We are now shifting focus a little bit, and we'll say a few words about another problem caused by private information. That is known as adverse selection. It is this problem that induced a famous article by George Akerlof that was published in 1970. It was called The Market for Lemons. George Akerlof studied the market failure in some markets with private information. The most simplistic example can be given like this. Supposedly, you sell your car, and you know much more about this car than any potential buyer. And, let's say that you know that your car is okay, and you charge $10,000 for this car. Now, let's say that I am a buyer, and we will imagine that our negotiations are sort of like, yes or no case, so we can not come back to that. This is clearly a simplification, but let's say, let's suppose that, you know the price that is 10 and then, I have to make a certain bid for you. Let's say, I say eight. In this case, you say no because you know that the car is more valuable. Now, I lost the opportunity to buy a nice car. If I said 12, you'll say yes, and then I got a lemon because, actually, a car is worth only 10, and I overpaid. So this is, sort of, on a very regular way. But you can see that this problem exists, and in reality, what people do, they either send a certain signal, let's say, I'm selling because I'm leaving the state. Let's say, you graduated from the business school, and you got a job in the other states, so you move out. So that, for you, it's better to sell it here in the state and then buy another car in the new state than to drive it across the country. Or you can say to potential buyer, let's go together to the independent technician. The technician checks your car with the computer and then tells what the actual price is or tells how much you have to spend in order to really fix all the minor things, minor defects in the car. Now, if this seems to be a funny example because although the used car market is really large, but it doesn't seem to be the case of such a huge damage in financial markets. Well, indeed, diverse selection does produce a lot of damage on capital markets too. Here, we will set up a model for that. That will be very much like the model that we used for moral hazard a couple of episodes before, but it will be sort of different in many important aspects too. Again, the world is as it was before. There was a high state and the low state. Again, they will occur with probability as one half. Now, we cannot change this probability. Now, we'll have two companies. Company 1 and then company 2. Again, all companies have projects that require $10 million to invest, and we will say that companies go to a bank, and they ask for a loan of six. So, 4 million, they have all by themselves. And again, the profile of the company 2 is riskless. So in both cases, it has the expected cash flow of $11 million. And company 1 is riskier. It has the cash flow of 20 here, and 0 in the low case. Now, companies arrive at the bank. An observability here plays the following role: the bank cannot distinguish company 1 and company 2. So the company comes and says, "Well I am," let's say "2". And I cannot check it. The only way for me to check is to do something to offer them a deal that, hopefully, will clarify who they are. Let's see what happens. I'm a bank. I'm a nice risk neutral bank. And, well, clearly, if the companies would finance them with their own money, the MPV here is, you can say, it's one half times 20, which is 10 minus 10, which is zero. Here, it's plus one. So clearly, company 2 is better. And when the company comes to me as a bank, if I could prove that it's number 2, I would give this company an interest free loan. I would say, "I will give you six. You pay back to me six." Now in this case, after having paid six, it will be five. And five I subtract my own, four. This will be of own funds. And I still preserve this MPV of plus one. But the bank cannot do that, and the bank says, "Well, I have to ascribe some probability that is company 1 or company 2." And because the bank does not have any preference, it should describe a probability of one half to them too. So, now, we have a matrix, and here, I ascribe probabilities of one half to these companies showing up in my bank office. Now, the bank says, "Well, if I give six, then what I know is that, for my F, the face value of the slow, it should be greater, equal to six." And let's say it should be less or equal to 11 because if it's higher than 11 then clearly, company 2 does not borrow money because it will not be able to repay this loan in either case. Now, if this is the case, then the bank looks at this matrix and says, "Where do I get back my F?" I get it here. I get it here because F is less or equal, and I get it here. Well, here, unfortunately, I get nothing. So what is the expected cash flow to the bank? The expected cash flow to the bank is equal to three quarters is the probability C, or each cell of this matrix occurs a probability of one quarter, one half here and one half of the case times F. And for the bank to break even, it should be equal to six, the amount you give out. Therefore, F is equal to eight. The bank thinks that it did fine, so kind of covered itself but see what happens now. Supposedly, bank charges F, what is the response of these companies? Let's start with company 2. Company 2 unfortunately says, "Sorry. It's too expensive for me." Why? Because see what happens, if the company does take this loan, it has enough money to pay back in both cases. But how much money is left to the company? It's 11 minus eight, which is three. But the company invested four of its own. So it loses money. The MPV of this company after having you repay the loan is minus one. Again, no magic. Before, it was plus one, but two is the interest of the loan. So it's too high. Now, so we can see that, unfortunately, if I charge that, then company 2 drop out. They say, "Sorry about that, too expensive." What happens to company 1? Company 1 is happy because see what happens to the company 1, this case, we forget altogether. So the company pays out eight. The remainder is 12 with probability of one half is six, minus four. It's MPV jumps from zero to plus two. So the company 1 says, "Great, I'll take the loan." Now, back to the bidding. If the bank made such a loan, these probabilities are no longer relevant because, now, this does not exist anymore. This becomes one because all the companies of type one borrow and, therefore, the expected cash flow to a bank drops from six to four, and we have all this. Well, the bank doesn't like this, and it says, "Well, now I have to recalculate." So, now, for me, expected cash flow to the bank should be equal to how Much? It should be equal to six. But, now, what it is, is it's F with probability of one half F cap. And now, we can see that F cap is 12. But if I charge 12, I am positive that I lend money over to companies like 1, and companies 2 are driven out of the market. And you know that the bank now is lending money to a really risky company with the probability one half. It loses all the money. Well, this is not nice at all. What can the bank do? Unfortunately, the solution like co-insurance here doesn't work. The only way is that we have to somehow restore observability. What can be done? Let's say, the bank tells these companies, "You know what? Please bring me some kind of report that tells that you are company 2 or 1. And let's say this report costs a minor $50,000, which is 0.5 in million. Now, company 2 will be happy to do so because if the company does prove that it's company 2, then the bank gives a loan with face value of six, not eight, and everything is great. However, if it's company 1, it will not do this because if I paid even a minor amount of money and prove that I'm 1, then I get the loan of 12. That sets my NPV to zero, and then I have to also compensate the offer of this report. Now, this situation is called monitoring, and that will be a key issue in this course from now on. And then we see that if only we can restore observability in such a way we can alleviate the problem of adverse selection. Now, in the next episodes, we will analyze adverse selection in capital markets. And we will see of that the damage it produce is really significant and it is worth while being elevated.
