plus
40% times $5,000, those coming together to be $11,000.
Now, where did I get that? The 60%,
it just goes back to that part of the pie graph where over half of
the cars in that market are of high quality,
and slightly less than half is the 40%,
are of low quality. And the 15 and then 5 come from the value we are
assuming a high quality car has and a low quality car has in this market.
And that's if you're risk neutral.
If you are averse to risk,
would you pay higher or lower?
Well if you said lower, you're right.
The risk averse is someone who doesn't want to play even a fair gamble.
A risk averse person,
if you had them flip a coin and it was
a fair coin and you would say you would get $10 if
it lands head and $0 if it lands tails,
they would not play the game for $5.
And risk neutral person would play that game repeatedly for $5.
It wouldn't be very exciting for them because
the $5 is exactly equal to the expected value.
They don't expect to make money by playing that game,
but $5 is a good price to pay for such a game for risk neutral.
Now, if you were a risk taker,
maybe you would pay a little bit more.
But most people are not going to be risk takers in a used car market.
So let's suppose you are risk neutral and that would mean you are really
indifferent between paying $11,000 and having the car,
versus keeping all of your money and not having the car.
Well this is not very satisfactory to
the owners of cars who think that they have good cars, right?
And if that's the case,
they are not going to continue to be in that market.
Sellers who are certain and not even just certain, but people
who are quite knowledgeable and they think they have a good car.
What are they going to do?
They are not going to be willing to give up a car that's worth $14,000 or
$15,000 in exchange for what
buyers are willing to pay, which is only...risk-neutral buyers, which is only $11,000.
So, what does that tell you about the kind of the cars that are on the market?
It should tell you something about the quality of the cars.
You either have a situation where sellers who think they have
a good car have to consider selling the car at some discount.
Something less than they believe it is truly worth
and probably something less than it is worth, okay?