$1.$ Consumer myopia and add$-$on pricing. Consider a market with $10$ banks that can all offer the

same base product, a basic checking account, to consumers. The cost per account is c $=3$ for each

bank. Consumers have a maximum valuation of $8$ for having a bank account. In case a consumer has a

negative balance, he has to pay an overdraft fee, f$,$ which can be set freely by each bank, but is limited

to a maximum fee of f $=6.$ Each consumer will have exactly one instance in which he is short of money

$($This means that each consumer only goes in overdraft trouble exactly and only once, even if he has

more than one bank account$).$ Preventing a negative balance would cost each consumer an effort cost of

$1$ in this case.

A fraction $=\mathrm{.}7$ of consumers is naive and does not know that there are overdraft fees for banks. The

rest of the consumers is sophisticated and knows about the overdraft fees. The timing of the game is

the following: Firms first set their checking account contracts $($base product price p and add$-$on price f

simultaneously. Consumers then make their choice of bank, where naive consumers only pay attention to

the base product price, while sophisticated consumers realize also the amount of add$-$on fee. Consumers

make a contract choice to maximize their perceived surplus. If there are multiple surplus$-$maximizing

alternatives, consumers choose their contract randomly among them. After having signed up with a

bank, when temporarily being short of money, consumers make a decision whether or not to avoid

having a negative balance.

$($a$)$ Assume first that firms cannot advertise the add$-$on fees of other firms to naive consumers, and that

each consumer can only own a single bank account. What contracts will firms set in equilibrium?

What will be the profits of firms and the surplus of the different consumer types?

$($b$)$ How do the results change when consumers can choose to own multiple bank accounts $($assume for

simplicity that each consumer could open an unlimited amount of accounts at each bank$)?$

$($c$)$ Assume one bank has the option to costlessly advertise a $0-$overdraft$$ fee policy that informs also

naive consumers about the add$-$on costs of all firms, while itself sets f $=0.$ Does the bank have an

incentive to do such an overdraft policy?

$($d$)$ Assume now that each bank can choose to costlessly inform naive consumers about all overdraft

fees, while also being able to choose its own overdraft fee $($it does not have to be $0).$ What will be

an equilibrium outcome?

$($e$)$ If naive consumers do not respond to advertising the add$-$on fees $($or forget about these fees$),$ what

would be a welfare$-$maximizing regulation $($assuming that no bureaucracy costs due to regulation$)?$