How can a product have more than one price?

If the transaction is not consummated entirely at one time but extends into the future, there can be a price to be paid now and one that will be paid later.

That's the case with mortgages. The price paid now consists of lender fees including "points," while the price paid later is the interest rate.

This is what makes mortgages more difficult to shop for than, say, a new sofa.

To illustrate how dual prices complicate shopping, here are two quotes that apply to a 30-year fixed-rate mortgage:

In quote A, the interest rate is 4 percent and the lender fee is $4,000.

In quote B, the interest rate is 4.25 percent and the lender fee is $2,000.

Which of them is the better deal? The correct answer is that it depends on the borrower.

If the borrower is income-constrained, meaning that she is grappling with a high ratio of monthly housing expenses to income, she will prefer quote A because it provides a lower monthly mortgage payment.

If the borrower is cash-constrained, meaning that she is grappling with a shortfall of money needed for down payment and other closing expenses, she will prefer quote B because it has a smaller cash requirement.

If the borrower is neither income-constrained nor cash-constrained, she should prefer the quote that will result in the lower cost during the period that is her best guess of how long she will have the loan. Borrowers with short time horizons should prefer B, while those with long horizons should opt for A.

This is a challenging decision. Few borrowers have more than a vague idea of how long they will have a mortgage, calculating the cost accurately is beyond most of them, and lenders don't help. At my website, www.mtgprofessor.com, a borrower can find out the total cost of a mortgage over a period specified by the borrower.

When we turn to reverse mortgages, the challenge is even greater because of the greater diversity in borrower objectives.

In the forward-mortgage market, borrowers use the loans to buy houses and want to minimize the cost. That's it.

In the reverse market, borrowers use mortgages to meet a variety of needs, each of which may involve one or more different objectives.

For example, the borrower looking to supplement her income might select the reverse mortgage that provides the largest tenure payment - the monthly payment that lasts until she dies or moves out of the house permanently.

A borrower looking to acquire a reserve for contingencies might shop for the largest initial credit line, or perhaps the line after some period of nonuse during which the line grows.

In both cases, the borrower interested in minimizing the loss of equity by their estate might shop for the reverse mortgage that generates the lowest loan balance after some period.

Perhaps the best head-to-head comparison of a forward and a reverse mortgage is the case where both are used to purchase a house.

Where the forward purchaser seeks to minimize loan costs, the reverse purchaser might have any of the following objectives:

Obtain the largest possible amount of cash at closing with a fixed-rate reverse mortgage.

Obtain the largest possible amount of cash at closing and after 12 months with an adjustable-rate reverse mortgage.

Incur the smallest loan balance after a specified number of years with a fixed-rate reverse mortgage.

Incur the smallest loan balance after a special number of years with an adjustable-rate reverse mortgage.

A senior dealing with a single reverse-mortgage lender might be offered different combinations of interest rate and origination fee from which to select, but she probably will not be offered any performance measures related to her objectives. Further, selecting from among the offerings of one lender is not shopping.

The difficulties in shopping effectively for reverse mortgages provide a very strong case for multilender networks. Such networks can offer shoppers more options from which to choose, and the performance measures that shoppers need to guide their selection.

Jack Guttentag is professor emeritus of finance at the Wharton School of the University of Pennsylvania. http://www.mtgprofessor.com.