Charlie Alfred’s Weblog

Utility Curves

In my earlier entry titled “Significance of Context” I identified five factors that would make a group of people have very similar views about value: 

o  They play the same (or very similar) role in the system.

o  They want the same small set of key benefits

The amount of value they perceive from different levels of these benefits is similar.

o  They have the same view when ranking these key benefits in order of importance

o  They are subject to similar environmental factors (e.g. constraints and uncertainties)

Let’s take a closer look at the third factor.

Economists have used the concepts of Ordinal Utility and Cardinal Utility as a means for expressing consumer preference.

Ordinal utility tries to eliminate the notion that utility is quantifiable by asking people to rank preferences.  For example, a hungry person might be asked to rank the following lunch items: Quarter Pounder, Whopper, slice of sausage pizza, tossed salad with chicken, or a ham and cheese sandwich.  Some measure of relative preference can be gotten by grouping the items and requesting choices.  For example, over the next 3 days, would you prefer a Quarter Pounder, Whopper, and salad, or 2 ham and cheese sandwiches and a slice of sausage pizza?  Combinations which leave the person indifferent (or confused?) identify equivalent value points.

Cardinal Utility seems to map a measurable quantity (such as a level of some benefit) to an abstract measure of its value, called a util.  This approach had fallen out of favor with economists for many years, until it was revived by von Neumann and Morgenstern in their analysis of behavior under uncertainty.  We will use the notion of Cardinal Utility in this post because the notion that value is a subjective perception is a key underlying concept for value modeling.

In 2003, the Software Engineering Institute at Carnegie Mellon University, published a method for software architecture analysis called CBAM (Cost Benefit Analysis Method).  This method uses a technique which is familiar to anyone who had their high school or college exam scores “graded on the curve”.  In particular, respondents are asked to pick the level of measurable benefit which corresponds to five levels of value:

F    Unacceptable      Benefits at or below this level are equally poor (as bad as it gets)

D    Adequate             Benefits at this level provide value that is barely passable

C    Satisfactory         Benefits at this level provide the expected level of value

B    Desirable             Benefits at this level provide more value than expected

A    Ideal                     Benefits at or over this level reach saturation (as good as it gets)

As a result, utility curves for fuel economy from a car might look something like this:

This artificial example shows three utility curves: one linear, one shaped like an “S”, and the third parabolic.  All three curves agree that 10 MPG is undesirable, and 50 MPG is ideal (this example must be artificial, since in the real world you’d need a pretty large group of people to find 3 reaching this much of an agreement).

What makes this example interesting is what happens between the undesirable and ideal levels.  The parabolic curve reaches the “acceptable” level with only 12 MPG fuel economy, while the s-shaped curve requires 25 MPG to reach this level.  The high frequency of “parabolic curves” in our society might explain why only one out of 5 vehicles on the road today seems to be a Hummer, Esplanade, Navigator or other tank-class SUV.

Acquiring meaningful utility values can be problematic.  Since the values cannot be directly measured, they are saturated with interpretation.  This makes it difficult to compare values from one individual or group to another.  It’s very difficult to know whether “acceptable” or “satisfactory” for one person means the same as for another.

Even so, the curves do have some usefulness.  In particular, they provide a sense of how the slope of the utility curve changes.  In the above example, the parabolic utility curve requires progressively more MPG for every increase in benefit level.  Economists refer to this concept as marginal utility (i.e. the rate at which utility changes w.r.t. benefits).

Let me illustrate with an example.  Imagine that you were blindfolded and driven in a car to a remote location.  Then you were taken for a 30 minute walk.  At any time during this walk, you might have a difficult time answering the question, “What is our present altitude in feet about sea level?”  You might estimate, but your guess could be off by hundreds of feet.  On the other hand, you might be able to provide a pretty accuate assessment of the slope of the land you just walked – mild uphill, mild downhill, steep uphill, flat, etc.  In general, people seem to be more attuned to changes, than to absolutes.

The reason that marginal utility is so important is that it highlights the places where tradeoffs are desirable (or undesirable).  When the marginal utility curve is steepest, it takes a relatively small change in benefit levels to achieve a relatively large change in value.  By contrast, when the marginal utility curve is flattest, it takes a relatively large change in benefit levels to achieve a relatively small change in value.  In other words,

Marginal Utility             Sacrifice Other to get This    Sacrifice This to Get Other
Steep                                  Generally a Good Idea          Generally a Bad Idea
Flat                                     Generally a Bad Idea            Generally a Good Idea







The investment community has a mantra known as “Buy Low, Sell High”.  For value models, the equivalent is “Sacrifice Flat to Gain Steep.”  Trade what I’m ambivalent about in order to gain what I desire.  While this explains the seller side of yard sales and flea markets, I’m not sure I can explain how it relates to the buyer side.


  1. Thanks for the explanation of utility curves. I was trying to explain it to a friend without a finance/ economic background and it was difficult. Yours was the best explanation I found on the internet.

    Comment by liz — September 15, 2010 @ 12:37 am

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