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In economics and consumer theory, a linear utility function is a function of the form: u ( x 1 , x 2 , … , x m ) = w 1 x 1 + w 2 x 2 + … w m x m {\displaystyle
Linear_utility
Concept in economics and decision theory
two bundles of goods. A cardinal utility function can be transformed to another utility function by a positive linear transformation (multiplying by a
Utility
Function linear in one argument, used in economics and consumer theory
quasilinear utility functions are linear in one argument, generally the numeraire. Quasilinear preferences can be represented by the utility function u
Quasilinear_utility
Concept in economics
individuals have linear utility functions, risk-seeking individuals have convex utility functions, and risk-averse individuals have concave utility functions
Expected_utility_hypothesis
Economical computational problem
piecewise linear function of xj. This assumption is common in computer science, as it allows a finite representation of the utility functions. Utilities that
Market equilibrium computation
Market_equilibrium_computation
Problem of allocation of money by consumers in order to most benefit themselves
In microeconomic theory, the utility maximization problem formalizes how a consumer allocates limited resources across different goods and services. The
Utility_maximization_problem
Concept in economics
indicated by the curve will provide the consumer with equal levels of utility, and the consumer has no preference for one combination or bundle of goods
Indifference_curve
Preference ranking
economics, an ordinal utility function is a function representing the preferences of an agent on an ordinal scale. Ordinal utility theory claims that it
Ordinal_utility
Utility assessment, also called utility measurement, is a process by which the utility function of individuals or groups can be estimated. There are many
Utility_assessment
Situation where total gains match total losses
most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash equilibrium. In contrast, positive-sum
Zero-sum_game
Economic equilibrium concept
x. 4. For existence and non-existence examples involving linear utilities, see Linear utility#Examples. When there are indivisible items in the economy
Competitive_equilibrium
French mathematician and economist
methods in decision theory such as linear utility theory for belief functions, bridging the gap between expected utility and the maximin rule by using subjective
Jean-Yves_Jaffray
Bmax are the maximum utility and budget, respectively. Orlin gave an improved algorithm for a Fisher market model with linear utilities, running in time O
Fisher_market
In contrast with ordinal utility, in economics
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
Cardinal_utility
earliness and tardiness to be non-linear—e.g., increasing tardiness may result in non-linearly decreasing utility, such as when detecting a threat. Thus
Time-utility_function
that it has a linear rate of convergence for agents with "strict" CES utilities (excluding the linear and Leontief utilities). When linear and Leontief
Proportional response dynamics
Proportional_response_dynamics
Vickrey showed that if preferences are restricted to the case of quasi-linear utility functions then the mechanism dominant strategy is dominant-strategy
Implementation_theory
shows that the utility function becomes linear in wealth; and for the limiting case as γ {\displaystyle \gamma } goes to 0, the utility function becomes
Hyperbolic absolute risk aversion
Hyperbolic_absolute_risk_aversion
the generalised Cobb–Douglas function. The Stone–Geary utility function gives rise to the Linear Expenditure System. In case of ∑ i β i = 1 {\displaystyle
Stone–Geary_utility_function
Characteristic in consumer theory
say, the Engel curve for each good is linear. Furthermore, the indirect utility function can be written as a linear function of wealth w {\displaystyle
Homothetic_preferences
Theory that attempts to blend economics and ergodic theory
non-linear utility function allows the encoding of behavioral patterns not represented in expected-value maximization. Specifically, expected-utility maximizing
Ergodicity_economics
Function in decision theory
u(99,x_{2})} - a cardinal utility on bananas when apples are at their maximum (the eastern boundary of the domain). Using linear transformations, scale the
Multi-attribute_utility
Finding linear approximation of function at given point
mathematics, linearization (British English: linearisation) is finding the linear approximation to a function at a given point. The linear approximation
Linearization
concave utility functions, where all resources are goods (the utilities are positive): When the utilities are SPLC (Separable Piecewise-Linear Concave)
Arrow–Debreu_exchange_market
with quasilinear utilities does not depend on the income at all (in this quasilinear case, the demand for the linear good is linear in income): x i (
Gorman_polar_form
Probability measure
the utility function of the payoff. The risk-neutral measure would be the measure corresponding to an expectation of the payoff with a linear utility. An
Risk-neutral_measure
Topics referred to by the same term
that is both quasiconvex and quasiconcave Quasilinear utility, an economic utility function linear in one argument In complexity theory and mathematics
Quasilinear
Type of particle accelerator
A linear particle accelerator (often shortened to linac) is a type of particle accelerator that accelerates charged subatomic particles or ions to a high
Linear_particle_accelerator
Experimental design framework
optimal experiment design depends on the particular utility criterion chosen. If the model is linear, the prior probability density function (PDF) is homogeneous
Bayesian_experimental_design
provably envy free and Pareto efficient. Moreover, when the agents have linear utility functions, the CEEI allocation can be computed efficiently. Unfortunately
Approximate Competitive Equilibrium from Equal Incomes
Approximate_Competitive_Equilibrium_from_Equal_Incomes
Theorem in mathematics and economics
differentiable. (One example is the class of trading problems with linear utility described in chapter 6.5 of Myerson (1991).) Note that the integral
Envelope_theorem
Algebraic structure in linear algebra
In mathematics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled")
Vector_space
Concept in economics
substitution (CES) is a common specification of many production functions and utility functions in neoclassical economics. CES holds that the ability to substitute
Constant elasticity of substitution
Constant_elasticity_of_substitution
Bicycling as transportation
Utility cycling encompasses any cycling done simply as a means of transport rather than as a sport or leisure activity. It is the original and most common
Utility_cycling
Set of vectors used to define coordinates
can be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components
Basis_(linear_algebra)
Problem of fair division
more general than quasilinear, in which the utility of each agent from each room can be any piecewise linear function of the rent. This setting generalizes
Rental_harmony
Concept in economics
isoelastic function for utility, also known as the isoelastic utility function, or power utility function, is used to express utility in terms of consumption
Isoelastic_utility
Type of fair division
examples, the utilities are weakly-convex and continuous. A. Many PEEF allocations: The total endowment is (4,4). Alice and Bob have linear utilities, representing
Efficient_envy-free_division
Method of spatial referencing
Linear referencing, also called linear reference system or linear referencing system (LRS), is a method of spatial referencing over linear or curvilinear
Linear_referencing
Generalization of the normal-form game
3. In a normal-form game, the utility function of each player i (denoted ui - a real-valued function on S) is a linear function in each of its components
Concave_game
Mathematical optimization concept
The dual of a given linear program (LP) is another LP that is derived from the original (the primal) LP in the following schematic way: Each variable in
Dual_linear_program
Concept in economics
convex, but not strictly-convex. 3. A preference relation represented by linear utility functions is convex, but not strictly convex. Whenever x ∼ y {\displaystyle
Convex_preferences
Ratio of active power to apparent power
cyclically accumulated in the load and returned to the source or because a non-linear load distorts the wave shape of the current. Where apparent power exceeds
Power_factor
Form of gambling
always make the bet (assuming a rational and risk-neutral attitude with linear utility curves and have no preferences implying loss aversion or the like).
Fixed-odds_betting
Economics concept of goods considered interchangeable
total quantity), the higher level of utility will be achieved, see figure 3. Perfect substitutes have a linear utility function and a constant marginal rate
Substitute_good
Statistical relationship
data. It usually refers to the extent to which a pair of quantities are linearly related. More generally, an arbitrary relationship between variables is
Correlation
Concept in economics
Lexicographic preference relation cannot be represented by a utility function. In Economics.SE Recognizing linear orders embeddable in R2 ordered lexicographically
Lexicographic_preferences
Frequency used on standard electricity grid in a given area
The utility frequency, (power) line frequency (American English) or mains frequency (British English) is the nominal frequency of the oscillations of
Utility_frequency
Research center at Stanford University
SLAC National Accelerator Laboratory, originally named the Stanford Linear Accelerator Center, is a federally funded research and development center in
SLAC National Accelerator Laboratory
SLAC_National_Accelerator_Laboratory
Proof of social welfare function being pareto efficient given three axioms
function W {\displaystyle W} can be represented as a linear combination of individual utilities: W ( x ) = ∑ i = 1 n a i u i ( x ) + c {\displaystyle
Harsanyi's utilitarian theorem
Harsanyi's_utilitarian_theorem
Economic formula of productivity
the same mistake." The Cobb–Douglas function is often used as a utility function. Utility u ~ {\displaystyle {\tilde {u}}} is a function of the quantities
Cobb–Douglas production function
Cobb–Douglas_production_function
Mathematical optimization problem restricted to integers
to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming
Integer_programming
countable linear ordering is isomorphic to a subset of Q {\displaystyle \mathbb {Q} } . For 2, first use the proposition to construct a utility u : { z
Debreu's representation theorems
Debreu's_representation_theorems
Statistical model for a binary dependent variable
political science, where discrete choice models and utility theory reign, while the "log-linear" formulation here is more common in computer science
Logistic_regression
Time Algorithm for Computing an Arrow–Debreu Market Equilibrium for Linear Utilities". SIAM Journal on Computing. 37 (1): 303–318. doi:10.1137/S0097539705447384
Algorithmic problems on convex sets
Algorithmic_problems_on_convex_sets
Solver for linear programs
lp_solve is a free software command line utility and library for solving linear programming and mixed integer programming problems. It ships with support
Lp_solve
Economics theory
less significant, and for such small amounts his utility function would be likely to be almost linear. For instance, if u(0) = 0 and u(100) = 10, then
Risk_aversion
Layouts of facilities including major transportation hubs, important linear utility networks, urban security and comprehensive disaster prevention system
Territorial_spatial_planning
Neither risk aversion nor risk seeking
and linear for a risk neutral agent. Thus in the risk neutral case, expected utility of wealth is simply equal to the expectation of a linear function
Risk_neutral_preferences
Measure of value difference between best possible decision and made decision
various observed decision patterns that deviate from standard expected utility theory, including status quo bias, inaction inertia, and the tendency to
Regret_(decision_theory)
also metric-based. Peak-linear preferences. The preferences can be represented by a utility function u that changes linearly on any ray emanating from
Star-shaped_preferences
development environments (IDEs), and other related development tools and utilities. Adns — asynchronous DNS resolver library Advanced Linux Sound Architecture
List_of_C_software_and_tools
Sandomirskiy and Segal-Halevi. In a Fisher market, when all agents have linear utilities, any market equilibrium is fPO. This is the first welfare theorem.
Fractional_Pareto_efficiency
Set of functions between two fixed sets
continuous functions from a topological space X to another one Y, with utility depending on the nature of the spaces. A commonly used example is the compact-open
Function_space
Economics theorem
unique up to positive linear transformations. Anscombe-Aumann subjective expected utility model von Neumann-Morgenstern utility theorem Referring to axiom
Savage's subjective expected utility model
Savage's_subjective_expected_utility_model
American economist
sunspot equilibrium was produced by Shell in an OLG framework with linear utility functions, which appeared in his "Monnai et allocation intertemporelle"
David_Cass
How two or more digital photo layers are mixed together
{\displaystyle a<0.5} one gets linear interpolation between 0 and 2 a {\displaystyle 2a} ; when a ≥ 0.5 {\displaystyle a\geq 0.5} one gets linear interpolation between
Blend_modes
Concept in economics
economics, additive utility is a cardinal utility function with the sigma additivity property. Additivity (also called linearity or modularity) means
Additive_utility
Hôtel particulier in Paris, France
Pompaodur, Delamair also set new standards in façade architecture. The sober, linear neoclassical façade was a novelty and a contrast to the ornate façades that
Hôtel_de_Besenval
(CEEI). David Gale proved a similar existence result for agents with linear utilities. Cake-cutting is more challenging than homogeneous good allocation
Weller's_theorem
Development along a single road
For as simple as linear construction emanating from a city is, the length of a ribbon corridor can pose financial concerns for utility companies as they
Ribbon_development
Episode of Neon Genesis Evangelion
techniques. Kaworu would then have spoken with Rei while standing atop a utility pole in a scene inspired by Kenji Miyazawa's Kaze no Matasaburo. The episode's
The Beginning and the End, or "Knockin' on Heaven's Door"
The_Beginning_and_the_End,_or_"Knockin'_on_Heaven's_Door"
generalization of the expectation. Nonlinear expectations are useful in utility theory as they more closely match human behavior than traditional expectations
Nonlinear_expectation
Software framework of Linux kernel
configured interactively—or from shell scripts—by using the dmsetup(8) utility. Both of these two userspace components have their source code maintained
Device_mapper
Concept in decision theory
outcome by his personal utility function. Thus, each lottery has an expected utility, a linear combination of the utilities of the outcomes in which
Lottery_(decision_theory)
Recursive algorithm for data compression
grammar) from a sequence of discrete symbols. The algorithm operates in linear space and time. It can be used in data compression software applications
Sequitur_algorithm
Mathematical model which is both linear and time-invariant
study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance;
Linear_time-invariant_system
induction was the dominant effect in these compounds, acidity should increase linearly with the number of available inductive pathways (linkers). However, the
Field_effect_(chemistry)
Piece-wise division of objects
piecewise-constant valuation is a kind of a function that represents the utility of an agent over a continuous resource, such as land. It occurs when the
Piecewise-constant_valuation
Project to construct a linear smart city in Tabuk, Saudi Arabia
The Line (Arabic: ذا لاين) is a planned linear settlement in Neom, Tabuk Province, Saudi Arabia, to be housed entirely in a single very long arcology.
The_Line,_Saudi_Arabia
Device used to slow or stop a moving object by generating eddy currents
quickly when power is turned off, and in electric meters used by electric utilities. An eddy current brake consists of a conductive piece of metal, either
Eddy_current_brake
Game theory solution
the utility function of one or more players is transformed by a linear function, then the agreement should also be transformed by the same linear function
Kalai–Smorodinsky bargaining solution
Kalai–Smorodinsky_bargaining_solution
Rule in social choice theory: choose the alternative maximizing the product of utilities
fair division of divisible private goods among agents with additive (linear) utilities, the allocation maximizing the Nash welfare coincides with the outcome
Nash_welfare_rule
Theory of behavioral economics
probabilities and underweight large ones. Thus, contrary to the expected utility theory (which models the decision that perfectly rational agents would
Prospect_theory
Family of functions to transform data
– introduced in the study of network utility maximization by Frank Kelly and collaborators as the α-fair utility function family. Tsallis entropy – a
Power_transform
Specification in economics of recursive utility
aggregate the risk associated with future utility. With Epstein–Zin preferences, the time aggregator is a linearly homogeneous CES aggregate of current consumption
Epstein–Zin_preferences
Measure of small-scale variations of amplitude in the height of a surface
projected onto a plane of best fit (POBF), where the POBF is a function (linear interpolation) of the boundary data only. Using a POBF, instead of an arbitrary
Rugosity
simplifies the proof of an expected utility representation, since it gives the set F {\displaystyle F} a linear structure inherited from Δ ( X ) {\displaystyle
Anscombe-Aumann subjective expected utility model
Anscombe-Aumann_subjective_expected_utility_model
Study of mathematical algorithms for optimization problems
function, criterion function, loss function, cost function (minimization), utility function or fitness function (maximization), or, in certain fields, an
Mathematical_optimization
Power supply with switching regulator
computer, while converting voltage and current characteristics. Unlike a linear power supply, the pass transistor of a switching-mode supply continually
Switched-mode_power_supply
Former railway trackbeds now used as recreational trails
escarpments, rivers and swamps. Rail trails often share space with linear utilities, such as pipelines, electrical transmission wires and telephone lines
Rail_trail
Coupe utility
The Chevrolet El Camino is a coupé utility vehicle that was produced by Chevrolet in 1959 and 1960, and from 1964 to 1987. Unlike a standard pickup truck
Chevrolet_El_Camino
Method of sound synthesis
Linear arithmetic synthesis, or LA synthesis, is a means of sound synthesis invented by the Roland Corporation when they released their D-50 synthesizer
Linear_arithmetic_synthesis
Square matrix without an inverse
if determinant, det ( A ) = 0 {\displaystyle \det(A)=0} . In classical linear algebra, a matrix is called non-singular (or invertible) when it has an
Singular_matrix
Types of lamp
5×8.5d Osram's Fluorescent Miniature (FM) tubes Sylvania Luxline Slim T2 Linear T4 1⁄2 12.7 G5 bi-pin Slim lamps. Power ratings and lengths not standardized
Fluorescent-lamp_formats
published by Wang et al. (2024). Frauenfelder et al. (2024) reevaluate the utility of sauropodomorph tooth measurement indices as proxies for classification
2024 in archosaur paleontology
2024_in_archosaur_paleontology
Subarea of optimal tax theory
linear too: y = y ( n , l ) = n ⋅ l {\displaystyle y=y(n,l)=n\cdot l} . Each individual decides on the amount of labour l which maximizes his utility:
Optimal_labor_income_taxation
Maximum size of an independent set of the matroid
utility functions of agents in problems of fair item allocation. If the utility function of the agent is an MRF, it means that: The agent's utility has
Matroid_rank
Professional baseball season in the United States and Canada
Ceddanne Rafaela (BOS) Right field Fernando Tatís Jr. (SD) Wilyer Abreu (BOS) Utility Javier Sanoja (MIA) Mauricio Dubón (HOU) Team Chicago Cubs Texas Rangers
2025 Major League Baseball season
2025_Major_League_Baseball_season
decrease the utility. Additivity (also called linearity or modularity) means that "the whole is equal to the sum of its parts." That is, the utility of a set
Utility functions on indivisible goods
Utility_functions_on_indivisible_goods
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