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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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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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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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?
That this utility function represents monotonic preferences, I think it's clear. Both goods have positive and constant marginal utilities. What I think is less clear is if this preference relation is ...
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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 ...
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revealed preference given an uncertain environment?
classical revealed preference is about a situation where we assume an agent has a preference over some set of possible choices $X$. We then construct a revealed preference relation on $X$ from choices ...
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The use of preference relations in choice theory and the $\succsim$ symbol
At least as from Edgeworth and Pareto we think about utility in mathematical terms. My question twofold
(i) about the start of the usage of binary relations to model preferences in economics, and ...
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Consumer preference and price in the Cobb-Douglas function
I believe I’m using the most basic version of Cobb-Douglas: $U(x,y)=x^\beta * y ^{(1-\beta)}$. The question I have is: in this example would a consumer’s preference ($\beta$) change if the price of ...
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preference relations
Can anybody give an intuitively explanation for the following problem?
Let $\succeq$ be a preference relation on a set X. Define I(x) to be
the set of all y ∈ X for which y ∼ x. Show that the ...
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Compare utility functions
I recently joined an econ class. I am so lost on how to prove their equality. As a math standpoint, these are completely different equations. Please help!
...
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Unusual perfect complements utility function min{ax+y, x+2y} [closed]
What's the graph for this utility function? How can it be represented graphically?
Is this function perfect complements? I do not fully understand that in the question attached in the picture, the ...
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Relationship between convexity and a perfect complements type utility function
Consider someone who consume two goods and hates them both.
Given the utility function:
U(x,y)= -max{x,y}
1.What would be the shape of the indifference curve?
2.Why are these preferences weakly ...
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Does SARP imply WARP? and GARP imply SARP?
It’s obvious that WARP does not imply SARP, since WARP does not rule out cyclic choices, whereas SARP does.
The term “Strong” axiom suggests that it encompasses the “weak” axiom. But this is not ...
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Inferior and normal good and the change in price of those goods
In general, We know that if a good is normal, then as your income increases, then demand of that good increases as well as price is fixed. Similarly, if a good is inferior, then as your income ...
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Indiference between two lotteries
Suppose that a binary relation satisfies only:
Independence axiom: $L≿L′⟺α\circ L+(1−α)\circ L′′≿α\circ L′+(1−α) \circ L′′$
Reduction to simple lotteries: For all $g$, $g~g'$, $g'$ is the simple ...
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Quasiconcavification
Let $f_1, f_2$ be two smooth strictly-quasiconcave functions.
Do there always exist monotone transformations $g_1,g_2$ such that the sum
$g_1\circ f_1 + g_2 \circ f_2$ is a strictly-...
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Why does the violation of a preference axiom not invalidate the discipline of economics?
There are many examples of the preference axioms of consumer theory being violated. I feel like there are very few cases where at least one of these axioms isn't broken, so is any theory or model ...
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Literature on Recursive Preferences and Time-Additive Expected Utility
In Chapter 20 of the book Economic Dynamics in Discrete Time, named "Recursive Utility", the author asserts that the Time-Additive Expected Utility Model (TAEU) has some shortcomings when applied to ...
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Problem with a Hal Varian Question from chapter 5
Remember our friend Ralph Rigid from Chapter 3? His favorite
diner, Food for Thought, has adopted the following policy to reduce the
crowds at lunch time: if you show up for lunch t hours before or ...
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MRS for quasi-linear preferences
I'm having difficultly understanding what my professor taught in class.
I thought, like cobb-douglas, when finding $U_1$ we take partial derivative with respect to $q_1$ and hold everything else ...
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Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?
We can write down the coefficient of absolute risk aversion $R_a$, or the coefficient of relative risk aversion $R_r$.
Are there intuitive interpretations of the numerical values of these ...
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Continuity of preference relation (iff?)
I have a question about the following definition of a continuous preference relation. I apologize for not providing a reference and will try to add one as soon as I can find one.
Definition:
A ...
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Why does local non satiation imply the constraint is binding?
Local non satiation says that for any $x \in X$ and $\epsilon > 0$, there exists $y \in X$ such that $d(x,y) < \epsilon$ and $U(x) < U(y)$.
I don't understand why this implies that $px^* = m$...
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Homogeneous of Degree Two Utility Functions and Homothetic Preferences.
The understanding that I am not clear is in when do homothetic preferences represent a utility function and vice-versa. My solution to the problem is posted below the problem:
A consumer’s preferences ...
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Weak axiom of Revealed Preference application
The following is a problem I am dealing with related to Weak Axiom of Revealed Preference. I have given my solution below to the situation. What I am not getting is how is WARP not violated?
A law ...
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Ordinal utility and monotonic transformations
If u(x) is an ordinal utility function that represents the (weak) preference relation R, then
(a) any strictly monotonic transformation of u(x) also represents $R$, or
(b) any monotonic transformation ...
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Existence of utility representation of a rational but discontinuous preference
This is related to Do discontinuous preferences imply no continuous utility function?
I think the title of the above-linked question is phrased in such a way that obscures a subtly different but more ...
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Do discontinuous preferences imply no continuous utility function?
I am trying to think of a preference relation that can be represented by a utility function but such that there does not exist a continuous utility function.
I know that you can represent continuous ...
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Stone-Geary preferences and competitive equilibrium
Does anybody know if a competitive equilibrium obtains under Stone-Geary preferences; are there multiple equilibria problems; do such preferences admit an analysis with more than one type of ...
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Properties of preference relation
Let $\succeq$ be a preference relation on $X$. Is it true that $x \succeq y$ if and only if $\lnot (y \succ x)$?
I think it is true and my proof is as follows. To prove $\implies$ direction, we have ...
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Are Cobb-Douglas preferences homothetic?
Our lecture defined a preference to be homothetic, if the following is true:
$$(x_1, x_2) \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$
Cobb-Douglas preferences can be ...
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