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.

Filter by
Sorted by
Tagged with
4 votes
2 answers
1k views

Convex Preference but Convex Utility

Can preference be convex when utility is not a concave function (e.g. $U=x_1^2 + x_2^2$)?
megg's user avatar
  • 41
4 votes
2 answers
22k views

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
  • 41
4 votes
1 answer
274 views

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 ...
High GPA's user avatar
  • 1,906
4 votes
1 answer
678 views

How do I represent this indifference curve graphically?

I am not able to visualize this indifference curve. I consume only two goods: sugar and milk. I will prefer a bundle X of sugar and milk over a bundle Y only if $x_{sugar} > y_{sugar}$, and $x_{...
Kartik's user avatar
  • 51
4 votes
2 answers
186 views

Are these preferences consistent with rationality?

Suppose there are three kinds of commodities, X Y and Z. We ask an agent about his preferences and receive the following answers: "I prefer Z to Y and Y to X". "For every $n$, I ...
Erel Segal-Halevi's user avatar
4 votes
1 answer
414 views

Strict preference relations and utility representations

Suppose I have a rational preference relation $\succsim$ on some consumption set $X$. Suppose also that there is a utility function $u:X \to \mathbb{R}$ representing $\succsim$. Definition: A ...
möbius's user avatar
  • 553
4 votes
2 answers
148 views

What would you call a preference relation that is intransitive yet complete?

I am trying to make sense of the following terminology and putting it into a table helps me keep concepts straight: If I am understanding correctly, irrational behavior is describe as a preference ...
Alejandro's user avatar
4 votes
1 answer
104 views

Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?

Why do people generalize EU instead of making an entirely new model, or create a model that is neither a special case nor an extension of EU? To my knowledge, most utility functions under risk and ...
High GPA's user avatar
  • 1,906
4 votes
1 answer
2k views

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
  • 151
4 votes
2 answers
1k views

Non-Constant Elasticity of Substitution

What's the literature on Non-Constant elasticities of substitution? Say, I'm interested in the elasticity between $c_1$ and $c_2$ increasing/decreasing in income/wealth. CES utility functions with ...
FooBar's user avatar
  • 10.7k
4 votes
1 answer
159 views

Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?

We can write down the coefficient of absolute risk aversion $R_a$, or the coefficient of relative risk aversion $R_r$. Are there intuitive interpretations of the numerical values of these ...
user56834's user avatar
  • 845
4 votes
2 answers
2k views

Homogeneous of Degree Two Utility Functions and Homothetic Preferences.

The understanding that I am not clear is in when do homothetic preferences represent a utility function and vice-versa. My solution to the problem is posted below the problem: A consumer’s preferences ...
Sky's user avatar
  • 75
4 votes
1 answer
5k views

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
4 votes
1 answer
82 views

In revealed preference (RP), is any two points $x,y$ related by the indirect revealed preference relation?

Let $X$ be the closed compact convex set of alternative and $B$ be a closed compact convex subset of $X$. $C$ is defined on all closed compact convex set $B\subseteq X$. $X$ is ordered by a strictly ...
High GPA's user avatar
  • 1,906
4 votes
1 answer
96 views

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
  • 29.5k
4 votes
1 answer
1k views

Equivalence of Definitions of Continuity of Preferences

We have two definitions of the continuity of preferences: Def 1: $\succcurlyeq$ is continuous if for any sequences $\{x^n\} \subset X$ and $\{y^n\} \subset X$, then $n \in \mathbb{N}$ such that, $\...
Kitsune Cavalry's user avatar
  • 6,628
4 votes
1 answer
2k views

Present-bias vs future-bias

There is a huge literature in economics that studies time-inconsistencies in decision-making and that consistently finds that individuals make present-biased choices in a variety of contexts: we do ...
Oliv's user avatar
  • 3,232
4 votes
2 answers
321 views

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
  • 8,345
4 votes
1 answer
174 views

If $\succsim$ is rational, then $B \mapsto C^*(B, \succsim)$ satisfies the weak axiom, and $\succsim=\succsim^*$

If $\succsim$ is rational, then $B \mapsto C^*(B, \succsim)$ satisfies the weak axiom, and $\succsim=\succsim^*$ Previously in the same theorem actually, they proved the following: If $C$ is a ...
Sunhwa's user avatar
  • 871
4 votes
3 answers
172 views

Binary Relations for Cobb-Douglas

I am reviewing old midterms to prepare for my upcoming midterm and ran across this question: Let $\alpha , \beta \in (0,1)$. Now, let $f_{\alpha}$ and $f_{\beta}$ on $\mathbb{R^2}$ be defined as $f_{...
123's user avatar
  • 2,911
4 votes
1 answer
106 views

Example of consumer preferences that switches from being concave to being convex

Question 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 ...
Pavel Kocourek's user avatar
4 votes
2 answers
214 views

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 ...
Daron's user avatar
  • 143
4 votes
1 answer
52 views

Economics of clubs(sport gym, language course, etc)

I am looking for economic research, theory or empirics, on production/profit maximization/competition for firms producing goods with network effects, such as clubs in which every one's utility depends ...
Dmitry's user avatar
  • 41
4 votes
2 answers
7k views

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
3 votes
2 answers
530 views

Are Indifference Curve graphs continuous given the preferential definition of continuity?

Assume the relation $\succeq$ is continuous (by the preferential definition). Does this mean the graph of Indifference Curves are continuous? Since $\sim$ satisfies the definition for $\succeq$, we ...
not tdm's twin's user avatar
3 votes
3 answers
2k views

Given a Utility function, U(x,y), why is multiplying U(x,y) * x not a monotonic transformation?

If $x$, is a commodity and it is s.t. $x \geq 0$ (it is always nonnegative) how will multiplying it times a utility function $U(x,y)$ NOT yield a simple monotonic transformation?
bloopton's user avatar
  • 387
3 votes
2 answers
403 views

Is Varian's definition of continuity of preference equivalent to standard definitions?

Here are two definitions of continuity of preferences. Denote the (weak) preference relation by ≽. We assume completeness, reflexivity and transitivity. Assume non-satiation or strict monotonicity ...
not tdm's twin's user avatar
3 votes
3 answers
2k views

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 ...
PGupta's user avatar
  • 227
3 votes
1 answer
396 views

Why does quadratic utility function imply $\mu-\sigma$ preference?

Why does investors having quadratic utility function mean that their optimal portfolios can be chosen by only considering mean and variance of returns i.e. imply $\mu-\sigma$ preference?
Aqqqq's user avatar
  • 392
3 votes
2 answers
3k views

Is non-monotonic local non-satiation supported by consumer theory in economics?

In general (Walrasian) equilibrium, local non-satiation is one of the assumptions that guarantee existence of equilibrium. Question is, is non-monotonic local non-satiation preference supported by ...
Newark's user avatar
  • 231
3 votes
2 answers
1k views

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/...
Alex's user avatar
  • 99
3 votes
2 answers
161 views

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=...
High GPA's user avatar
  • 1,906
3 votes
1 answer
954 views

Axiom: More is Better; But when is more better?

I'm taking an introductory microeconomics course and have been introduced to the 3 axioms of economic preferences. These include Completeness Transitivity Non-satiation My understanding of non-...
Gustavo Louis G. Montańo's user avatar
3 votes
3 answers
379 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
2 answers
350 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
  • 10.7k
3 votes
1 answer
179 views

Sufficient conditions for connectedness of indifference sets of a preference relation defined on a compact and convex set only

Let $\succsim$ a complete, reflexive and transitive binary relation defined on $X$, a non-degenerated (i.e not identical to a singleton) convex compact subset of $\mathbb{R}^n_{++}$ (the set of n-...
Peter's user avatar
  • 33
3 votes
1 answer
143 views

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
  • 901
3 votes
1 answer
70 views

Is electoral abstention an example of non-complete preference?

In order for a preference to be rational, it has to be transitive and complete. Complete preference means that any two different bundles can be compared. I.e., a consumer can weakly prefer bundle X ...
cc88's user avatar
  • 172
3 votes
1 answer
178 views

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 ...
Maybeline Lee's user avatar
3 votes
1 answer
17k views

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 ...
Anishka Mishra's user avatar
3 votes
1 answer
188 views

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. ...
Alex's user avatar
  • 99
3 votes
1 answer
532 views

Completeness from an example

I have a set $X = \{1,2,3\}$ and a binary relation $B = \{(1,1),(1,2),(1,3),(2,3),(3,1)\}$. I am trying to understand if this relation is complete. The completeness definition I am using is if for ...
Ravendi's user avatar
  • 33
3 votes
1 answer
6k views

Are Cobb-Douglas preferences homothetic?

Our lecture defined a preference to be homothetic, if the following is true: $$(x_1, x_2) \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$ Cobb-Douglas preferences can be ...
user7802048'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
3 votes
1 answer
118 views

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 ...
Tomas R's user avatar
  • 133
3 votes
1 answer
901 views

Can we have a Non-Reflexive Preference Relation?

I've been thinking about preferences alot recently and have been specifically thinking about the reflexivity requirement. That is: $$x \succsim x$$ Though this is apparent and obvious, I have been ...
EconJohn's user avatar
  • 8,345
3 votes
1 answer
48 views

revealed preference given an uncertain environment?

classical revealed preference is about a situation where we assume an agent has a preference over some set of possible choices $X$. We then construct a revealed preference relation on $X$ from choices ...
user56834's user avatar
  • 845
3 votes
1 answer
2k views

Does SARP imply WARP? and GARP imply SARP?

It’s obvious that WARP does not imply SARP, since WARP does not rule out cyclic choices, whereas SARP does. The term “Strong” axiom suggests that it encompasses the “weak” axiom. But this is not ...
user56834's user avatar
  • 845
3 votes
1 answer
743 views

Leontief preferences and 2nd welfare theorem

Does the 2nd welfare theorem hold with Leontief preferences? If not, which of the assumptions does not hold?
Peter's user avatar
  • 31
3 votes
1 answer
8k views

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(...
FooBar's user avatar
  • 10.7k

1
2
3 4 5
8