Menger's Value Scale

This post is part of a series exploring Principles of Economics by Carl Menger.  The following explores content from chapter 3.

Previously in this series: Mengerian Marginalism

A chief insight of Menger's value theory is the recognition that, it is not enough to simply ask the question, "which good is more important?", which is basically asking "which satisfaction of a need that particular goods provide is more important?".  For example, the question implied in the "value paradox", namely "which is more important, bread or diamonds" is basically asking, "which is more important (1) the satisfaction of a man's need for bread or (2) the satisfaction of a man's need for diamonds?"  This question makes no sense stated so simply, because different DEGREES of satisfaction have different levels of importance.  Ignoring questions of general scarcity, and ignoring questions of saving for the future, if an individual man has already engorged himself on bread, obviously the tiniest speck of diamond, used only for ornament for a single day, would be more valuable to him than a whole pantry of bread made available for that same day.  To model this, Menger invented the value scale, which is presented below.

In the above scale, the Roman numerals signify certain satisfactions.  Each descending step below the numeral represents one more "unit" of satisfaction.  The Arabic numerals indicate the ordinal utility ascribed to that particular degree of satisfaction.  For every satisfaction, the ordinal utility diminishes with each marginal increase in satisfaction.  This represents the obvious fact that, the more one consumes of something, the less valuable is the next degree of consumption.  In general, acquiring a 10th slice of bread to eat is less important than acquiring the second one was.  And acquiring the 10th diamond to adorn oneself with is less important than acquiring the second one was.  This is now known as the law of diminishing marginal utility.

Menger presents an example in which column I represents satisfaction for a man's need for food; column V represents satisfaction for his need for tobacco.  The first "degree" of satisfaction of his need for food is ranked at 10 (which is the highest possible rank).  This makes sense, because the first degree of satisfaction for food represents bare sustenance.  The first degree of satisfaction of his need for tobacco is given the rank of 6.  10 is greater than 6, so that first bite of food will be more valued than that first drag of a cigarette.  So will the second degree of food satisfaction, because it is ranked at 9, which is still greater than 6.  It is only at the fifth degree of satisfaction (where the value is ranked at 6) for the man's need for food, when the man will consider another bite of food equal in importance to a first drag of a cigarette.  But once satisfaction for his need for food is attained beyond that degree, he would value a first pinch of tobacco over ANY increase in his consumption of food.

Next in this series: Menger on Multi-Purpose Homogenous Goods