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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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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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 ...
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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 ...
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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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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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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-...
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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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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 ...
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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 $U =...
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Heckscher-Ohlin with heterogeneous preferences
could someone really help me out I would need to show a situation in which the Heckscher-Ohlin result does not necessarily hold when preferences are heterogeneous.
Does someone have an idea how I ...
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Thin indifference curves
If a consumer follows the rationality axiom of continuity (i.e. no jumps in his preferences), the indifference curves of a utility function are said to be thin.
Why does continuity ($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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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:
$$ \frac{\partial(1-...
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Risk Premium in the Expected Utility Theory
Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have
$$ Eu(w+x) = u(w+E(x)-R). $$
The classical derivation ...
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Lexicographic Preference Relation on the QxR
I would like to ask for your help. I recently learned that the Lexicographic Preference relation can be represented by a utility function $u:X\to\mathbb{R}$ on $\mathbb{Q}\times\mathbb{R}$ (but not $\...
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Do discontinuous preferences imply no continuous utility function?
I am trying to think of a preference relation that can be represented by a utility function but such that there does not exist a continuous utility function.
I know that you can represent continuous ...
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Is MRS supposed to have a minus sign or not? What's there to say about convexity of preferences?
If we have a utility function $U(x_1, x_2) = x_1(x_2+1)^2$ of some consumer, then
$$MRS_{x_1, x_2} = \frac{\color{red}{-}(x_2+1)}{2x_1}$$
Some books have a $\color{red}{-}$. Others and Wiki don't ...
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What are the economic benefits of SLAPP in file sharing/piracy?
Spin-off from Piracy/File sharing - Why aren't songs, movies or ebooks given for free (+ads) like TV?
What are the economic benefits of SLAPP in or out of file sharing/piracy?
There's a comment in ...
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Utility function for introductory microeconomics
What are the utility functions standardly used in introductory microeconomics courses. My own list would include
Perfect substitutes: $U(x,y) = ax+by$
Perfect complements: $U(x,y) = \min(ax,by)$
Cobb ...
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What utility functions are equivalent to additive functions?
Call a utility function $u(x,y)$ additive if there exist functions $v_x,v_y$ such that:
$$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 ...
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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?
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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? ...
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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 ...
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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 ...
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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 ...
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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$...
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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 ...
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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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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: ...
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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 ...
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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 $\...
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$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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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 ...
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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 ...
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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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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 ...
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