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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In revealed preference (RP), is any two points $x,y$ related by the indirect revealed preference relation?
Let $X$ be the closed compact convex set of alternative and $B$ be a closed compact convex subset of $X$. $C$ is defined on all closed compact convex set $B\subseteq X$.
$X$ is ordered by a strictly ...
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Why is monotonic preference and monotonic utility function non-decreasing?
Obviously a monotonic function can be either nondecreasing or nonincreasing:
However, in Economics, a quick google search gives:
I am interested in the history or the motivation behind the econ ...
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What was the study that shows peoples' tax preferences shift when they get more information about their income?
I am trying to find a study I read a few years ago, but I forgot the names of the authors and the title of the study. I have already tried to search for the study on Google Scholar without much luck. ...
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Example to Demonstrate that with Uncountably Infinite Outcomes We do not Have A Representing Utility Function [duplicate]
Suppose we define $\Omega$ = $\mathbb R_+$. The preference relation $\succeq $ is defined as $$(x_1, x_2)\succeq(y_1,y_2)\iff x_1>y_1 \text{ or } [x_1=y_1 \text{ and }x_2\geq y_2]$$
where $x_1, x_2,...
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Determine Whether A Preference Relation Satisfies The Continuity Axiom - from Exercise 1.1 in Game Theory: Analysis of Conflict by Roger Myerson
I am self-studying game theory using Game Theory: Analysis of Conflict by Roger Myerson. Here is an exercise from the textbook. I tried it myself, but I am not sure if it is correct. I would really ...
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y is weakly preferred over x if and only if x+y ≤ 4 defines a preference relation on {0,1,2,3} why is this incomplete?
y is weakly preferred over x if and only if x+y ≤ 4 defines a preference relation on {0,1,2,3}. True or False?. I can see why it's not transitive but I was told it was incomplete if we take 2 and 3. ...
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Transitivity of Preferences paper
I am going through some of my old grad school notes, and in my microeconomics notes on transitive preferences, the teacher made a note of a behavioral economics result where when presented with two ...
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Give bundles $x,y\in \mathbb R^n$, there must exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?
For a problem in revealed preference. Give bundles $x,y\in \mathbb R^n$, must there exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?
Intuitively, this mean that we have two bundles, and ...
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Lexicographic preference relation not continuous
I’m having trouble understanding why lexicographic preference relations aren’t continuous. I need inspiration on how this proof would work.
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Properties of Consumer Preferences - Monotonicity
Was reviewing topics and I came across this question. I am confused because there is no reference to strict or weak monotonicity in this case. I first thought that monotonicity is violated b/c an ...
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Quasiconvex and quasiconcave utility function
I saw that the model of the quasi-convex utility function is similar to the concave utility function and also the quasi-concave utility function is similar to the convex utility function. How can ...
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Convexity preferences
What is the difference between convexity and strict convexity preferences? What is the difference between quasi-concavity and quasi-convexity? And is MRS still true in concave preferences?
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Continuity of preference
"A preference is continuous if for any $a,b\in X$ with $a\succsim b$ there are some neighborhoods $N_{\varepsilon}(a)$, $N_{\delta}(b)$ around $a$ and $b$ such that for every $x \in N_{\...
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Generalization of Debreu's additive utility function $\sum_nu_n(x_n)$ with infinite number of commodities
I want to generalize: $\sum_nu_n(x_n)$.
Here $x_1,x_2,..,x_n,...$ are commodities. There are infinite number of commodities: $n\in\mathbb N$ or $n\in \mathbb R_+$
The following not a candidate: $\...
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Reference for monotonicity: $x\geq y\implies x\succsim y$ and $x>y\implies x\succ y$
I've seen this definition for monotonicity many times on different papers and on this site:
$x\geq y\implies x\succsim y$ and $x>>y\implies x\succ y$.
However, what I read on MWG's ...
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McKelvey-Schofield Chaos Theorem Without Agenda Setter
The McKelvey-Schofield Chaos Theorem states that in a multidimensional preference space, it is almost always possible to reverse engineer the implementation of your desired policy by constructing an ...
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labor leisure model, quasilinear preferences
There is a quasilinear utility function $u= (1-t)wl - p(l)$, where $l$ is labor supply. I don't quite understand what happens, if the budget changes (due to $w$ or $t$) since it is quasilinear. Does ...
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Sufficient conditions for connectedness of indifference sets of a preference relation defined on a compact and convex set only
Let $\succsim$ a complete, reflexive and transitive binary relation defined on $X$, a non-degenerated (i.e not identical to a singleton) convex compact subset of $\mathbb{R}^n_{++}$ (the set of n-...
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Order relations and preferences using logic
I want to understand order relations using their underlying implication mechanics and what this means for certain results, specifically looking at preference relations.
Using the logical rules of ...
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Is it possible to get back the consumer’s utility function from their demand functions?
I am curious about if it’s possible to reverse the utility maximization process, i.e. given the consumer’s Marshallian demand functions, find their utility function.
I was thinking of trying to find ...
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Preference relations based on Varian
I understand that there is no universally agreed terminology for preference relations. However I need to pin down a definitive way to think about them (both for my exam, and my own sanity). Please can ...
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Assigning dollar value to intangible costs and benefits
I am trying to develop a framework that a person can use to help them decide where to live. The idea is to assign a dollar value to various attributes (e.g. work opportunities, cost of living, climate,...
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Conflicting Definitions of Weak Monotnocity (preferences)
Strong Montonicity my sources seem to agree on Strong monotonicity, i state equivalent definitions below. But weak montonicity i keep finding what appear to be conflicting definitions. In the ...
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Risk aversion and utility transformation: are preferences still the same?
If you have two utility functions $u(\cdot), \; v(\cdot)$ such that $v(x) = f(u(x))$ for some monotonic transformation $f(\cdot)$, then $u(\cdot)$ and $ v(\cdot)$ represent the same preference ...
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Willingness to sell a lottery ticket vs. willingness to buy a lottery ticket
I'm struggling with this question: There is a lottery which gives you D with p = 0.25 and L with p = 0.75 while initial wealth is w (w > D > L > 0). What is the minimum price the person would ...
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Linear Engel Curve
How to prove that if the Engel curves (expenditures as a function of wealth) are linear in wealth, then the indirect utility function has the form $v_{i}(p,a_{i})=\alpha_{i}(p)+\beta(p)a_{i}$ for an ...
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What is the difference between preferences of the producer vs the consumer?
The book I am working with (Rubinstein) states that in the case of the profit-maximizing producer, preferences are linear and the constraint is a convex set. Meanwhile, in the consumer model, ...
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How to rationalize the following behaviors using preference relations?
The producer wishes to produce at least $y^*$ units. Once he has
achieved that goal, he maximizes profit.
The producer maximizes profit, but already employs $a^*_1$ workers
and will incur a cost c (...
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What are the conditions to determine whether demand function is rationalizable?
A consumer chooses a bundle (z, z, . . . , z) where z satisfies $z Σp_k = w$.
The book (Rubinstein's) states that the demand function x(p,w) can be rationalized if there exists a preference such that ...
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What does it mean if the derivative of the Utility function (at the optimal bundle) is 0?
It states in my book that under strict monotonocity, the derivative of U(x*)=0 can be possible although it's unlikely to happen.
What does this exactly mean?
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What does differentiability of Utility function at an optimal solution x* mean?
I am working with Rubinstein's book. It states there that if preferences are differentiable, then value per dollar at a bundle of a commodity is as large as value per dollar of the bundle of any other ...
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Help with checking work for preferences over consumption and leisure question
I was wondering if anyone could help me check my work for the following question, and if I am wrong, help me correct my mistakes?
Question:
Work:
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Are homothetic additively separable preferences always equivalent to CES?
Are homothetic additively separable preferences always a monotonic transformation of CES preferences?
In technical language, the question is the following:
Let $n>1$, and let $f:\mathbb{R}^n_{\ge 0}...
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Can strict preference be represented by Utility function if not complete?
The definition states that a Utility function represents the preference relation because the relation on R satisfies transitivity and completeness. Yet, strict preferences (and indifference ...
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Can a preference relation not satisfy monotonicity and still be represented by an Utility function?
The book I am working with (Microeconomics Theory by A. Rubinstein) states that:
"In the case that preferences are represented by a utility function, preferences satisfying monotonicity (or ...
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Can the following statement be rationalized if it yields a choice function?
A person choose an alternative to maximize another person's suffering.
I thought we could define a sort of relation where the person suffers more from x than y. And if we can always do this, we can ...
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Can the following behavior be rationalized if it yields a choice function?
The decision maker has an ideal point in mind and chooses the alternative closest to it.
I am not sure if I am right, but in order to rationalize it, we first have to construct a choice function. So, ...
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Challenging question in microeconomics - local nonsatiation
I'm studying advanced micro from the Mas-Colell book (exercise 16.C.1)
I was wondering if anyone can help me to solve the following exercise. I have no idea how to deal with it
Show that if a ...
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Strict monotonicity and strict convexity - prefences
I've just encountered the following exercise from GEOFFREY A. JEHLE micro's book
Strict monotonicity comes from the fact that any increase in $x_1$ or $x_2$ increases utility, and strict convexity ...
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Are the indifference curves for bads concave?
While I was studying microeconomics, a question arose:
I know what the indifference curve for one “good” good and one “bad” good looks like. But if both goods are bad, is the indifference curve ...
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Example of consumer preferences that switches from being concave to being convex
Question
Is there an example of consumer preferences over consumption bundles $(x,y)\in \Bbb R^2$ that would be concave when $x$ is abundant relative to $y$ and convex otherwise?
Are there known ...
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Decomposition of preferences into set of CES functions
CES function as a tool
Hello everyone,
I have this idea: CES function basically tells us what is the elasticity of substitution between two (and more) goods, therefore giving us the exact complement/...
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State dependent preferences vs state independent preferences in utility theory
I am working on changes in preferences and found papers on state-independent preference. What is the difference between state-dependent and state-independent preferences and utility functions? What ...
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Which Choice Rule follows Always Chosen axiom and No Binary Cycle axiom?
Source: taken from ISI PhD entrance exam questions.
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Does consumer demand in the secondhand market actually affect the firsthand market for high-cost goods
In the 21st Century, there is an increasing consumer awareness of the externalities of manufacturing and along with it a stronger consumer preference to buying used goods rather than new.
My question ...
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How to check if a utility function represents locally non-satiated preferences?
I understand the distant definition of LNS but I don't get how to actually apply it to given utility functions like u=x1/x2 or u=x1-x2 or of any form? Is there structured math-y way to check if they ...
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How to prove that any preference relation on (countable) X has a utility representation with a range (0,1)?
Theorem: If $X$ is countable, then any preference on $X$ has a utility representation with a range $(0,1)$.
The stated proof in Rubinstein's lecture notes:
Proof: Let $\{x_n\}$ be an enumeration of ...
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Can "thick preferences" be represented by a utility function?
From microeconomics,
$u$ is strictly quasi-concave if for all $x\ne y\in\mathbb{R}^2_+$ and $t \in (0,1)$, if $u(x)\ge u(y)$, then $u(tx + (1-t)y)>u(y)$.
You may also check the figure below.
Here ...
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Is the leontief utility function homogeneous of degree zero? And if that is true, how can that be prove? [closed]
I have not been able to find a mathematical prove is such statement.
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Shape of indifference curves and quasi-concavity of utility
So my professor told that quasi-concave utilities lead to convex preferences/indifference curves. I have some conceptual problems understanding this statement.
Indifference curves are plotted from ...
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