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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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what is monotonicity and strict monotonicity in preferences?
I am really confused between monotonic preferences and strictly monotonic preferences, I saw some video and read certain answer where it is mentioned that the
When preferences are monotone / weak ...
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Showing utility function gives preferences that are rational and convex
Consider a consumer with preferences relation $\succsim$ over non-negative commodities $x_1$ and $x_2$ such that their utility U = $x_1$ + $\ln(x_2)$
Are these preferences rational and are they convex/...
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Understanding the Choice Rule in MWG
I am reading the Microeconomics Theory book by MWG, and I am having a tough time interpreting what things mean to a real life example, so any help would be appreciated.
For example, it gave this. ...
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HARA preferences details
I am searching for some exntensive details about HARA preferences. Where could I find some extensive details for HARA preferences? Something like a textbook or notes
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Could lexicographic preferences on N^2 be represented by a utility function u: $N^2$ to $Z$?
I got this question on a homework:
Could lexicographic preferences on $N^2$ be represented by a utility function u: $N^2$ to $Z$?
I've heard countless times that lexicographic preferences can't be ...
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What is the observable definition of "preference" by Frisch?
To make things weird, although Frisch was fully aware of the importance of random distribution in economics relations, he never mention the randomness in binary preference relations!
How to define ...
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Question about Strict Preference Relation
Strict Preference usually states that
x is strictly preferred to y if : < x is weakly preferred to y and not y is weakly preferred to x >.
Let me split the < > part into two segments:
x ...
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Strictly increasing but not convex preferences
Is it possible to have preferences that is strictly increasing but not convex?
Will perfect substitutes indifference curves show strictly increasing but not convex preferences? I am confused, as won't ...
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Binary relation on the set $X = \{v, w, x, y , z\}$ that is asymmetric and transitive but not negatively transitive
So I am trying to find a binary relation on the set $X = \{v, w, x, y, z\}$ that is asymmetric and transitive but not negatively transitive, and is quite tricky.
Will $R = (v, w)$ be asymmetric and ...
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Prove that Choice Coherence Implies IIA
Prove that Choice Coherence implies Independence of Irrelevant Alternatives (IIA).
From the definition of choice coherence, we have this:
A choice function c satisfies choice coherence if, for every ...
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MWG_3D4_C, why the solution seems in reverse?
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 is ...
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Convex Preference but Convex Utility
Can preference be convex when utility is not a concave function (e.g. $U=x_1^2 + x_2^2$)?
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What are the correct utility functions?
It is common to talk about utility functions. For example in a universe with only two goods, we might assume each person (or group of people) carries a function $u(x,y)$ in their heads. When offered ...
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Are Cobb-Douglas preferences monotone according to the marginal utility condition?
I understand that Cobb-Douglas preferences represented by $U(x,y)=x^ay^b$ are strictly monotonic, because increasing at least one of the goods in the bundle increases utility.
However, another ...
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Expenditure function. Prove that this set is bounded
I need to prove that the following set is bounded in order to derive the expenditure function:
$e(p,v)=min_x px$
ST
$\{x \in R^n_+$ such that $U(x)\geq v\}$.
Knowing that $U(x):R^n \longrightarrow R$ ...
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Examples of risk-neutral firms or people in business
I am looking for examples of approximately risk-neutral firms or people in business.
Is there an industry where risk-neutrality is common for some agents (firms or people)?
Are there perhaps time ...
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Remove Linear Good From Quasi-linear Utility Function
Given a quasi-linear utility function: $u(x_1, x_2) = f(x_1) + \beta x_2$, $\beta > 0 $
What would happen if good 2 ($x_2$) is removed from the market? Would the new utility function be: $u(x_1) =...
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Differentiability of the utility function and indifference curves
Comment on the following affirmative:
In the traditional consumer model, the hypothesis of differentiability of the utility function and of convexity of preferences, assure the indifference curves ...
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Ordering of bundles for which the axioms of transitivity, continuity, strong monotonicity and convexity are valid
Let there be two bundles which are obtained from the sequences $x^n = (x_1,x_2)= \left( 2 + \frac{1}{n},5 \right)$ and $y^n = (y_1,y_2) = \left(4 + \frac{2}{n}, 5 \right)$. Is it possible to obtain an ...
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Show that if $\succsim$ is continous on $X$, then the sets $ \precsim (x^0)$ and $\succsim (x^0)$ are closed
For a set to be continuous, it's contour sets must be closed. Since we can define $$ \succsim x^0 = \{x, x^0 \in X: x \succsim x^0 \} $$ and $$ \precsim x^0 = \{x, x^0 \in X: x \precsim x^0\}$$
it ...
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Strong monotonicity and weak monotonicity
We say $\succsim$ represents weak monotonic preferences if $$x,y \in X, \,\, y >> x \implies y \succ x $$
where $y >> x$ means that every element of $y$ is greater than every element of $...
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Completeness of the strict binary relation
How do I show that considering the preference relation $\succsim$, then $\succ$ is not complete?
I tried the following (which I don't know if it's right) but I'd also like to know if it's possible ...
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Is the satisficing choice function rationalizable if the ordering isn't observable?
Edited: Say an observer observes only the choices made by the decision maker (and the sets from which these choices are made), but does not know the ordering. Then would the decision maker's choices ...
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How to describe a utility function in words?
Suppose I have a utility function of Cobb-Douglas form
$$U(x, y) =x^{0.2}*y^{0.8}$$
I want to describe it in words. I would say like:
The utility of consumer is captured by number of good x and ...
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$a\geq 0$, $x\succsim y$ implies $x+a\succsim y+a$ so the preference is linear?
$\succsim$ is a continuous and local non-satiate weak order.
$x,y,a$ are vectors in $\mathbb R^n$
We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero.
We want to prove (or ...
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Continuity of preferences
Let $\succsim$ be a transitive and reflexive relation on a metric space $X$ with closed upper and lower contour sets. If $\succsim$ is not complete, does it hold that: for all converging sequences ...
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$a\geq 0$, $x\sim y$ implies $x+a\sim y+a$ so the preference is linear?
$\succsim$ is a countinuous and convex weak order.
$x,y,a$ are vectors in $\mathbb R^n$
We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero.
We want to prove (or ...
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