FazBrowse Wikipedia Viewer | Main Page |
Search Wikipedia:
|
Viewing: https://en.wikipedia.org/wiki/Utility_function

Utility

Contents
Expected utility
    Von Neumann–Morgenstern
Indirect utility
    Constrained utility optimisation
Discussion and criticism
Measuring utility functions
See also
References

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.

The relationship between these two kinds of utility functions has been a source of controversy among both economists and ethicists, with most maintaining that the two are distinct but generally related.

x is the number of apples and y=16 chocolates; alternative B has x,y into the utility function yields u:X→ℝ ranks each possible outcome in the consumption set. If the consumer strictly prefers x to y or is indifferent between them, then x∈ℝ+L is a vector containing the amounts of each commodity. For the example, there are two commodities: apples and oranges. If we say apples are the first commodity, and oranges the second, then the consumption set is

Instead of giving actual numbers over different bundles, ordinal utilities are only the rankings of utilities received from different bundles of goods or services. For example, ordinal utility could tell that having two ice creams provide a greater utility to individuals in comparison to one ice cream but could not tell exactly how much extra utility received by the individual. Ordinal utility, it does not require individuals to specify how much extra utility they received from the preferred bundle of goods or services in comparison to other bundles. They are only needed to tell which bundles they prefer.

When ordinal utilities are used, differences in utils (values assumed by the utility function) are treated as ethically or behaviorally meaningless: the utility index encodes a full behavioral ordering between members of a choice set, but tells nothing about the related strength of preferences. For the above example, it would only be possible to say that juice is preferred to tea to water. Thus, ordinal utility utilizes comparisons, such as "preferred to", "no more", "less than", etc.

If a function u(x) is cardinal, it is not equivalent to

Economists distinguish between total utility and marginal utility. Total utility is the utility of an alternative, an entire consumption bundle or situation in life. The rate of change of utility from changing the quantity of one good consumed is termed the marginal utility of that good. Marginal utility therefore measures the slope of the utility function with respect to the changes of one good. Marginal utility usually decreases with consumption of the good, the idea of "diminishing marginal utility". In calculus notation, the marginal utility of good X is MRS=MU1MU2

Expected utility

edit
EU=Pr⁡(z)⋅u(Value(z))+Pr⁡(y)⋅u(Value(y))

Von Neumann–Morgenstern

edit
L=pA+(1−p)B

More generally, for a lottery with many possible options:

M, either L,M,N, if L⪯N.
  • convexity/continuity (Archimedean property): If pL+(1−p)N is equally desirable as L⪯M if and only if N is no more preferable than the lottery formed by the same probabilistic combination of L⪯M.

    • Axioms 3 and 4 enable us to decide about the relative utilities of two assets or lotteries.

    In more formal language: A von Neumann–Morgenstern utility function is a function from choices to the real numbers:

    L1 if and only if, for the utility function characterizing that agent, the expected utility of L1⪯L2 iff u(L1)≤u(L2).

    Of all the axioms, independence is the most often discarded. A variety of generalized expected utility theories have arisen, most of which omit or relax the independence axiom.

    Indirect utility

    edit
    p2 are prices of the two goods, slope=−P(x)P(y)

    Constrained utility optimisation

    edit

    Rational consumers wish to maximise their utility. However, as they have budget constraints, a change of price would affect the quantity of demand. There are two factors could explain this situation:

    • Purchasing power. Individuals obtain greater purchasing power when the price of a good decreases. The reduction of the price allows individuals to increase their savings so they could afford to buy other products.
    • Substitution effect. If the price of good A decreases, then the good becomes relatively cheaper with respect to its substitutes. Thus, individuals would consume more of good A as the utility would increase by doing so.

    Discussion and criticism

    edit

    Cambridge economist Joan Robinson famously criticized utility for being a circular concept: "Utility is the quality in commodities that makes individuals want to buy them, and the fact that individuals want to buy commodities shows that they have utility". Robinson also stated that because the theory assumes that preferences are fixed this means that utility is not a testable assumption. This is so because if we observe changes of peoples' behavior in relation to a change in prices or a change in budget constraint we can never be sure to what extent the change in behavior was due to the change of price or budget constraint and how much was due to a change of preference..

    Other questions of what arguments ought to be included in a utility function are difficult to answer, yet seem necessary to understanding utility. Whether people gain utility from coherence of wants, beliefs or a sense of duty is important to understanding their behavior in the utility organon. Likewise, choosing between alternatives is itself a process of determining what to consider as alternatives, a question of choice within uncertainty.

    An evolutionary psychology theory is that utility may be better considered as due to preferences that maximized evolutionary fitness in the ancestral environment but not necessarily in the current one.

    Measuring utility functions

    edit

    There are many empirical works trying to estimate the form of utility functions of agents with respect to money.

    See also

    edit

    References

    edit
      "nonsatiation". Oxford Reference. Retrieved 18 July 2024.
    1. ↑ Lin, Chung-Cheng; Peng, Shi-Shu (2019). "The role of diminishing marginal utility in the ordinal and cardinal utility theories". Australian Economic Papers. 58 (3): 233–246. doi:10.1111/1467-8454.12151. S2CID 159308055 – via Wiley Online Library.
    2. ↑ Castro, Luiz Carvalho; Araujo, Antônio Souza (2019). "Marginal Utility & its Diminishing Methods" (PDF). International Journal of Tax Economics and Management: 36–47. eISSN 2618-1118.
    3. ↑ Robinson, Joan (1962). Economic Philosophy. Harmondsworth, Middle-sex, UK: Penguin Books.
    4. ↑ Pilkington, Philip (27 February 2014). "utility Hans Albert Expands Robinson's Critique of Marginal Utility Theory to the Law of Demand". Fixing the Economists. Archived from the original on 19 July 2015.
    5. ↑ Capra, C. Monica; Rubin, Paul H. (2011). "The Evolutionary Psychology of Economics". Applied Evolutionary Psychology. Oxford University Press. doi:10.1093/acprof:oso/9780199586073.003.0002. ISBN 9780191731358.
    6. ↑ Fishburn, Peter C. (1970). Utility Theory for Decision Making. Huntington, NY: Robert E. Krieger. ISBN 0-88275-736-9.
    7. Gilboa, Itzhak (2009). Theory of Decision under Uncertainty. Cambridge University Press. ISBN 978-0-521-74123-1.
    8. Neumann, John von & Morgenstern, Oskar (1944). Theory of Games and Economic Behavior. Princeton University Press.
    9. Category
    Economics
    Theoretical
    View original on Wikipedia | Back | FazBrowse Home