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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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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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33 views

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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51 views

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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1answer
15 views

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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55 views

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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53 views

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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67 views

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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39 views

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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68 views

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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1answer
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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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1answer
62 views

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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1answer
55 views

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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1answer
68 views

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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1answer
140 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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225 views

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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137 views

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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1answer
145 views

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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1answer
49 views

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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126 views

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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1answer
257 views

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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2answers
135 views

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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1answer
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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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1answer
47 views

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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1answer
81 views

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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188 views

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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1answer
207 views

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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1answer
829 views

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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465 views

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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1answer
484 views

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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1answer
179 views

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 ...