# Math Help - Profit maximizing

1. ## Profit maximizing

Assume that a local bank sells two services, checking accounts and ATM card services. Mr. Donethat is willing to pay $8 a month for the bank to service his checking account and$10 a month for unlimited use of his ATM card. Ms. Beenthere is willing to pay only $5 for a checking account, but is willing to pay$15 for unlimited use of her ATM card. To keep this example simple, assume that the bank can provide each of these services at zero marginal cost.

a. If the bank is unable to use tying, what is the profit-maximizing price to charge for a checking account?

b. If the bank is unable to use tying, what is the profit-maximizing price to charge for unlimited use of an ATM card?

c. If the bank is able to use tying to price checking account and ATM service, what is the profitmaximizing price to charge for the "tied" good?

d. How much additional profit does the bank make when it switches to the use of a tying strategy to price checking account and ATM service?

e. How much total surplus is generated from using tying to price the checking account and ATM service? How does that compare to the nontied pricing strategy? Which strategy has the largest deadweight loss?

I think a. would be $8, b would be$15, c would be $18, and d would be$3. Would those be correct if not what is the proper method to use and what about d?

2. ## Profit maximizing

If I understand it correctly:

a. One person would pay $8/month, the other only$5/month. (1) If you charge more than $8/month, you'll get nothing, because no one would pay it. (2) If you charge$8/month, you'll get $8, as only one person would pay that. (3) If you charge more than$5/month up to $8/month, you'll get the amount you charge from only one person - which is worse than the$8/month option in (2). However (4) if you charge $5/month, you'll get$10, since both people would pay it. Finally, (5) anyhting less than $5/month nets you less than$10/month, so it would be sub-optimal as well. So I'm thinking the answer is (4).

b. Can be calculated the same way as a., above.

c. can also be calculated like a., above. However, you would add the fees for the two services together when doing it.

I think d. and e. should fall out from doing the work for a-c above.

- Steve J