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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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 ...
2 votes
1 answer
39 views

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 ...
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1 vote
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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, ...
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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 (...
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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 ...
2 votes
2 answers
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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?
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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 ...
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:
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Help with checking work for utility preferences 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: Part a. Part b.
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}...
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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 ...
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1 answer
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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 ...
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 ...
1 vote
1 answer
27 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, ...
3 votes
1 answer
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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 ...
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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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2 votes
2 answers
281 views

Are the indifference curves for bads concave?

While I was studying microeconomics, a question arose: I know what the indifference curve for one “good” good and one “bad” good looks like. But if both goods are bad, is the indifference curve ...
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3 votes
1 answer
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Example of consumer preferences that switches from being concave to being convex

Question Is there an example of consumer preferences over consumption bundles $(x,y)\in \Bbb R^2$ that would be concave when $x$ is abundant relative to $y$ and convex otherwise? Are there known ...
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Decomposition of preferences into set of CES functions

CES function as a tool Hello everyone, I have this idea: CES function basically tells us what is the elasticity of substitution between two (and more) goods, therefore giving us the exact complement/...
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2 votes
1 answer
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State dependent preferences vs state independent preferences in utility theory

I am working on changes in preferences and found papers on state-independent preference. What is the difference between state-dependent and state-independent preferences and utility functions? What ...
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32 views

Which Choice Rule follows Always Chosen axiom and No Binary Cycle axiom?

Source: taken from ISI PhD entrance exam questions.
2 votes
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Does consumer demand in the secondhand market actually affect the firsthand market for high-cost goods

In the 21st Century, there is an increasing consumer awareness of the externalities of manufacturing and along with it a stronger consumer preference to buying used goods rather than new. My question ...
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1 vote
1 answer
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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 ...
2 votes
1 answer
60 views

How to prove that any preference relation on (countable) X has a utility representation with a range (0,1)?

Theorem: If $X$ is countable, then any preference on $X$ has a utility representation with a range $(0,1)$. The stated proof in Rubinstein's lecture notes: Proof: Let $\{x_n\}$ be an enumeration of ...
2 votes
1 answer
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Can "thick preferences" be represented by a utility function?

From microeconomics, $u$ is strictly quasi-concave if for all $x\ne y\in\mathbb{R}^2_+$ and $t \in (0,1)$, if $u(x)\ge u(y)$, then $u(tx + (1-t)y)>u(y)$. You may also check the figure below. Here ...
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1 answer
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Is the leontief utility function homogeneous of degree zero? And if that is true, how can that be prove? [closed]

I have not been able to find a mathematical prove is such statement.
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Shape of indifference curves and quasi-concavity of utility

So my professor told that quasi-concave utilities lead to convex preferences/indifference curves. I have some conceptual problems understanding this statement. Indifference curves are plotted from ...
1 vote
2 answers
230 views

Intuitive Explanation of Convex Preference

Could you explain intuitively why the phenomena of convex preference exist in the market?
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1 answer
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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/...
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1 answer
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Can every continuous preference relation be represented by a discontinuous utility function?

In this question, it is shown that a continuous preference relation can have a discontinuous utility function. Is it true in general that every continuous preference relation must have a discontinuous ...
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Indifference curves drawing

Can indifference curves be drawn when we know only preference relation that defined below? To be precise about condition given: $[x_1 > x_2] or [x_1 = y_1$ and $ x_2 ≥ y_2]$ I’ve tried to find an ...
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120 views

Strict preference relation implies weak preference relation

Condition A: Given x, y in X such that $yRx$ then it follows that $\lambda y +(1-\lambda)xRx$ for all $0< \lambda<1$ Condition B: Given x, y in X such that $yPx$ then it follows that $\lambda y +...
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Cost, disutility and loss aversion applied to a queuing system

I am currently working with a queueing system where customers enter a system and are served. Service takes a random amount of time $\Delta t \sim F(\cdot)$ where $F:\mathbb{R}\to[0,1]$ is a cumulative ...
2 votes
1 answer
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On risk aversion and validity of 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. The investor has a current ...
1 vote
1 answer
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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 $w$, ...
2 votes
1 answer
334 views

A preference relation is continuous if and if there exists a utility function that represents it

Suppose that $X \subset \mathbb{R}^n$. A preference relation $\preceq$ is reflexive, complete, transitive and continuous if and only if there exists a utility function $u:X \rightarrow \mathbb{R}$ ...
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strict monotonicity definition in Reny textbook and strong monotonicity

Reny-advanced microeconomic theory-page 10 wiki-monotonicity preference This capture is the definition of strict monotonicity in Reny's textbook, and I've compare it with wikipedia also other ...
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In Austrian economics, do producers have an ordering of preferences similar to consumers?

I watched a video from the Mises Institute where the lecturer mentioned that in Austrian economics, the consumer behavior that is observed is a result of their perception of the utility of the ...
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3 votes
1 answer
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Indifference curve - corner point - Q about notation

I wonder if someone can help me interpret the vertical bar notation used in the picture. From the graph, it is apparent that the consumer will consume only good $x_1$, since the indifference curve is ...
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Is it possible to have mean-variance preferences with different states of nature? Mean-Variance and Expected utility together?

I have to maximize mean-variance preferences like this (where Pi is a profit function): \begin{align} \label{eq:9} \max\limits_{Q_{F}^{\{x\}}}Z_{w}= E[\pi{\{x\}}]-\frac{A}{2}Var[\pi{\{x\}}] \nonumber\\...
3 votes
1 answer
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Convexity of preferences (dissimilar definitions)

Varian's Intermediate Microeconomics describes convexity as $$\text{Given } x, y \in X: x \sim y \implies \forall t \in [0,1], tx + (1-t)y \succeq x,y$$ The other definition I read everywhere is: $$\...
0 votes
1 answer
130 views

Are these preferences locally non satiated? U(x1,x2)=(x1-1)/(2-x2)^2

I got this utility function representing certain preferences. Are these preferences locally non satiated? Can somebody please explain me with the exact definition of local non satiation why these ...
0 votes
2 answers
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Does Concavity or quasi-concavity imply local non satiation?

I got a utility function with convex Indifferences curves and therefore convex preferences. Convexity of preferences implies Quasi-concavity. I would like to know if there is a relation between ...
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Representation theorem for $\succsim\supset>\cup\sim$

On $\mathbb R^2$, define $x=(x_1,x_2)>(y_1,y_2)=y$ if $x_i\geq y_i$ for all $i$ and $x_j>y_j$ for some $j$. Let $\sim $ be an equivalence relation that $x\sim y$ implies $x\not> y$. Define ...
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Proof that weak Monotonicity and local non satiation imply monotonic preference

Weak monotonicity in my case is defined as follows: If x is weakly larger than y, then x must be weakly preferred over y. Monotonicity is defined as follows: If x is strictly larger than y, then x ...
1 vote
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Say a preference is "constant“, by analogy with a constant function

Let $f$ be a function with range of $\{-1,1\}$ and $f(x,y)=-f(y,x)$. Let the preference $\succ\subset X\times X$ where $x\succ y \iff f(x,y)=1$. In math we can define $f$ to be a constant function on ...
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Is this a function or vector space?

I want to make a function that states consumer $i's$ consumption $C_i$ in a shared bundle $X^n$ $\subset$ $\mathbb R^n$ depends on their preferences. That is, something like $C_i(\succeq_i)$. Since $\...
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1 vote
1 answer
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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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4 votes
1 answer
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Does Debreu's representation theorem of ordinal utility require Hausdorff topology?

By Debreu's theorem of ordinal utility, any continuous weak order on $X$ is represented with a continuous utility function, if $X$ is a second countable or connected separable topological space. My ...
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Preference notation by agent $i$

I want to say that the preferences of agent 1 on a consumption set $X$ are the same as agent 2's and the inverse of agent 3's (hence 2's is also the inverse of 3's). How would I do this using the ≽ ...

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