therealchips *** Veteran
Joined: 04 Jan 2003 Posts: 174 Location: Henderson, Nevada, USA

Posted: Thu Oct 30, 2003 9:14 pm Post subject: Didn't Daniel Bernoulli get there first, in 1738? 


Quote: 
Consume less to enjoy life more. Living with this new state of mind works because of what economists call the Law of Diminishing Marginal Utility. I call it the Coin Toss Law. 
Who published first, Terhorst or hocus? I haven't followed the discussion so I don't know who might have plagiarized whom. I find TMF too gloomy to visit  a pale, grim, distorted shadow of what it once was, rather like a ghost for scaring folks at Halloween.
Terhorst's description of the Law of Diminishing Marginal Utility seems erroneous to me. Simply stated, the law of marginal utility asserts that the value of the next dollar you add to your wealth depends on the how much wealth you have already and declines the more you have. Terhorst's Coin Toss bears no useful resemblance to Bernoulli's Paradox on a cointossing game. Terhorst seems to have oversimplified Bernoulli to the point of missing its significance.
Pardon me for yet one more quotation of the following material, but it isn't clear to me that either hocus or Terhorst got there ahead of Daniel Bernoulli in 1738:
Quote: 
The expected utility hypothesis stems from Daniel Bernoulli's (1738) solution to the famous St. Petersburg Paradox posed in 1713 by his cousin Nicholas Bernoulli (it is common to note that Gabriel Cramer, another Swiss mathematician, also provided effectively the same solution ten years before Bernoulli). The Paradox challenges the old idea that people value random ventures according to its expected return. The Paradox posed the following situation: a fair coin will be tossed until a head appears; if the first head appears on the nth toss, then the payoff is 2n ducats. How much should one pay to play this game? The paradox, of course, is that the expected return is infinite. . .Yet while the expected payoff is infinite, one would not suppose, at least intuitively, that realworld people would be willing to pay an infinite amount of money to play this!
Daniel Bernoulli's solution involved two ideas that have since revolutionized economics: firstly, that people's utility from wealth, u(w), is not linearly related to wealth (w) but rather increases at a decreasing rate  the famous idea of diminishing marginal utility, (Chips: here it gives some expressions using the notation of the calculus with the intuitive meaning that each additional dollar contributes something to the owner's utility, but that the increase is less for each subsequent dollar) ; (ii) that a person's valuation of a risky venture is not the expected return of that venture, but rather the expected utility from that venture. 
_________________ He who has lived obscurely and quietly has lived well. [Latin: Bene qui latuit, bene vixit.]
Chips

