Note (3/18/99, 11:35 am)--An alert student pointed out to me that in the version I first posted, the posted answer to question 2 was incorrect.   I have now fixed this. 


    Adverse Selection Problems

                                  Economics 1


    1.  Residents of the town of Los Carburetors currently own 15
        "lemons" and 30 good used cars. A lemon is worth $100 to its
        current owner and a good car is worth $2,500 to its current
        owner. The only buyer for used cars is a used car dealer who
        happens to be a monopolist.  The dealer can not tell good cars
        from lemons when he buys them, but as soon as he buys them and
        brings them into his shop, he will know. A lemon is worth $600 to
        the used car dealer and a good car is worth $5,000 to the used
        car dealer. In order to be able to buy a car from its current
        owner, the car dealer  must pay at least $1 more than its value
        to its current owner. If the used car dealer offers to buy used
        cars at a price of  $101, how much profits will she make?  

        (a) $7,485 
        (b) $154,455 
        (c) $82,455 
        (d) $1,500 
        (e) $750 

    2.  Suppose that the monopoly used car buyer in Los Carburetors
        decides to offer $2,501 for every used car that she buys. How
        much profits will she make? 

        (a) $154,455 
        (b) $82,455 
        (c) $74,970 
        (d) $46,455
        (e) None of the above. 


    3.      In Sparkplug, Nevada, there are many used car buyers and
        the market is highly competitive. There are currently 40 good
        used cars and 60 lemons in the hands of local residents.  The
        current owners of good used cars will sell their cars if and only
        if they can get at least $2,000 for them and the current owners
        of lemons will sell their used cars if and only if they can get
        at least $0 for them.  The value of a good used car to a used car
        buyer is $4,000 and the value of a lemon to a buyer is $300. 
        Used car buyers can not tell good cars from lemons until after
        they have purchased them.  In the used car market in Sparkplug  

        (a) there is an equilibrium with self-confirming beliefs in which
            everyone believes that all used cars will be sold by their
            original owners and the price of a used car is approximately
            $1,780. 
        (b) the only equilibrium with self-confirming beliefs is one in
            which only the lemons are sold by their original owners and
            the price is $300. 
        (c) the only equilibrium with self-confirming beliefs is one in
            which only the lemons are sold by their original owners and
            the price is $0. 
        (d) there is an equilibrium with self-confirming beliefs in which
            everyone believes that only the good used cars will be sold
            by their original owners and the price of a used car is
            approximately $4,000. 
        (e) there is an equilibrium with self-confirming beliefs in which
            everyone believes that all used cars will be sold by their
            original owner and the price of a used car is approximately
            $800. 


                                  Answer Key
  

                            


         1.   A  
         2.   D  
         3.   B