# Fake long-term deposits

Story#1 Say banks have two saving options for you: one-year option or month-by-month flex option.

Say the flex option give a annualized rate of 2 percent, and the one-year option gives 5 percent (which is the current US norm). Both option gives you interests each month.

If you have a fund free to allocation for 11 month only, the only option for you seems to be the flex option.

However, there is a hidden option.

The usual penalization of early-termination of long-term saving is one month (for my bank), or two to three month of interests.

So, the best choice is choose the long-term option, then, terminate it early, pay the penalization, and still get more money!

Story#2 A merchant is selling apple laptop for 2000 usd. Some hidden coupon can save you 300usd; however, it might cost you four hours to search for hidden coupon, acquire the information, get verified, and get the actual coupon. If you make more than 75 dollars per hour, you won't care about spending time to get the coupon. That is, your hidden type is indirectly revealed by the merchant.

NOTE: the merchant cannot give the coupon for free, otherwise the revelation fails!

How to model the economics behind?

I am thinking about a monopolist analyst model using price-discrimination to exploit different types of saving account customers:

Price of good: $$p$$

Continuum of consumers: $$\theta,\psi\in [0,1]\times [0,1]$$. Utility of good for each type is $$u\theta$$. Wage rate of each type is $$r\psi$$. Disutility of spending $$p$$ is: $$p/(r\psi)$$; this is because, for individual who makes a lot, the marginal utility of money is lower.

Suppose: $$ur>p$$

Classic economic problem, the consumer will purchase the good if $$u\theta-p/(r\psi)>0$$ which is $$\theta\psi>p/(ru)$$.

The income of merchant can be therefore calculated.

Non-classic problem, with the hidden option added,

Cost of time for searching: $$t$$. The merchant set the $$t$$.

The benefit of hidden option: $$b$$. The merchant set the $$b$$.

the consumer will use the hidden option if $$b-tr\psi>0$$.

Some of low $$\psi$$ type who wouldn't choose to purchase the good will now use the option and purchase the good.

I think that it is always possible to set $$b$$ and $$t$$ such that the income of the company will increase.

I'd like to learn if there is already many literature covering similar topics.