# singalling and the market for lemnos Watch

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1. Any ideas how to approach this problem?

There are two types of used cars: good (1) and bad (2). There are N1 good
cars and N2 bad cars for sale, The number of buyers is large and they value good cars at v1 and bad cars at v2. The valuations of sellers are c1 and c2 respectively. The following inequalities hold: c2<v2<c1<v1. Sellers can buy a signal, which does not change the value of the car, for s1 if they have a bad car, and for s2 if they have a good car (assume s1<s2).

i) Under what condition would there be no good cars traded in the absence of a signal?
ii) Under what conditions would there exist an equilibrium where sellers of good cars buy the signal and sellers of bad cars do not?
iii) Under what conditions would there exist an equilibrium where sellers of both good and bad cars buy the signal? Would this equilibrium be efficient (i.e. maximising social welfare)?

I know this is an asymmetric information problem and I suppose the results for ii) and iii) are related to separating and pooling equilibriums. I also know how to solve the standard lemons problems using numerical examples but I'm quite confused how to do it using letters only... Any tips or ideas how to do or approach this exercise???
Thanks.
2. draw a line representing the 4 values c1,c2,v1, and v2. Think about market price (good cars, bad cars, universal price?) and how signalling affects the value to sellers.
3. for i) i've calculated the expected value for the buyer in the case of incomplete information.

q*v2+(1-q)*v1=p where q is prob. that a car is a bad one

so if p is lower than c1 (value of a good car for a buyer) then only the owners of lemons want to sell. Knowing that the buyers are ready to pay only v2 and in the equilibirum bad cars will be traded at price between c2 and v2 and the lemons would push the good cars out of the market.

I think this reasoning is correct...

I still have problems with this signals. Do they lower the value of the car for a seller?
4. (Original post by marot)

so if p is lower than c1 (value of a good car for a buyer) then only the owners of lemons want to sell.
That is exactly wrong.

c1 is the value, not the cost, to the seller. Hence if p < c1 he does NOT want to sell.

I still have problems with this signals. Do they lower the value of the car for a seller?
Well I would not say that they lower the value as such, c1 stays constant, but instead you are interested in (c1 - s1) instead of c1 only.

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Updated: December 11, 2010
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