Download Question 7 - WebCampus

Corporate Finance and Financial Intermediation
Professor Alain de Crombrugghe
2016-2017
Homework 2
University of Namur
Faculty of economics, social sciences and business
administration
Van Acker Didier (noma: 52241200)
Pay-Pay Wani Harvell (noma: 96731600)
Question 7
“Take a simple case of the second hand car market (peaches and lemons), explain how
signalling would work. Make it as similar as possible to the signaling solution of section 2.3.
You can drop risk aversion if needed”
The second hand car market is characterized by the fact that there are good and bad
quality cars. The presence of both types of car lead to an equilibrium price which is
too low and not beneficial for the high quality car owners. The latter will rather leave
the market due to the impossibility of distinguishing the two types of cars for the
customers. This last act will diminish the supply, lead the market to a higher
equilibrium price, less cars will be sold and there’ll be an inefficiency.
The good quality car owners have an incentive to signal themselves in order to
achieve mutually beneficial exchange opportunities but also obtain an higher price.
Signalling is a contribution of information from the informed party and can take
several forms.
-A quality label as a seller: given by the authorities it would certify the quality of the
seller. However this could be difficult to get for the private individual seller and could
only concern garage and companies.
-A quality label for the car: given by the authorities it would certify that the car is a
high quality car.
-An insurance provided by the seller: knowing the good quality of its car the seller will
not hesitate to partially refund the customer in case of a breakdown.
-Contract an agent: in exchange of a commission the agent will sell the car at the
best price.
(Advertising is another possibility which will be discussed later)
1
Just as in the case of lending, there might be a problem of adverse selection
because of the asymmetry of information.
In the case of lenders, signals can be given by self-financing a part of the project , in
order to show the bank that the project is not a bet and that the borrower
(entrepreneur) will put enough effort in it.
However, if the borrowers are risk-averse, they might refuse to put their own money
in the project.
Leland and Pyle showed how borrowers could form coalitions to get better
conditions, individually they would get less mild conditions.
In our case , this would be a coalition of buyers.
Let’s denote σ² the variance of the quality of the car due to bad luck ( malfunctioning
independant from the quality of the car when sold on the second hand car market).
It’s the same for all cars since it’s a random variable.
θ is the quality of the car , this varies of course and only the seller has this
information.
So the buyer gets a car with “utility” R(θ) = θ + σ²
Since θ is not observable and buyers can’t distinguish the quality of the cars , they
will only want to pay a median price P for each car.
This is the main problem on this market of course.
They will only sell their car on this public second-hand market if P > P(θ) + (½)p*σ²
(price if the quality was observable ; where small p is a coefficient of risk-aversion)
So high-quality cars are driven out of this market , here occurs the problem of
adverse selection.
If we suppose a binomial distribution of θ , with two probabilities π 1 and π2 .
π1 gives a low-quality car θ1 whereas π2 give a high quality car θ2.
P depends on these probabilities , buyers will want to give a higher median price if
the probability of having a lemon is lower of course.
Let’s denote P= π1*θ1 + π2* θ2
So π1*θ1 + π2* θ2 + (½)p*σ² = θ2
and thus when π1*(θ2-θ1)
≤
(½)p*σ² , the seller of high-quality car will accept to
go to the second-car market. This happens when the adverse selection problem (low
median price) is outweighed by the aversion of risk.
α is in the Leland and Pyle model , the fraction of self-financing ( the signal thus).
In our case, alpha could be the cost of verification of the quality of the car by an
independent auditor. Sellers with high quality cars are more willing to do this
investment since it will prove their car is worth more than the median price on the
market.
But a “lemon”-seller will refuse this because this cost will be proportionally higher for
him and it will lower the price he can reasonably ask on the market.
So (1-α)θ2 + θ1 -(½)p*α² ≥ θ1
2
Low-quality sellers will still refuse to do this audit so they get the full price whereas
high-quality sellers lose the cost α.
We can imagine there will be a new lemon-car market with the low-quality cars , with
cars closer to the average quality and other cars with deplorable quality , here the
same problem occurs if signalling is too expensive for the sellers of the “best of the
rest” so to speak.
Let’s take a look at section 2.3.2. Selling a car is a form of project and we saw earlier
that there are case of asymmetry of information between seller and customer.
Sellers have an incentive to signal themselves and their good cars as the good
entrepreneurs. We saw four different types of signalling which require a funding from
the seller(getting the label, saving the money of the insurance, giving the
commission). So it can be seen as self-financing from the point of view of the seller
who expects to obtain a larger amount than the average in the sale of his high quality
car. Signalling for high quality owners can be done if the bad car owners don’t follow
them. However, we know that the low quality owners will not get the labels, provide
an insurance or contract an agent. So that condition is fulfilled.
Therefore, we can observe equation 2.14 from the angle of the second hand car
market:
The left side of the inequality represents the utility of bad car owner who is selling his
car at a low price P1=θ1. The right side of the inequality is the utility that he’ll get if try to
signalling as the high quality owner.
Simplified equation 2.14
We believed that owners of bad cars wouldn’t use the forms of signaling describe
above (they wouldn’t get the label and they would be denied by the agents).
However, they could take the risk of providing an insurance but the best form that
they will use is probably advertising.
As long as the following condition (equation 2.15) is respected, they will not selffinancing (advertising).
For the good car owners, if there was perfect information they would get a utility level
of:
3
By signaling themselves, they obtain a lower utility:
Their informational cost is representing in equation 2.16:
where p is > 0 and a measure of risk aversion.
We can see it as their lost income which will increase with alpha. In the case of the
book, alpha represents the self-financing of the project. In our case, it’s the price of
the label, the commission, the advertising or the insurance provided. So, the good
car owners have an incentive to get the lowest possible alpha. This is called the
Pareto-dominating signaling equilibrium such that there’s no other combination able
to make one type of owner better off without hurting the other one. It can be done by
solving the alpha when we equalize the utilities of equation 2.15 for the bad car
owner (the point where he’s indifferent between selling directly his car and do a little
of advertising to signal himself).
And thus the possible minimum cost of signaling is:
As a conclusion, we can say that the adverse selection affecting the investorsentrepreneurs activity is also affecting the second hand car market and lead to
inefficiency. The solution found by the entrepreneurs was to give more information to
the market and the investors. Without that solution, in the book, entrepreneurs are
self-financing thus investors lose the ability to benefit from the really good projects.
In the second hand market the good car owners are leaving so that customers lose
the possibility to get really good cars. The customers aren’t really indifferent to the
several forms of signaling realised by the owners of good quality car owners
because they can find the high quality cars. On the other hand, signaling also brings
a better utility for the owners of good quality cars at least. Finally, efficiency is
reached and more cars are sold due to the positive return of the good car owners on
the market.
Bibliography
4
Freixas, X & Rochet, J.C. (2008). Microeconomics of Banking (section 2.3 pp. 2429). Cambridge: MIT Press.
5