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In economics, a utility representation theorem shows that, under certain conditions, a preference ordering can be represented by a real-valued utility function, such that option A is preferred to option B if and only if the utility of A is larger than that of B.
The conditions are increasingly general, so for example, condition 1 implies 2, which implies 3, which implies 4. 1. The set of equivalence classes of the relation ∼ {\displaystyle \sim } (defined by: x ∼ y {\displaystyle x\sim y} iff x ⪯ y {\displaystyle x\preceq y} and x ⪰ y {\displaystyle x\succeq y} ) are a countable set .
When faced with several alternatives, the person will choose the alternative with the highest utility. The utility function is not visible; however, by observing the choices made by the person, we can "reverse-engineer" his utility function. This is the goal of revealed preference theory. [citation needed] In practice, however, people are not ...
In economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it is only meaningful to ask which option is better than the other, but it is meaningless to ask how much better it is or how good it is.
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. In a normative context, utility refers to a goal or objective that we wish to maximize, i.e., an objective function.
This is the expected utility hypothesis. As stated, the hypothesis may appear to be a bold claim. The aim of the expected utility theorem is to provide "modest conditions" (i.e. axioms) describing when the expected utility hypothesis holds, which can be evaluated directly and intuitively:
Marshall was the second-generation marginalist whose work on marginal utility came most to inform the mainstream of neoclassical economics, especially by way of his Principles of Economics, the first volume of which was published in 1890. Marshall constructed the demand curve with the aid of assumptions that utility was quantified, and that the ...
In economics, a cardinal utility expresses not only which of two outcomes is preferred, but also the intensity of preferences, i.e. how much better or worse one outcome is compared to another. [ 1 ] In consumer choice theory , economists originally attempted to replace cardinal utility with the apparently weaker concept of ordinal utility .