Questions tagged [preferences]

Binary relations that reflect which states of the world an agent considers to be most desirable. Preferences are a fundamental ingredient in the axiomatic study of consumer choice decision theory.

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Why does quadratic utility function imply $\mu-\sigma$ preference?

Why does investors having quadratic utility function mean that their optimal portfolios can be chosen by only considering mean and variance of returns i.e. imply $\mu-\sigma$ preference?
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Net Preference Relations

Let say the electorate consists of three segments of voters: 1, 2, and 3 with corresponding weak preference relations defined over the candidates. Let the preferences be given by -- Segment 1: Biden >...
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Given a rational $\succsim$ over a finite set $X$, show that there exists $x \in X$ such that $x \succsim y, \forall y \in X$

I have been able to show this constructively, but would like to prove it by induction. However, I am stuck with the induction step: Consider $\succsim$ defined over $X=\{x_1,...,x_n\}$ and where ...
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Study whether $\succsim$ represented by $u(x)=\lfloor x \rfloor$ is continuous

Using the following definition of continuity: $\succsim$ is continuous if for any bundles $x,y,z$ such that x$\succ$y$\succ$z, there exists $\alpha \in (0,1)$ such that $\alpha x + (1-\alpha)z \sim y$....
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A preference relation $\succ$ is defined as $(x_1,y_1)\succ (x_2,y_2)$ if $x_1>x_2$ and $y_1> y_2$

Does this satisfy completeness property? I need an intuitive explanation of this preference relation as well. I am confused about the way how this relation is defined. The commodity Y in the first ...
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51 views

Framing Effect Risk-Aversion Risk-Pursuit

I am an economics' graduate seeking to study Law and I want to illustrate the importance of legal certainty. Penalties, Costs are negativelly framed. I am trying to word. 200 dollars with 50% ...
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Assumption of sufficient wealth in quasi-linear preferences

Whenever we talk about quasi-linear preferences, we assume that the consumer is sufficiently wealthy. As far as I understand is that we need that assumption in order to obtain an interior solution. ...
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Representing preference orderings over a finite set of outcomes by two payoffs

I have read the following statement and I am having difficulty understanding the second part: Any set of preference orderings over a finite set of outcomes can be represented either by ...
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Showing that a preference relation admits a utility function representation

Setting: We have two choices of goods $(x_1,y_1)$ and $(x_2,y_2)$ from the set of choices $[-1,1]^2$. Moreover, we have the following preference relation $$(x_1,y_1)\mathcal{R}(x_2,y_2)\iff |x_1|\geq|...
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171 views

Preference: Convexity and Monotonicity

I need an example of a Convex, non-monotonic preference Non-convex, monotonic preference I figured that an example of non-convex, monotonic utility preference could be $U(x,y)=x^2+y^2$. For convex, ...
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The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them?

I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality. But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
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Everyone has the same marginal rate of substitution

I'm currently reading Varian's Intermediate Microeconomics and what struck me, is this statement on page 89 of the 8th edition. If everyone faces the same prices for the two goods, then everyone ...
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Linear Homothetic Utility

A Homothetic Utility is where $$ \forall x,y, \forall a \in \mathbb{R}_+: \ u(ax,ay)=au(x,y) $$ (or its monotonic transformation). A linear Homothetic utility is defined as $$ \forall x,y, \forall ...
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If an ordinal-scaled utility function is defined via strictly increasing transformation, how can it represent a case of indifference?

Problem: According to Wulf Gaertner’s (2009, p. 13) A Primer in Social Choice Theory, any strictly increasing transformation of an individual’s ordinal utility function is informationally equivalent. ...
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Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?

$\succsim$ is a weak order over $\mathbb R^L$. For a closed budget set $B\subset\mathbb R^L$, define demand correspondence: $$D(B)=\{x\in B|x\succsim y\forall y\in B\}$$. We know that $D$ is always ...
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Compound lottery preference implies simple lottery preference

Suppose $\alpha>\beta$ and for two lotteries $L, L'$ $\alpha L + (1 - \alpha)L' \succ \beta L + (1- \beta) L'$ where $\succ$ implies preference. If the independence theorem holds, how do you ...
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Obligations of a company

Any company may "feel" obligated towards several parties at once: its shareholders its employees its customers its partner companies (sub-contractors and suppliers) its country and social environment ...
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WARP implies completeness, transitivity and thus rationalizability. What is wrong with the statement?

Let $A$ be a menu and $R$ be a complete and transitive binary relation. Define choice correspondence generated by $R$: $$c_R(A)=\{x\in A|| xRy \ \forall y\in A\}.$$ Theorem (from Kreps 1988): for ...
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Substitution effect when price of both goods change by the same percentage

I am trying to grasp the concept of income- and substitution effects. The way, I've understood it, the decomposition bundle is found, at the original indifference curve, where the slope equals that ...
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How are preferences related to relative prices?

For instance, across regions of a country or between countries. Is that different preferences for food lead to distinct relative prices in different regions or countries? Or is it the other way ...
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GARP and SARP assumed mononticity?

Monotonicity means the decision maker prefer more goods than less. It is not mentioned in textbook that SARP and GARP preasumed monotonicity. GARP: if $a$ is indirectly revealed preferred to $b$, ...
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Is GARP trivially satisfied with only 1 good?

As with all revealed preference work, when the number of goods is greater than 1, then GARP (Generalised Axiom of Revealed Preference) is not always trivially satisfied. However, is it always the case ...
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Proof of monotonocity of preferences

Question from Intermediate Microeconomics by Hal Varian: "We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve ...
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An example of preferences over a countable set that cannot be represented by a utility function

Give an example of preferences over a countable set in which the preferences cannot be represented by a utility function that returns only integers as values. I know a utility function exist that ...
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Preference relations defined by $x_1^n + x_2^n$ converge to $\max\{x_1, x_2\}$

In the problem set 2 of Rubinsteins Microeconomics (btw is there a comparably nice written book on macroeconomics?) there is the following question: Let $\succ_n$ be the preference relations defined ...
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Finding Optimal Bundle and Change in Satisfaction after Changes in Budget Constraint

I am looking at the following exercise and struggling with the solution proposed by my microeconomics book. A consumer spends all his income on two goods, X and Y. The prices he paid and the ...
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Proof of Choice Coherence in Kreps (2013)

In the first chapter of Kreps (2013), there is a proof that the choice function satisfies choice coherence. Kreps writes: I do not understand how the third sentence of (b) logically follows from the ...
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Question about Locally non-satiated preferences

If a consumer has locally non-satiated preferences, which of these 2 bundles is preferred and why? Bundle A: (1,3) Bundle B: (4,2) This is what I've reasoned from my very limited understanding of ...
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How can two different utility functions represent the same preferences?

I have this question for microecon that asks do the following utility functions represent the same preferences: $u(x_1, x_2) = x1 \cdot x2, \; v(x_1, x_2) = \ln x_1 + \ln x_2$ $u(x_1, x_2) = x1 \cdot ...
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If a weak preference relation is complete and transitive, why is the strict preference relation negatively transitive?

My textbook says that "if a weak preference relation is complete and transitive, the strict preference relation MUST be asymmetric and negatively transitive". Now, I think I understand why it must be ...
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144 views

indifference curve slope from utility function

in the economics book that I'm reading right now it is written that this utility function: $$u(x_1,x_2) = 2x_1 + x_2$$ yields indifference curves with a slope of $−2$. Could someone please explain me ...
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Completeness Axiom in Preference Relation

My textbook, Microeconomic Theory by Mas-Colell, Whinston, and Green states that given a preference relation $\succsim$ on $X$, Strict preference relation $\succ$ is defined by $ x \succ y \iff ...
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Consumer Preference when Consumer only consumes $A$ or $B$

Let's say Sally either wants to coke or pizza, but never both. I am aware of the standard consumer preferences, such as Perfect Complements as well as Perfect Substitutes. But I have never heard ...
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Homothetic preferences from indirect utility

Consider an indirect utility function on the form $v^{i}(\textbf{p},w^{i}) = a^{i}(\textbf{p}) + b^{i}(\textbf{p})w^{i}$ Where $\textbf{p}$ is a vector of prices and $w$ denotes income of ...
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Majority Rule and Single Peakedness

Majority Rule will induce non empty choice set if individual preferences are single peaked Is this statement true? I have some trouble in understanding the meaning of 'single peakedness' in context ...
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Archimedean but not mixture continuous

In the context of preferences on a set of lotteries on a finite set $X$, what is an example of a preference that is independent, Archimedean but not mixture continuous? I know the mixture continuous ...
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Does Preference have a Hierarchy? A Silly Question

I have what is probably a very silly question, but I have gone down the rabbit hole and can’t get back out..... Is there is a hierarchy of preference, and within each level of choice do we reset the ...
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Economics of clubs(sport gym, language course, etc)

I am looking for economic research, theory or empirics, on production/profit maximization/competition for firms producing goods with network effects, such as clubs in which every one's utility depends ...
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375 views

Can a continuous preference be represented by a discountinuous function?

I can think of some examples, but what can be an outline of the proof?
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Quasi-linear Optimal Consumption Bundle

I have a question involving optimal consumption bundles for quasi-linear preferences. Utility is given by $$U(x_1,x_2) = 16\sqrt{x_1} + 2x_2$$ and $p_1 = 8, p_2 = 4, I = 30$. What I have so far ...
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Prove that $u$ is a utility function for $\succsim$

If X is finite, define this function $u : X \rightarrow \mathbb{R}$ by $u(x) = |\{z\in X:z \prec x \}|$. Prove that $u$ is a utility function for $\succsim$. Is it sufficient to prove that the ...
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Does $U(x,y) = x^2 + y^2 + 2xy$ represent transitive, monotonic preferences?

I'm a monitor for a microeconomics course and a student came up with this question. That this utility function represents monotonic preferences I think it's clear. Both goods have positive and ...
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Completeness from an example

I have a set $X = \{1,2,3\}$ and a binary relation $B = \{(1,1),(1,2),(1,3),(2,3),(3,1)\}$. I am trying to understand if this relation is complete. The completeness definition I am using is if for ...
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Doubt about equivalence relation

In class I was taking notes about equivalence relations defined as: Given a generic relation $R$ on $X$, $xIy$ if both $xRy$ and $yRx$ Now, I don't really understand the following proposition: ...
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If $\succsim$ is transitive but irreflexive, then it is asymmetric, proof

If $\succsim$ is transitive but irreflexive, then it is asymmetric. this is my proof: Suppose $\succsim$ is not asymmetric, which means that for any $x,y \in X$ $x\succsim y \rightarrow y \succsim ...
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Revealed preference if we know that the decisionmaker is rational?

In standard revealed preference, we don't assume that the agent has rational preferences over a choice set $X$, and we can then ask: under what conditions can $X$ be rationalized by a rational ...
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Slutsky Decomposition from Indirect Utility Function [closed]

Given the indirect utility function: V={M^2}/{4P1P2}, how do we establish the Slutsky Decomposition? I used Roy's Identity to get the Demand, but I'm stuck with the other components of the Slutsky ...
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Efficient revealed preference check of whether two preferences over lotteries are the same?

I want to find conditions under which two utility functions can be known to be linear transformations of each other. Consider a (possibly finite) arbitrary set of outcomes $X$ (Not necessarily ...
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Lexicographic Preference Relation on the QxR

I would like to ask for your help. I recently learned that the Lexicographic Preference relation can be represented by a utility function $u:X\to\mathbb{R}$ on $\mathbb{Q}\times\mathbb{R}$ (but not $\...
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preference relations and monotonic transformations of utillity functions

Given a choice set $X$ (NOT assumed to be a commodity set...), and utility functions $u,u'$ on $X$, it is clear that if $u'$ is a strictly monotonic transformation of $u$ then they induce the same ...