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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Conditions to use the Lagrangian method

I have seen that the prices and $\text{MU}_{i}$ are assumed to be positive (or, the preferences monotonic). This is always mentioned when a utility maximization problem is being solved with the ...
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Weak preferences and negative transitivity

Let $ \succ $ be a binary relationship on the set $X$ such that, given any $ x, y, z\in X $, if $x\succ y$: (Asymmetry): $\neg(y\succ x)$, (Negative transitivity): $(x\succ z) \vee (z\succ y)$. ...
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Non well behaved preference

I have to discuss a consumer making a choice between 2 bundles, and the consumer has a non- well-behaved preference. What real example can I use to represent a non-well behaved preference?
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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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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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How to mathematically denote that a consumer behaves according to their preference structure at every point in time?

As the title says, I would like to mathematically denote that a consumer behaves according to their preference structure at every time $t$, $t+1$, $t+2$ and so on in a finite consumption set $X$, by ...
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Proving properties for preferences?

I have a midterm coming up and I am still not entirely sure on the formal arguments for proving (strict)\convexity, monotonicity, continuity, quasi-concavity e.t.c. I think I have a pretty strong ...
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WARP implies SARP: A 2 Good Case

I am considering an example where there are two goods and three budget sets $(\mathbf{p}^{(n)},w^{(n)}),n=1,2,3$. If we assume $\mathbf{p}^{(n)} \cdot \mathbf{x}(\mathbf{p}^{(n+1)},w^{(n+1)}) \leq w^{(...
kékszajkók's user avatar
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Understanding the Continuity axiom of preference

Let $x^{1}, x^{2}, \cdots \to x$ where each $x^{i}$ and $x$ are elements of the set of consumption bundle or the choice set $X$. If $x^{i} \succeq y$ for each $i \geq 1$ then $x \succeq y$. This is ...
not tdm's twin's user avatar
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preference convexity and existence of equilbria

Consider a production economy with $L$ goods, a single consumer and a single producer whose production set are given by $Y\subset R^L$. Question is to find the existence condition of equilibria of ...
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For the case of two goods, give an example of preferences that are represnted by a continuous utility function that allows for fat indifference curves

The question in the title sounds like a trick question, due to the monotonicity property that indifference curves have, such that for two goods x and y, strong monotonicity implies y > x. Possible ...
CorporateNationalism's user avatar
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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 ...
TheLight OI's user avatar
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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 ...
mathuser121's user avatar
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Preference ordering relation

≳ is a preference ordering if it is reflexive , transitive and complete. In Mathematics relations are said to be in a equivalence relation if they are reflexive, symmetric and transitive. Can we ...
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Determining whether preferences are rational given a utility function

Alex's preferences: U(x;y)=x-(1/y). Are his preferences rational?
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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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Does x ≽ y imply x > y or x ~ y in preferences?

Mas Collel Micro Theory question: Suppose that X is a set. Let ≽ be a binary preference on X. And ~ represents indifference defined from ≽. If ≽ satisfy completeness, is it okay to assume that: x ≽ y ...
Wizard74's user avatar
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Do the continuity axiom and transitivity axiom justify non-satiation?

Let's assume on the contrary that the indifference curve is "thick" or crosses. We can only assume the four axioms: completeness, transitivity, reflexivity and continuity. We do not assume ...
not tdm's twin's user avatar
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Strong monotonicity and weak monotonicity

We say $\succsim$ represents weak monotonic preferences if $$x,y \in X, \,\, y >> x \implies y \succ x $$ where $y >> x$ means that every element of $y$ is greater than every element of $...
Pedro Cunha's user avatar
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Why are indifference curves (often) of infinite length?

Indifference curves are often of infinite length. Is this implied by monotonicity or non-satiation? If not, what is/are some condition(s) that are sufficient for indifference curves to have infinite ...
High GPA's user avatar
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A question about MWG Exercise 3.D.4

I'm doing exercises of Chapter3 of MWG, there's a problem that I don't understand (I didn't figure out the solution manual either...). It is about exercise 3.D.4, the full statement of the exercise ...
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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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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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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 ...
Pedro Cavalcante's user avatar
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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: ...
plastico's user avatar
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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 ...
eigenvector's user avatar
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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 ...
Eric '3ToedSloth''s user avatar
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Preference relation value representation without uncertainity

Let $\succeq $ be a weak order in $\mathbb{R}^n$. If $ x\geq y \Rightarrow x\succeq y$ for any $x\succ y\succ z$ there exists a unique $\lambda \in (0,1)$ such that $y\sim \lambda x+(1-\lambda)z$, ...
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How to force two utility functions representing the same preference to generate expected utility functions representing the same order on lotteries?

Let $i$ be an agent, and let $A=\{x,y,z\}$ be a set of three alternatives. Then, suppose that player $i$’s linear order (i.e., complete, transitive, antisymmetric and reflexive binary relation) on $A$,...
EoDmnFOr3q's user avatar
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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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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 ...
High GPA's user avatar
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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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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 ...
reindeer's user avatar
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Does strongly monotone preference imply local non-satiation?

How to prove this? I understand monotonicity implies local non-satiation but does strongly monotone also imply it? How to prove it like this - https://felixmunozgarcia.files.wordpress.com/2017/08/...
reindeer's user avatar
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On quadratic utility functions

Question A risk-averse, non-satiated investor has decided to use the utility function $$U(w) = w + dw^2,$$ where $$d \leq 0$$ is a constant, to describe his preferences. Derive an upper bound for $w$, ...
Ethan Mark's user avatar
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Lagrangian when ICs are tangent to the budget line

Suppose the graph below shows three Indifference Curves such that $t > s > r$, and the budget line $p_1x + p_2y = I$. I was wondering if we set the Lagrangian as $\mathcal{L}= U(x,y) - \lambda (...
not tdm's twin's user avatar
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Different ways of writing CIES/CARA utility

I frequently encounter the following two versions of writing CIES or CRRA preferences: $$u(c_t) = \frac{c_t^{1-\theta}-1}{1 - \theta}$$ ...and... $$u(c_t) = \frac{c_t^{1-\theta}}{1 - \theta}$$ The ...
maddonis's user avatar
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In a setting with N goods how many combinatorial bits do we need to construct a preference map

I am reading this paper: https://www.researchgate.net/publication/5208445_The_market_for_preferences By P.E Earl and J.Potts On page 3 the following is written: "If we think of individual ...
ra514's user avatar
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Marshall demand for simple CES utility

Assume that preferences are given by a utility function is given $$u(x_1,x_2) = (x_1^\rho + x_2^\rho)^{1/\rho}$$ what then are the Marshall demand given budget constraint $$p_1x_1 + p_2x_2 \leq I$$
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Remove Linear Good From Quasi-linear Utility Function

Given a quasi-linear utility function: $u(x_1, x_2) = f(x_1) + \beta x_2$, $\beta > 0 $ What would happen if good 2 ($x_2$) is removed from the market? Would the new utility function be: $u(x_1) =...
Pycruncher's user avatar
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Is the satisficing choice function rationalizable if the ordering isn't observable?

Edited: Say an observer observes only the choices made by the decision maker (and the sets from which these choices are made), but does not know the ordering. Then would the decision maker's choices ...
user avatar
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1 answer
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How to describe a utility function in words?

Suppose I have a utility function of Cobb-Douglas form $$U(x, y) =x^{0.2}*y^{0.8}$$ I want to describe it in words. I would say like: The utility of consumer is captured by number of good x and ...
Alex's user avatar
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$a\geq 0$, $x\sim y$ implies $x+a\sim y+a$ so the preference is linear?

$\succsim$ is a countinuous and convex weak order. $x,y,a$ are vectors in $\mathbb R^n$ We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero. We want to prove (or ...
High GPA's user avatar
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Prove that a preference is linear

Given the following two conditions: $x\succ y$ implies $x+a\succsim y+a$, And, $x\prec y$ implies $x+a\precsim y+a$ We want to prove that $\succsim$ is a linear preference. One of the ...
High GPA's user avatar
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Linear Utility?

Consider a preference relation $\succeq$ on $X\subseteq\mathbb R^2$. If $\succeq$ satisifies: $$ \begin{align} &1.\mbox{ }(a_1,a_2)\succeq (b_1,b_2)\implies(a_1+t,a_2+s)\succeq (b_1+t,b_2+s),\...
High GPA's user avatar
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A question about the property of quasi-linear preference

In case of quasi-linear preference, why would one unit more of the numeraire good (good 1) give the same additional utility as spending an additional amount of wealth equal to the cost of one unit of ...
Aqqqq's user avatar
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Does non-monotonicity imply non-satiation always? Why or why not?

I understand that monotonic preferences imply non-satiation. But I am not sure 100% if non-monotonic functions always have satiation. An intuitive and mathematical explanation would be very helpful.
Frodo Baggins's user avatar
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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% ...
George Ntoulos's user avatar
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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 ...
Ryan da Silva's user avatar
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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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