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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Lexicographic preference relation cannot be represented by a utility function

I am stuck on the following exercise, related to preference relations and von-Neumann-Morgenstern utility function. A farmer wants to dig a well in a square field $[0,1000]\times[0,1000]$. The ...
Erel Segal-Halevi's user avatar
13 votes
4 answers
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What is the definition of exogenous and endogenous preferences?

Wikipedia states: Exogenous Preference -- one that comes from outside the model and is unexplained by the model. Endogenous Preference -- preferences then cannot be taken as given, but are affected ...
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What is the difference between "aggregation" and a "representative agent?"

What is the difference between "aggregation" and a "representative agent?" I'm sorry if I'm not entirely clear on this question, but that's why I ask. It seems to me as if a representative agent is ...
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(Preference Relation/Set) Continuous $\succsim$ imply closedness of upper and lower contour sets

[ADDED/MODIFIED] : I have put my proof where the commodity space is simply $\mathbb{R_+}$(e.g. nonnegative reals) for simplicity below. Please share your 2 cent. I have put words to aid my own ...
Frank Swanton's user avatar
4 votes
1 answer
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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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What is an example of a utility function where one good is inferior?

Say the consumer has a standard convex, monotonic preference over Apples and Bananas. (Update: I'd like the preference to be as 'standard' as possible. So ideally we have diminishing MRS everywhere ...
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7 votes
1 answer
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Lexicographic Preference Relation on the QxR

I would like to ask for your help. I recently learned that the Lexicographic Preference relation can be represented by a utility function $u:X\to\mathbb{R}$ on $\mathbb{Q}\times\mathbb{R}$ (but not $\...
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Local Non-Satiation Proof

I have been having trouble with how to go forward with a proof for about three days now. I know the basic structure of the proof, but can't seem to construct it. Basically, I am trying to do a proof ...
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3 answers
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Preferences where wealth effect dominates

King-Plosser-Rebelo preferences satisfy balanced growth requirements, we have that income and substitution effects of labor cancel. Labor does not respond to a change in the wage level. Greenwood-...
FooBar's user avatar
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Monotone transformation of utility

We have learned that any "strictly positive monotonous transformation" of utility functions is okay, as long as they preserve the ranking of choices implied by the underlying preferences. Consider $U(...
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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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Mathematical definition of perfect substitutes

If $X$ and $Y$ are perfect substitutes such that a unit of $X$ can be replaced by $n$ units of $Y$, how do we get the mathematical equation from it? I know the equation is of the form $ax+by$ (and $U =...
not tdm's twin's user avatar
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1 answer
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Marginal utility meaning and properties

Consider goods $X$ and $Y$ such that the marginal utility of a unit of good $X$ is always that of $n$ units of good $Y$. $X$ and $Y$ are perfect substitutes. Question 1: What does the above mean ...
not tdm's twin's user avatar
9 votes
2 answers
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Thin indifference curves

If a consumer follows the rationality axiom of continuity (i.e. no jumps in his preferences), the indifference curves of a utility function are said to be thin. Why does continuity ($x \succeq y \...
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Existence of utility representation of a rational but discontinuous preference

This is related to Do discontinuous preferences imply no continuous utility function? I think the title of the above-linked question is phrased in such a way that obscures a subtly different but more ...
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Risk Premium in the Expected Utility Theory

Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have $$ Eu(w+x) = u(w+E(x)-R). $$ The classical derivation ...
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Generalized KPR: Frisch Elasticity

Consider the following version of KPR preferences (with $l$ being leisure): $$ U(c,l) = \left(\left(c\right)^\gamma l^\omega\right)^{1-\sigma}$$ I'm after the Frisch elasticity: $$ \frac{\partial(1-...
FooBar's user avatar
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5 votes
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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 ...
Jesper Hybel's user avatar
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Do discontinuous preferences imply no continuous utility function?

I am trying to think of a preference relation that can be represented by a utility function but such that there does not exist a continuous utility function. I know that you can represent continuous ...
user345's user avatar
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Is MRS supposed to have a minus sign or not? What's there to say about convexity of preferences?

If we have a utility function $U(x_1, x_2) = x_1(x_2+1)^2$ of some consumer, then $$MRS_{x_1, x_2} = \frac{\color{red}{-}(x_2+1)}{2x_1}$$ Some books have a $\color{red}{-}$. Others and Wiki don't ...
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What utility functions are equivalent to additive functions?

Call a utility function $u(x,y)$ additive if there exist functions $v_x,v_y$ such that: $$u(x,y)=v_x(x)+v_y(y)$$ Consider the function $u(x,y)=xy$. It is not additive, but, it can transformed using a ...
Erel Segal-Halevi's user avatar
5 votes
1 answer
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What are the economic benefits of SLAPP in file sharing/piracy?

Spin-off from Piracy/File sharing - Why aren't songs, movies or ebooks given for free (+ads) like TV? What are the economic benefits of SLAPP in or out of file sharing/piracy? There's a comment in ...
BCLC's user avatar
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Can a continuous preference be represented by a discountinuous function?

I can think of some examples, but what can be an outline of the proof?
plastico's user avatar
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How can I tell if 2 different utility functions represent the same preferences?

I need to verify that $u(x,y)=x^{1/3}y^{1/3}$ represents the same preferences as $v(x,y)=x^3y^3$. Obviously these are completely different functions with different derivatives, so what am I comparing? ...
Henry's user avatar
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1 answer
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Homothetic preferences for international trade

In international trade class, we assume homothetic preferences for every country, and each country has an endowment. Why do we assume homothetic preferences? Is this because we see (from data) that ...
Giskard's user avatar
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Research Design: Indifference curves and budget lines

I have a basic Idea on how to construct indifference curves such that we must use two goods and then ask for pairs of bundles which are preference indifferent. When doing applied research on ...
EconJohn's user avatar
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Why does local non satiation imply the constraint is binding?

Local non satiation says that for any $x \in X$ and $\epsilon > 0$, there exists $y \in X$ such that $d(x,y) < \epsilon$ and $U(x) < U(y)$. I don't understand why this implies that $px^* = m$...
Neucoder's user avatar
4 votes
1 answer
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Symmetric and asymmetric preferences

I encountered a question where it was given that the consumers had asymmetric preferences. I couldn't find the definition of the term in any of the microeconomics book available to me. Can anybody ...
Dhruv Goel's user avatar
3 votes
2 answers
343 views

King-Plosser-Rebello Preferences: Scale leisure

KPR preferences are given by $$ U(c, l) = \frac{\left(cv(l)\right)^{1-\sigma}-1}{1-\sigma}$$ with concave increasing $v$ and $c$, $l$ denoting consumption and leisure. In the limiting case of $\...
FooBar's user avatar
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3 votes
1 answer
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Preference relations based on Varian

I understand that there is no universally agreed terminology for preference relations. However I need to pin down a definitive way to think about them (both for my exam, and my own sanity). Please can ...
CormJack's user avatar
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3 votes
3 answers
376 views

Consumer preferences

I want to know under what preferences relation will I not want to consume all of my budget. Because if my preferences are strictly monotonic, strictly convex or convex, even LNS or continuous. I would ...
Dashmone's user avatar
3 votes
1 answer
377 views

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: $$\...
Kur_Kush's user avatar
3 votes
2 answers
16k views

Relation between linear utility function and U=max{x,y}

I'm studying general equilibrium theory, and in the study guide I came across a utility function of the type $U=\max\{x,y\}$, which I'm not that familiar with. I study mainly from two books: ...
José Julián Parra's user avatar
2 votes
1 answer
81 views

$a\geq 0$, $x\succsim y$ 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 ...
High GPA's user avatar
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2 votes
1 answer
349 views

Consumer preference and price in the Cobb-Douglas function

I believe I’m using the most basic version of Cobb-Douglas: $U(x,y)=x^\beta * y ^{(1-\beta)}$. The question I have is: in this example would a consumer’s preference ($\beta$) change if the price of ...
vizie's user avatar
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1 vote
1 answer
778 views

Ordinal utility and monotonic transformations

If u(x) is an ordinal utility function that represents the (weak) preference relation R, then (a) any strictly monotonic transformation of u(x) also represents $R$, or (b) any monotonic transformation ...
Eric '3ToedSloth''s user avatar
0 votes
1 answer
170 views

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 ...
Dave's user avatar
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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 ...
Aqqqq's user avatar
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