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 importance of Epstein-Zin preferences?
I've heard that there is a lot of work being done recently that applies Epstein-Zin preferences. The Wikipedia page doesn't seem to be very full.
Why are Epstein-Zin preferences important?
How does ...
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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 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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When treating a relative, normalized utility function as a pmf, what is the interpretation of Shannon entropy or Shannon information?
Suppose $\Omega$ is a set of mutually exclusive outcomes of a discrete random variable and $f$ is a utility function where $0 < f(\omega) \leq 1$, $\sum_\Omega f(\omega) = 1$, etc.
When $f$ is ...
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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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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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Has the assumption that individuals' tastes do not change over time been rigorously challenged?
In their seminal paper De Gustibus non est Disputandum, Stigler and Becker (1977) surveyed four classes of phenomena widely believed to be inconsistent with the stability of tastes: addiction, ...
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Fair voting procedure when there are many issues
When several people have to decide about a single yes/no issue*, the natural decision rule to use is the majority rule.
But when there are many issues to decide upon, the majority rule is "unfair" ...
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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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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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Weakly monotone preferences with singleton indifference curves: do any of them admit a utility representation?
Inspired by this question. The original question was answered by Amit with some nice examples. I would like to know the generalized answer:
Suppose we have a preference ordering $\succeq$, which is ...
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What are different ways of specifying utility and decision making?
This question is related to this question about the Machina paradox and about the expected utility model. In this question, I'd like to know a little more about various or even competing ways of ...
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Translog Preferences
What are translog preferences? The wikipedia article only clears up that it stands for transcendental logarithmic preferences, and that they are a generalization of Cobb-Douglas preferences.
Do they ...
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Are homothetic preferences monotonic?
I'm trying to understand intuitively what a homothetic preference is, and I am still not quite there. I understand the definition, that a homothetic preference implies that the slope of the ...
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Linear Homothetic Utility
A Homothetic Utility is where
$$
\forall x,y, \forall a \in \mathbb{R}_+: \ u(ax,ay)=au(x,y)
$$ (or its monotonic transformation).
A linear Homothetic utility is defined as $$
\forall x,y, \forall a \...
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Relationship between strong and weak axioms of revealed preference
I keep seeing these following facts just asserted while reading:
Let W = weak axiom of revealed preference
Let S = strong axiom of revealed preference
Let C = the commodity vector
$W \iff S$ ...
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What are good dataset alternatives to estimate value functions?
Suppose we want to estimate for many goods in the economy (or classifications thereof) the preferences of each household for these goods. We may want to restrict the analysis to specific utility ...
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Proving the De Finetti Theorem
Let us have a finite state space, $\Omega = {\omega_1,\cdots,\omega_s}$, where $2 \leq s < \infty$. Define a bet as a function $x:\Omega \rightarrow X$, where $X \subseteq \mathbb{R}^s$ is the set ...
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What is the purpose of the local non-satiation assumption in the first welfare theorem?
The profit maximization assumption implies
$$\text{if } x_i \succ x_i^* \text{ then } p_ix_i > p_i w_i$$
Okay so this just says if the agent is utility maximizing / rational, then if he doesn't ...
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Selecting the best utility function for households
I have little to no background in micro, but I'm learning about utility functions.
It seems that there are many forms of utility functions for households. In general terms, how does one go on to ...
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Risk Premium in the Expected Utility Theory
Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have
$$ Eu(w+x) = u(w+E(x)-R). $$
The classical derivation ...
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(Preference Relation/Set) Continuous $\succsim$ imply closedness of upper and lower contour sets
[ADDED/MODIFIED] : I have put my proof where the commodity space is simply $\mathbb{R_+}$(e.g. nonnegative reals) for simplicity below. Please share your 2 cent. I have put words to aid my own ...
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Consequences of hyperbolic discounting
In reading the Wikipedia article about hyperbolic discounting, I read that it says that hyperbolic discounting created strange consequences:
But note, the time inconsistency of this behavior has ...
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If all indifference curves are parallel lines, then preference has linear representation
Given a continuous preference relation $\succeq$ over $X=\mathbb{R}^2_{+}$ where all sets:
$$
I_x\equiv\{y\in X:y\sim x\}
$$
are lines on $X,\forall x\in X$, and are parallel to $I_y,\forall y\notin ...
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Local Non-Satiation Proof
I have been having trouble with how to go forward with a proof for about three days now. I know the basic structure of the proof, but can't seem to construct it.
Basically, I am trying to do a proof ...
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Lexicographic Preference Relation on the QxR
I would like to ask for your help. I recently learned that the Lexicographic Preference relation can be represented by a utility function $u:X\to\mathbb{R}$ on $\mathbb{Q}\times\mathbb{R}$ (but not $\...
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GARP and SARP assumed mononticity?
Monotonicity means the decision maker prefer more goods than less. It is not mentioned in textbook that SARP and GARP preasumed monotonicity, implicitly.
GARP: if $a$ is indirectly revealed preferred ...
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Generalized KPR: Frisch Elasticity
Consider the following version of KPR preferences (with $l$ being leisure):
$$ 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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Tactical voting when the voting rule is unknown
The Gibbard-Satterthwaite theorem implies that, in every non-dictatorial voting system with 3 or more candidates, there is a preference profile in which some of the voters can gain by lying about ...
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Why do some game theory textbooks explicitly require preference relations to be reflexive?
A binary relation on a set of outcomes is called a preference relation if it is complete and transitive. Completeness of course implies reflexivity. But the authors of some game theory textbooks add ...
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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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Why are we taking the logarithm for risk-averse decision-makers?
I'm a mathematics student learning a bit of Game theory. Many examples are given within a very economic setting and up to know I could follow most of it because they were very basic and I learnt some ...
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Completeness of Preferences
Economists assume that consumers have a set of preferences that they use to guide them in choosing between goods. These preferences have to satisfy three properties: completeness, transitivity and "...
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What is the difference between preferences lacking "completeness" and being indifferent?
If two preferences are complete, at least one must have a relationship to the other. If neither has a relationship, doesn't that mean that the consumer doesn't care which one he/she purchases?
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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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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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The Price and Demand Index in Homothetic Kimball Utility
Suppose with Kimball preferences, utility $Q$ from consuming $\left\{q_{\omega}\right\}_{\omega \in \Omega}$ is implicitly given by $$\int_{\omega \in \Omega} Y\left(\frac{q_{\omega}}{Q}\right) d \...
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Continuous rational and monotone preference relation implies $x\succsim0$?
I updated my proof to a general version as follows: please share your thoughts & 2cent. Thanks
Show a monotone continuous complete preorder on $\mathbb{R^L_+}$ has $y\geq x\rightarrow y\succsim ...
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What utility functions are equivalent to additive functions?
Call a utility function $u(x,y)$ additive if there exist functions $v_x,v_y$ such that:
$$u(x,y)=v_x(x)+v_y(y)$$
Consider the function $u(x,y)=xy$. It is not additive, but, it can transformed using a ...
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What are the economic benefits of SLAPP in file sharing/piracy?
Spin-off from Piracy/File sharing - Why aren't songs, movies or ebooks given for free (+ads) like TV?
What are the economic benefits of SLAPP in or out of file sharing/piracy?
There's a comment in ...
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Utility function for introductory microeconomics
What are the utility functions standardly used in introductory microeconomics courses. My own list would include
Perfect substitutes: $U(x,y) = ax+by$
Perfect complements: $U(x,y) = \min(ax,by)$
Cobb ...
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Quasiconcavification
Let $f_1, f_2$ be two smooth strictly-quasiconcave functions.
Do there always exist monotone transformations $g_1,g_2$ such that the sum
$g_1\circ f_1 + g_2 \circ f_2$ is a strictly-...
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Is MRS supposed to have a minus sign or not? What's there to say about convexity of preferences?
If we have a utility function $U(x_1, x_2) = x_1(x_2+1)^2$ of some consumer, then
$$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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Comparing voting methods when there are only two voters
Consider the Schulze, Kemeny-Young, Ranked Pairs and Borda count voting methods. (The last is obviously the odd one out in this list!)
Suppose that there are only two voters. Each voter gives a ...
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Consumption-Leisure Elasticity
The macro-literature insists on a consumption-leisure elasticity of 0 to match the balanced growth fact of constant labor supply.
Is there any paper that tries to evaluate this elasticity using ...
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Utility Representation of Lotteries
We went over a lemma in class leading up to a larger theorem. The Lemma states:
Let $\succeq$ be a rational preference relation on $\mathscr{L}$ and let $\succeq$ admit utility representation under ...
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Order relations and preferences using logic
I want to understand order relations using their underlying implication mechanics and what this means for certain results, specifically looking at preference relations.
Using the logical rules of ...
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Sum of Homothetic Functions
If two utility functions represent homothetic preferences, will their sum also be homothetic?
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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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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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