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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3
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1answer
53 views

Can we have a Non-Reflexive Preference Relation?

I've been thinking about preferences alot recently and have been specifically thinking about the reflexivity requirement. That is: $$x \succsim x$$ Though this is apparent and obvious, I have been ...
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79 views

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),\...
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1answer
29 views

Question about the relationship between Weak Axiom and Slutsky Matrix

We know that if a differentiable Walrasian demand function $x(p,w)$ satisfies Walras' law ($p^Tx=w$), homogeneity of degree zero ($x(\alpha p,\alpha w)=x(p,w)$), and the weak axiom of revealed ...
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33 views

Why does Figure 2.F.1(b) (MWG page 30) satisfy the WARP (Definition 2.F.1)?

I can see that Figure 2.F.1(a) satisfies the WARP (Definition 2.F.1) in MWG (page 30). However, as the choice $x(p',w')$ is only feasible under the price-income level $(p',w')$ and $x(p'',w'')$ is ...
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43 views

Cardinal Voting, Incentive Compatibility and Secrecy

Is there any available/feasible/practical way to make a Cardinal Voting both Incentive Compatible and Secret? A method to make a cardinal voting incentive compatible would be to force them to put ...
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1answer
57 views

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 ...
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2answers
47 views

Why is the nature of graph of utility function different from indifference curve?

I am new to Economics, but I have this doubt. The indifference curve and utility function both have the same equation, so their graph must also be similar, which is true I guess. Then why is it that ...
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28 views

Heckscher-Ohlin with non homothetic preferences [duplicate]

Can someone tell me how I can show with an example that the Heckscher-Ohlin result does not necessarily hold when preferences are not homothetic. I was asked if it similar as a case in which the ...
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44 views

Heckscher-Ohlin with heterogeneous preferences

could someone really help me out I would need to show a situation in which the Heckscher-Ohlin result does not necessarily hold when preferences are heterogeneous. Does someone have an idea how I ...
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1answer
82 views

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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35 views

Does quasilinear preference contain rationality, monotonicity or other assumptions?

I have a question when I'm doing exercise 3.C.5(b) of MWG. The exercise asks to prove that a continuous preference on $(-\infty,\infty)\times R^{L-1}_+$ is quasilinear with respect to the first ...
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78 views

Weakly monotone preferences with singleton indifference curves: do any of them admit a utility representation?

Inspired by this question. The original question was answered by Amit with some nice examples. I would like to know the generalized answer: Suppose we have a preference ordering $\succeq$, which is ...
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1answer
38 views

Why might a monotone increasing but nonlinear transformation of a utility function not represent the same preferences?

According to a textbook, a monotone increasing but nonlinear transformation of a utility function might not represent the same preferences. Why is it so? An example of such preference would be ...
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1answer
53 views

Why is a monotone increasing but nonlinear transformation of a utility function not represent the same preferences if the preference is complete?

According to a textbook, in the context of uncertainty (e.g. in lottery), if the preference is complete, a monotone increasing but nonlinear transformation of a utility function would not represent ...
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Kreps Porteus Certainty Equivalent Intuition

In Epstein-Zin recursive preferences, the Kreps-Porteus certainty equivalent is defined by \begin{equation} \mathcal{R}_t(V_{t+1}) = (\mathbb{E}_t V_{t+1}^{1 - \gamma})^{1 /(1 - \gamma)}. \end{...
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2answers
48 views

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.
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1answer
39 views

Why does quadratic utility function imply $\mu-\sigma$ preference?

Why does investors having quadratic utility function mean that their optimal portfolios can be chosen by only considering mean and variance of returns i.e. imply $\mu-\sigma$ preference?
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Net Preference Relations

Let say the electorate consists of three segments of voters: 1, 2, and 3 with corresponding weak preference relations defined over the candidates. Let the preferences be given by -- Segment 1: Biden >...
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1answer
19 views

Given a rational $\succsim$ over a finite set $X$, show that there exists $x \in X$ such that $x \succsim y, \forall y \in X$

I have been able to show this constructively, but would like to prove it by induction. However, I am stuck with the induction step: Consider $\succsim$ defined over $X=\{x_1,...,x_n\}$ and where ...
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1answer
47 views

Study whether $\succsim$ represented by $u(x)=\lfloor x \rfloor$ is continuous

Using the following definition of continuity: $\succsim$ is continuous if for any bundles $x,y,z$ such that x$\succ$y$\succ$z, there exists $\alpha \in (0,1)$ such that $\alpha x + (1-\alpha)z \sim y$....
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A preference relation $\succ$ is defined as $(x_1,y_1)\succ (x_2,y_2)$ if $x_1>x_2$ and $y_1> y_2$

Does this satisfy completeness property? I need an intuitive explanation of this preference relation as well. I am confused about the way how this relation is defined. The commodity Y in the first ...
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1answer
53 views

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% ...
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2answers
96 views

Assumption of sufficient wealth in quasi-linear preferences

Whenever we talk about quasi-linear preferences, we assume that the consumer is sufficiently wealthy. As far as I understand is that we need that assumption in order to obtain an interior solution. ...
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1answer
46 views

Representing preference orderings over a finite set of outcomes by two payoffs

I have read the following statement and I am having difficulty understanding the second part: Any set of preference orderings over a finite set of outcomes can be represented either by ...
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87 views

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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1answer
219 views

Preference: Convexity and Monotonicity

I need an example of a Convex, non-monotonic preference Non-convex, monotonic preference I figured that an example of non-convex, monotonic utility preference could be $U(x,y)=x^2+y^2$. For convex, ...
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2answers
68 views

The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them?

I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality. But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
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91 views

Everyone has the same marginal rate of substitution

I'm currently reading Varian's Intermediate Microeconomics and what struck me, is this statement on page 89 of the 8th edition. If everyone faces the same prices for the two goods, then everyone ...
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77 views

Linear Homothetic Utility

A Homothetic Utility is where $$ \forall x,y, \forall a \in \mathbb{R}_+: \ u(ax,ay)=au(x,y) $$ (or its monotonic transformation). A linear Homothetic utility is defined as $$ \forall x,y, \forall ...
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1answer
47 views

If an ordinal-scaled utility function is defined via strictly increasing transformation, how can it represent a case of indifference?

Problem: According to Wulf Gaertner’s (2009, p. 13) A Primer in Social Choice Theory, any strictly increasing transformation of an individual’s ordinal utility function is informationally equivalent. ...
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1answer
72 views

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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14 views

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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1answer
34 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 ...
2
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1answer
150 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
24 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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21 views

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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1answer
71 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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2answers
62 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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1answer
132 views

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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1answer
192 views

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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2answers
91 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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2answers
183 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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2answers
74 views

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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1answer
120 views

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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1answer
237 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
140 views

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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2answers
175 views

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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0answers
172 views

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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1answer
57 views

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 ...
2
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1answer
91 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 ...