performance as utility function / price? I am trying to define a 'model' for the perceived performance of a product based on this definition:


  Presumably, customers take both price and quality
  into account as they form an overall evaluation about
  a product's performance. To avoid a confounding of
  the two, each was measured in light of the other—
  perceived performance is thus measured by price (given
  quality) and quality (given price). (Fornell, 1992)


I thought that a utility function might be a good way to describe the quality of a product, so ended up with:

$$P(x) = \frac{u(x)}{c}$$

Where the perceived performance P of a product x is equal to its utility function u(x) divided by its total price c.
Is this more or less ok? Or should I include the price variable in a different way, such as e.g.:

$$ P(x) = u(x,c)$$

...or even simpler

$$ P(x) = u(x)$$

As cost might be assumed to be part of the trade-offs of the function? Any ideas or help with the notation or function would be really appreciated.
There is a long tradition in economics (some 50 years worth of research) called "Hedonic Price Analysis".

It consists of "allocating" (through regression estimation) the price of a product to its various qualitative features ("characteristics") quantified, that presumably are valued by the consumers, i.e. those that are utility-enhancing. These characteristics are either quantified (e.g. Computer RAM measured in GB), or "1/0" dummy variables (the characteristic exists/it doesn't). Note that in the related empirical studies actual transacted prices are used, i.e. prices that the consumers have accepted to pay.

The estimated coefficients from the regression provide the monetized "willingness to pay" per unit of characteristic (or per existence of it). Once you have them, you can extrapolate outside the sample to find the total "willingness to pay" for a product $i$, say $W_i$, by multiplying its characteristics by the marginal willingness to pay for each characteristic.

In essence, in this way you transformed something that is considered ordinal and un-measurable (utility) into a monetized equivalent (using the "revealed preference" approach, since you used prices that the consumers actually paid).

If you then compare this magnitude to some advertised price of this product, $P_{ai}$, then a ratio like

$$\text{Prf}_i = \frac {W_i}{P_{ai}}$$

could be your "Performance" index. If for example it is higher than unity, it means that the product "is a good bargain" for the consumers, because the monetary value of the utility they will get out of it, is higher than the money they will have to pay to acquire it.

NOTE: Hedonic Price Analysis is not just something that academic economists do. In many nations, official Price Indexes are for several years now adjusted for quality, using the methods developed by economists throughout the years.