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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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Reconciling Continuity of Binary/Preference Relations with Continuity of Functions/Correspondences

There are various ways to express the concept of continuity of a binary relation, but one I've come across seems to imply the closed-graph property is sufficient. That is to say: For a nonempty set $X$...
hillard28's user avatar
2 votes
1 answer
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Equivalence of two definitions of monotone preference

In MWG, the definition of weak preference is for all $x,y \in X$, $y>>x$ implies $y\succ x$ . But I have read some other articles that define weak preference as $y\geq x\implies y\succeq x$. ...
Nonenicht's user avatar
1 vote
1 answer
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What are the most common axioms to define a strict preference relation?

I am wondering which are the standard axioms with which indifference and (particularly) strict preference are usually defined. Normally, a weak preference relation for agent $i$ on a set $X$, denoted $...
EoDmnFOr3q's user avatar
6 votes
1 answer
62 views

Question About Proving $\alpha(\cdot)$ is Continuous in the Proof of Proposition 3.C.1 from MWG

See Proposition 3.C.1 from MWG Continue from this post, Microeconomic Theory by Mas-Colell et al. book said the following: What remains is to establish that all convergent subsequences of $\{\alpha(x^...
Champa's user avatar
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Proof: Let $\epsilon>0$ and $x'\in\mathbb{R}^L_+$ be such that $\|x'-x\|\geq\epsilon$. Then $\alpha(x')$ belongs to some $[\alpha_0,\alpha_1]$

See Proposition 3.C.1 from MWG Continue from this post, the book (MWG) then started the proof that $\alpha(x)$ is a continuous function: We now argue that $\alpha(x)$ is a continuous function at all $...
Champa's user avatar
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5 votes
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Question About the Step Proving $\alpha(x)$ Represents Preferences in the Proof of Proposition 3.C.1 from MWG

Continue from this question, the book Microeconomic Theory by Mas-Colell et al. said We now take $\alpha(x)$ as our utility function; that is, we assign a utility value $u(x)=\alpha(x)$ to every $x$. ...
Champa's user avatar
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Question About the Step Involving the Connectedness of $\mathbb{R}_+$ in the Proof of Proposition 3.C.1 from MWG

This is a small issue, but it confuses me. In the proof of Proposition 3.C.1 of Microeconomic Theory by Mas-Colell et al, the book said ... $\mathbb{R}_+\subset (A^+\bigcup A^-)$. The nonemptiness ...
Champa's user avatar
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Revealed preferences - Commuter preferences

I'm working on a paper about commuter preferences and their level of satisfaction in a South American country. Do they prefer the metro or informal buses? That sort of thing. The data tells me that ...
KEll's user avatar
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Prove a preference preserved under limits if and only if its upper and lower contour is closed

I'm concerned with the reverse direction, that upper and lower contour is closed implies the preference is continuous, that is for any sequence $x_n$ and $y_n$, $x_n\succcurlyeq y_n$ for all $n$, ...
Nonenicht's user avatar
2 votes
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Positive monotonic transformation

I want to draw an indifference curve for this preference relation on $ℝ^2$ $$x ≿ y \leftrightarrow (x_1+x_2)^2 ≥ (y_1+y_2)^2$$ Can I just take the square root(and then drop the absolute value sign ...
Jonathan's user avatar
1 vote
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39 views

Indifference curves given preference relation

Let's say I have a preference relation on $ℝ^2$ given by $$x≥y \leftrightarrow x_1+x_2 ≥ y_1+y_2$$ So, from my understanding, the bundle x is preferred at least as much as the bundle y if and only if ...
Jonathan's user avatar
2 votes
0 answers
82 views

Prove that any lexicographic preference $(u_1,u_2)$ must be complete and transitive

Let $\succsim$ be a lexicographic preference represented with $(u_1,u_2)$. $x\succsim y$ if $u_1(x)>u_1(y)$ OR $u_1(x)=u_1(y)$ and $u_2(x)\geq u_2(y)$. Is it obvious that $\succsim$ must be both ...
dodo's user avatar
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Equivalent assumptions in Revealed Preference and Classical Preference Theories

I have read that there are dualities between Revealed Preference Theory and Classical Preference Theory. Suppose, I have $X$ as the set of all conceivable choices, and $\mathscr{B} \subseteq 2^X$ the ...
Ishan Kashyap Hazarika's user avatar
3 votes
1 answer
84 views

Question About Proof of Proposition 3.C.1 in MWG - Step 1

I have difficulties understanding the first step of the proof of Proposition 3.C.1 in MWG. Proposition 3.C.1$\quad$ Suppose that the rational preference relation $\succsim$ on $X$ is continuous. Then ...
Beerus's user avatar
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1 answer
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Understanding the definition of monotone

In Microeconomic Theory by Mas-Colell, Whinston, and Green, the definition of monotone preference relations is given as follows: Definition 3.B.2$\quad$ The preference relation $\succsim$ on $X$ is ...
Beerus's user avatar
  • 505
2 votes
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20 views

Preference aggregation rules that satisfy the property that the most frequent best alternative is the collective best alternative?

Let $X$ be the set of alternatives, and $(R_i)_{i\in N}$ a profile of partial orders for $n= \#N$ individuals. I make the assumption that those partial orders are so that they all give rise to one ...
MiKiDe's user avatar
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What is a utility function rationalizes these preferences?

For a consumer deciding between goods A and B, with a budget of w: If A and B are the same price (or if A is cheaper), the consumer will spend their entire budget on A. As the relative price of A ...
H Rogers's user avatar
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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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27 views

Varian Analysis Non satiation question

Consider preferences defined over the nonnegative orthant by (xl,x2)> (yl,y2) if X1 + X2 < y1+ y2. Do these preferences exhibit local nonsatiation? If these are the only two consumption goods ...
Chavi Dusad's user avatar
1 vote
1 answer
108 views

Cobb-Douglas utility function

Why in Cobb-Douglas utility function, the exponents have to sum to one? Can they not be equal to 1 and why?
Huy Lê Thanh's user avatar
1 vote
1 answer
40 views

Convex preference and convex utility

What are the differences between convex preferences and covex utility function? Why are convexity preferences usually represented by the quasi-concave function and not the convex function?
Huy Lê Thanh's user avatar
5 votes
1 answer
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Question on Isolating The Wealth Effect in Analysis of Changes in Price-Wealth Combinations - MWG Exercise 2.F.3 Parts (e) and (f)

I am doing exercises in Chapter 2 of MWG. I feel I got completely lost in exercise 2.F.3 parts (e) and (f). $\textbf{Exercise}$ Here is the question: I have solved parts (a) to (d). In particular, I ...
Shenron's user avatar
  • 105
3 votes
1 answer
143 views

Question on The Weak Axiom of Revealed Preference and The Definition of Revealed Preference Relation

I am solving the following problem (from Exercise 2.F.3 (b) in MWG) and I got confused by the weak axiom of revealed preference and the definition of the revealed preference relation. Here is the ...
Shenron's user avatar
  • 105
1 vote
0 answers
38 views

Considering there are four different goods {w,x,y,z}, how many different relations can be defined using all goods

In this problem, you can either prefer a good to another, disprefer a good to another or be indifferent between the two goods. While I have been able to do it mechanically, I am very confused as to ...
Sasha Blain's user avatar
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0 answers
23 views

What does GARP in revealed preferences mean and how to regocnize it graphically?

I have a froblem understanding GARP in revealed preferences. I know what WARP means, and that SARP adds transivity such that it allows for indirect preferences, but what about GARP? How can you ...
EcoSTUD233's user avatar
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0 answers
30 views

How do I prove 2 indifference curves have the same properties?

I understand questions a) but I'm completely stumped at c). What do they mean by U'=1 having same properties as U=10?? And w,for questions b and c, what are they asking by "general expression for ...
Jess Franc's user avatar
1 vote
1 answer
61 views

Stock market existence and saving money

I have a generic question that perhaps has more to do with psychology than with anything else. The question is, how effective is the stock market's existence in being effective in making people save ...
Joselin Jocklingson's user avatar
1 vote
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98 views

Proof for convex preference relation

⪰ is a strictly convex preference relation on a set X which is the set of all N-tuples of nonnegative real numbers. Further are x,y,z element of this set X and i have the preferences x ≻ y ≻ z given. ...
mediation_boy's user avatar
4 votes
1 answer
83 views

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 ...
High GPA's user avatar
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1 vote
1 answer
138 views

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 ...
dodo's user avatar
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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. ...
csilvia's user avatar
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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,...
Luka's user avatar
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1 vote
1 answer
123 views

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 ...
Beerus's user avatar
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1 vote
1 answer
92 views

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. ...
Froter's user avatar
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2 votes
1 answer
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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 ...
Kitsune Cavalry's user avatar
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1 vote
1 answer
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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 ...
dodo's user avatar
  • 293
2 votes
2 answers
368 views

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.
GraceLynn87's user avatar
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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 ...
Sperbs's user avatar
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0 votes
1 answer
743 views

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 ...
Huy Lê Thanh's user avatar
0 votes
0 answers
29 views

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?
Huy Lê Thanh's user avatar
3 votes
1 answer
155 views

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_{\...
Huy Lê Thanh's user avatar
3 votes
0 answers
102 views

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: $\...
High GPA's user avatar
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1 vote
1 answer
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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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0 answers
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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 ...
user10478's user avatar
  • 423
2 votes
2 answers
89 views

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 ...
tk420's user avatar
  • 21
3 votes
1 answer
181 views

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-...
Peter's user avatar
  • 33
4 votes
2 answers
189 views

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 ...
CormJack's user avatar
  • 991
1 vote
0 answers
93 views

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 ...
Nicolas Torres's user avatar
3 votes
1 answer
153 views

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 ...
CormJack's user avatar
  • 991
0 votes
2 answers
133 views

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,...
Kerrick Staley's user avatar

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