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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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 $A$,...
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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
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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
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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
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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 ...
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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
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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 ...
Huy Lê Thanh's user avatar
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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?
Huy Lê Thanh's user avatar
3 votes
1 answer
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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_{\...
Huy Lê Thanh's user avatar
3 votes
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101 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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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-...
Peter's user avatar
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4 votes
2 answers
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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 ...
Nicolas Torres's user avatar
3 votes
1 answer
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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 ...
CormJack's user avatar
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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,...
Kerrick Staley's user avatar
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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 ...
CormJack's user avatar
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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 ...
Joao Francisco Cabral Perez's user avatar
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1 answer
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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 ...
papagena's user avatar
2 votes
1 answer
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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 ...
DRM's user avatar
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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, ...
aliosha karamazov's user avatar
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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 (...
aliosha karamazov's user avatar
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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 ...
aliosha karamazov's user avatar
2 votes
2 answers
161 views

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?
aliosha karamazov's user avatar
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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 ...
aliosha karamazov's user avatar
1 vote
1 answer
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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:
josephjones1472's user avatar
1 vote
1 answer
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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}...
cfp's user avatar
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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 ...
aliosha karamazov's user avatar
2 votes
1 answer
185 views

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 ...
aliosha karamazov's user avatar
1 vote
1 answer
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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 ...
aliosha karamazov's user avatar
1 vote
1 answer
34 views

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, ...
aliosha karamazov's user avatar
3 votes
1 answer
110 views

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 ...
Maximilian's user avatar
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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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