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Nicolaus Bernoulli described the St. Petersburg paradox (involving infinite expected values) in 1713, prompting two Swiss mathematicians to develop expected utility theory as a solution. Bernoulli's paper was the first formalization of marginal utility, which has broad application in economics in addition to expected utility theory. He used ...
The classical resolution of the paradox involved the explicit introduction of a utility function, an expected utility hypothesis, and the presumption of diminishing marginal utility of money. According to Daniel Bernoulli: The determination of the value of an item must not be based on the price, but rather on the utility it yields ...
In expected utility theory, a lottery is a discrete distribution of probability on a set of states of nature.The elements of a lottery correspond to the probabilities that each of the states of nature will occur, (e.g. Rain: 0.70, No Rain: 0.30). [1]
A single-attribute utility function maps the amount of money a person has (or gains), to a number representing the subjective satisfaction he derives from it. The motivation to define a utility function comes from the St. Petersburg paradox: the observation that people are not willing to pay much for a lottery, even if its expected monetary gain is infinite.
Bernoulli normalizes the expected value by assuming that p i are the probabilities of all the disjoint outcomes of the value, hence implying that p 0 + p 1 + ... + p n = 1. Another key theory developed in this part is the probability of achieving at least a certain number of successes from a number of binary events, today named Bernoulli trials ...
Bernoulli's imaginary logarithmic utility function and Gabriel Cramer's U = W 1/2 function were conceived at the time not for a theory of demand but to solve the St. Petersburg's game. Bernoulli assumed that "a poor man generally obtains more utility than a rich man from an equal gain" [ 3 ] an approach that is more profound than the simple ...
Cardinal utility has been implicitly assumed in decision theory ever since Daniel Bernoulli's analysis of the St. Petersburg paradox. Rigorous mathematical theories of cardinal utility (with application to risky decision making) were developed by Frank P. Ramsey, Bruno de Finetti, von Neumann and Morgenstern, and Leonard Savage. However, in ...
Daniel Bernoulli's contributions: Bernoulli's principle is of critical use in aerodynamics. [20] Expected utility theory; He laid the basis for the kinetic theory of gases, and applied the idea to explain Boyle's law (Hydrodynamica 1738). [21] He worked with Euler on elasticity and the development of the Euler–Bernoulli beam equation. [22]