## Multiple Choice

Question 1

An online stock trading firm has a fixed cost of \$1020 and a variable cost of \$14x, where x is the number of clients that subscribe to the firm's trading service.  If the firm has 170 clients, what is the lowest price it can charge each client without pushing total revenue below cost?

Question 2

Say that a buyer of bonds values good bonds at \$400 and values bad bonds at \$250.  Sellers of both good and bad bonds value them at \$300.  If the fraction of good sellers is 70%, then the maximum price an uninformed buyer will pay is ____ and this ___ high enough to sustain trade in both types of bonds.

Question 3

A loan buyer in a secondary market believes that x% of the loans are high quality, and the rest are low quality.  The buyer values high quality loans at \$100,000 and low quality at \$75,000.  Banks selling loans value high quality loans at \$82,500 and value low quality at \$55,500.  If the buyer cannot observe the bond's type, then the maximum price the buyer will pay is equal to the seller's value of high quality loans when x is

Question 4

A financial intermediary is hired to make a transaction "go forward".  The intermediary can do a good job that costs the intermediary \$400, or do a bad job that costs zero.  If the intermediary does a good job the transaction will go forward.  If the intermediary does a bad job the transaction will go forward with probability 0.75, and will fail with probability 0.25.  The customer can't observe the intermediary's job choice and simply pays the intermediary \$X if the transaction goes forward and pays \$0 if it fails.  What is the minimum X the customer must pay in order to persuade the intermediary to do a good job?

Question 5

When a bank makes its loans, if it screens its borrowers it will collect repayment revenue of \$40,000 per loan, but if it doesn't screen its borrowers then it will collect \$40,000 per loan with probability 0.8 and collect \$0 with probability 0.2.  The cost of screening is \$2,000 per loan.  In this case, the expected payoff for the bank from screening is ____ and the expected payoff from not screening is ____ .

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