Glenn Fox, in “Reason And Reality In The Methodologies Of Economics” provides a concise exposition of some general methodological issues that are in the background of similar tensions within economics.

Thank you, DL, for suggesting additional literature.

While we see in a infinite number of plays of this bet it becomes negligible whether or he plays, as the risk is removed and he earns a average winning of what he already had, since a gambler does not play an infinite number of time he must make the decision of whether this bet is the best use of the money-i.e. whether it gets the most good for him of any choice he can make.

You see, even though the next $2000 is worth less to him than the first $2000 is the time savings in earning that extra money makes up for the possible cost of a loss.

In your example, at the jumps in utility, delta_utility/delta_dollars is 2/150, 6/150, 15/150, 9/150, 3/150.

To me, this strongly suggests that the article is incorrect in equating the concepts of “marginal utility” and “derivative of utility functions”

Additionally, it even appears like the concept of “homogenous good” may not apply to your example. In the sense that each unit of money does not have the same set of potential uses. If you take the least common multiple of the prices of the items, i.e. $1400 as your “unit” in this example, then you will get a diminishing utility for each new unit added.

William Smart, An Introduction to the Theory of Value 1910, Chapter III, The Difference Between Utility and Value:

[...] “while utility is the importance which a good possesses as generally capable of ministering to the wellbeing of a subject, Value is the importance which a good possesses as the indispensable condition of the wellbeing of a subject. Or more fully: Value is the importance which a good acquires as the recognised condition of something that makes for the wellbeing of a subject, and would not be obtainable without the good.1 It cannot be too firmly grasped then, that the relation between utility and value is quantitative, and that the same thing may or may not have value according to change of circumstances, or difference in points of view and comparison.”

http://praxeology.net/WS-ITV-E2-3.htm

Friedrich von Wieser, Natural Value 1889, Chapter XI, The Antinomy of Value and the Service of Value:

“The cases where there is a conflict between value and utility – where increase of the one is decrease of the other – occur but seldom.[...] The service of value consists, then, in representing utility wherever both show the same tendency.[...] Value is the form in which utility is calculated”

http://praxeology.net/FW-NV-I-11.htm#NV-I-11.2

If I have $150, I can buy a all-in-one printer/scanner. But I don’t have a computer to use it with. All I can do is use it to make copies, not terribly useful… call the utility 2.

If I have $200, I can buy a camera. I have to go to the print shop to get anything off of it, so it’s not terribly useful… call the utility 1, I’d be better off with the printer/scanner (so $200 still has utility 2).

If I have $350, I can by a (small) laptop. This is actually useful to me, I can buy/sell things online or make websites… call the utility 10.

If I have $400, I can by the laptop and lots of coffee. But because I don’t like coffee, the utility is still 10.

If I have $500, I can by the laptop *and* the printer/scanner. I can print things from the internet, and scan things to post… call the utility 15, the laptop and printer/scanner are complementary.

If I have $550, I can buy the laptop and the camera. So I can take pictures of what people are selling to put on their websites, and can use the camera as a kind-of scanner… call the utility 18, the laptop and camera are also complementary.

If I have $700, I can buy the laptop, printer/scanner, and camera. Say the utility is 21, the camera is a partial substitute for the printer/scanner.

…do I see money as having increasing or decreasing marginal utility?