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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30 views

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 ...
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37 views

A matter of completeness and preference relations [closed]

I have a question about preference relations and completeness. Prove that: i) There exists a complete relation $\succcurlyeq$, such that $\sim$ is not complete. ii) There exists a complete relation $\...
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56 views

How to solve a general equilibrium problem with lexicographic preferences?

I have been unable to find a good example of this type of GE problem in our textbooks, and our professor has indicated that something like this may appear on our exam. So, here is a hypothetical ...
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1answer
62 views

Is electoral abstention an example of non-complete preference?

In order for a preference to be rational, it has to be transitive and complete. Complete preference means that any two different bundles can be compared. I.e., a consumer can weakly prefer bundle X ...
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58 views

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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43 views

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 ...
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31 views

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 ...
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1answer
49 views

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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215 views

Violation of Monotonicity of preferences

Hi I am reading Jehle and Reny in my master's course and I have come across a problem in one of the exercises. My instructor herself was a bit confused when a student gave her a counter-example and ...
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17 views

Asking for reference of trading strategy without inherent preference?

Han et. al.,2021 mentioned that So in contrast with traditional behavioral finance models, active strategies tend to spread through the population even if investors have no inherent preference for ...
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53 views

Part of proof of Gibbard-Satterthwaite Theorem

I'm currently working through Nisan's Algorithmic Game Theory, Chapter 9 (Introduction to Mechanism Design). A part of the proof for the Gibbard-Satterthwaite Theorem is given as "obvious," ...
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26 views

Does the second derivative of a concave function need to be negative? [closed]

I have just watched the first part of this video and noticed that the second derivative of the utility function is positive. But I thought the second derivative had to be negative to be a concave ...
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197 views

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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How to explain satiated preferences with algebra?

From looking at the graphical illustrations, I understand that satiated preferences violate the monotonicity assumption. I was wondering if there is algebra which can be used to show this?
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74 views

Can any three of the four vNM axioms (of expected utility theory) be satisfied without satisfying the fourth?

Is it true that any three of the four vNM axioms (of expected utility theory) can be satisfied without satisfying the fourth? Any examples which support such claim? Basically I'd like to prove that ...
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43 views

How do you establish uniqueness of a rational preference relation?

Going through a proof in Mas Colell and I am not understanding how (iii) shows uniqueness of the rationalizing preference relation. I understand that well $\beta$ is the power set so it contains all ...
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1answer
129 views

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^{(...
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48 views

Is this Incomplete or Indifferent? [closed]

Given X = {1,2,..., 100}. For x, y in X, define x # y if and only if x - y is a positive prime number. Is the # relation incomplete? I don't particularly understand the reasoning as of yet, and though ...
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Comparing voting methods when there are only two voters

Consider the Schulze, Kemeny-Young, Ranked Pairs and Borda count voting methods. (The last is obviously the odd one out in this list!) Suppose that there are only two voters. Each voter gives a ...
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255 views

Are Indifference Curve graphs continuous given the preferential definition of continuity?

Assume the relation $\succeq$ is continuous (by the preferential definition). Does this mean the graph of Indifference Curves are continuous? Since $\sim$ satisfies the definition for $\succeq$, we ...
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198 views

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 ...
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95 views

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 ...
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72 views

King–Plosser–Rebelo Preferences and Additively Separable

The wiki of King–Plosser–Rebelo preferences says that the utility function has the multiplicatively separable form $$u(C, L)=\frac{1}{1-\sigma_{c}} C^{1-\sigma_{c}} v(L)$$ and "in the limit case ...
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68 views

How are weak preferences different to strict preferences/indifference?

Given a utility function $u(\cdot)$ and two bundles $x$ and $y$. Assuming $u(x)=u(y)$. I am to prove or disprove that $x \succcurlyeq y$. Now I'm confused by this. We say $x$ is strictly preferred to $...
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95 views

The Price and Demand Index in Homothetic Kimball Utility

Suppose with Kimball preferences, utility $Q$ from consuming $\left\{q_{\omega}\right\}_{\omega \in \Omega}$ is implicitly given by $$\int_{\omega \in \Omega} Y\left(\frac{q_{\omega}}{Q}\right) d \...
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1answer
99 views

The Intuition of CES Utility

Suppose a (symmetric) CES utility function $$U(\mathbf{x})=\left[\int_{\Omega}\left(x_{\omega}\right)^{\frac{\sigma-1}{\sigma}} d \omega\right]^{\frac{\sigma}{\sigma-1}}, \sigma>1$$ 1 The indirect ...
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Definition of strictly convex preference

Let $x,y\in X$. Does strictly convex preference (which implies that the utility is strictly quasiconcave) mean that: $x\succsim y$ implies $\alpha x+(1-\alpha)y\succ y$ for any $\alpha\in (0,1)$?
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Social welfare in terms of preferences

How does one define a social welfare in terms of individuals’ preferences $\succeq_i$? If we have utility functions $u_i$ then a social welfare maximizing outcome $x$ is simply one that maximizes $\...
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132 views

Convex rationalization when the budget sets are segments?

Backgroud: SARP can be defined on general budget set. SARP: Assume for all $B$ the choice $c(B)$ is only one element. If $x_i,x_{i+1}\in B_i$, and $x_i = c(B_i)$, for all $i\in \{1,N-1\}$, then $x_1=...
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1answer
463 views

How to prove that a utility function U(x,y)=min(x,2y) is quasiconcave?

I have a question that asks: "Let there be two goods 1 and 2.Let $x$ and $y$ denote their respective quantities.$(x,y)$ represents a bundle. Suppose a consumer’s preferences over bundles in $R^2_+...
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245 views

Necessary and sufficient conditions for the existence of a utility function

I was reading Jehle and Reny, Advanced Microeconomic Theory, where they discuss in detail, the choice problem of a consumer. The Consumption Set (or Choice Set) $X$ is a subset of $R_+^n$, is closed ...
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1answer
87 views

Local nonsatiation

Suppose that $x^*$ satisfies $x^*\succsim x$ for $\forall x\in\{{x∈X|p·x\leq m}\}$. How can we prove that $x\succsim x^*$ $\Rightarrow$ $p·x≥m$ if $\succsim$ is locally nonsatiated? My idea for this ...
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44 views

What is the usefulness of Cobb Douglas functions? Why do we use them so often?

Hard to find much explanation as to why we generally use CD functions so often. My understanding is that it is usually well behaved when used for utility functions and preferances, since it is convex,...
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48 views

Assumptions on preference relation

This question is from Harvard seminar problem set (Q-3 part b) https://www.studocu.com/en-us/document/harvard-university/economics/mandatory-assignments/econ2020a-14-ps01-please-give-as-much-...
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96 views

max{x1,x2} where P1not=p2

I have seen min{x1,x2} functions representing perfect compliments but have never seen a max{x1,x2} function anywhere in my book or lectures, I also have never seen anything about p1 not equaling p2. ...
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149 views

Utility function for introductory microeconomics

What are the utility functions standardly used in introductory microeconomics courses. My own list would include Perfect substitutes: $U(x,y) = ax+by$ Perfect complements: $U(x,y) = \min(ax,by)$ Cobb ...
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1answer
91 views

Market with changing number of goods and services

In the General Equilibrium framework of Arrow, Debreau and others, there are a fixed number of commodities, which I feel is a valid assumption in the short run but maybe not in the long run. Over time,...
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1answer
74 views

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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64 views

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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28 views

Question regarding preferences in Gale and Shapley (1962)

Is it correct to say that preferences in the classic Gale and Shapley College Admissions problem are quasi-linear? Or is this something thats introduced later in the literature, vis a vis Shapley and ...
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1answer
49 views

Can you please help me find this topic in Mechanism design/Rational choice theory?

When I was in university, I remember studying some kind of topic in adv microeconomics where someone gives you three options, where one is obviously worse and is put there just to deceive you so that ...
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1answer
55 views

If a rational preference relation over simple lotteries $\succsim$ are convex then they satisfy independence?

Let´s say there is an uncertain situation with $N$ possible consequences $C = \{C_1, . . . C_N\}$. Assume that there is a rational preference relation $\succsim$ over simple lotteries. I know that if ...
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1answer
90 views

Quadratic utility: monotonicity and risk aversion

I am taking macro class this fall. One of the problems asks whether decreasing absolute risk-aversion and ever-increasing consumption are two unattractive implications of the quadractic utility ...
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64 views

A question from MWG 2F12

This question is from MWG if walrasian demand function is generated by a rational preference relation then it must satisfy weak axiom. I cannot prove this statement. How can I do?Thanks alot.
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239 views

which type of goods maximum utility function represent?

I am not sure, which type of goods does the maximum utility function represent i.e., $U(X_1, X_2) =\max(X_1, X_2)$. As the $U(X_1, X_2) =\min(X_1, X_2)$ represent the complementary goods, and $U(X_1, ...
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130 views

MATLAB code: Plot utility function and budget constraint

how do i plot these? i have this utility function: $$U(x_1,x_2)=\log(x_1)+\beta \log(x_2)$$ and this budget constraint: $$p_1 x_1+p_2 x_2=R$$ where $R=3, p_1=0.5, p_2=0.5$ i dont know how to plot ...
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1answer
249 views

Rational preferences/individual decision-making theory

I am taking advanced micro course this semester. In one of the problems we need to determine whether the preference relation is rational (i.e. complete and transitive). Since we have not really ...
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1answer
218 views

Proof on weak axiom of revealed preferences

I read the following statement. “ A utility maximizer with strictly convex and strongly monotonic preferences satisfies weak axiom of revealed preferences.” How can I prove or show this? I cannot ...
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1answer
47 views

Measuring and assigning utility numbers

I was recently introduced to the concept of cardinal utility. In real life, how do we assign these utility levels? For example if i wanted to assign numbers to my own utility indifference curve for ...
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47 views

Does transitivity qualify as a reason for Indifference curves intersecting each other?

Transitivity in preferences seems as a flawed concept because there might be a situation where A>B, B>C but A<C. Going by this analogy it seems that it does not qualify as a reason for ...

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