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 ...
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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 ...
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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 ...
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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 ...
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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.
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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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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 ...
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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 ...
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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, ...
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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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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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Example of consumer preferences that switches from being concave to being convex
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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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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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Which Choice Rule follows Always Chosen axiom and No Binary Cycle axiom?
Source: taken from ISI PhD entrance exam questions.
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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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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 ...
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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 ...
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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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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 ...
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Intuitive Explanation of Convex Preference
Could you explain intuitively why the phenomena of convex preference exist in the market?
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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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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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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 ...
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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 ...
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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 $w$, ...
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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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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\\...
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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: $$\...
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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 ...
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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 ...
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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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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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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 ≽ ...
