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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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36 views

Homothetic preferences from indirect utility

Consider an indirect utility function on the form $v^{i}(\textbf{p},w^{i}) = a^{i}(\textbf{p}) + b^{i}(\textbf{p})w^{i}$ Where $\textbf{p}$ is a vector of prices and $w$ denotes income of ...
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1answer
30 views

Majority Rule and Single Peakedness

Majority Rule will induce non empty choice set if individual preferences are single peaked Is this statement true? I have some trouble in understanding the meaning of 'single peakedness' in context ...
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0answers
23 views

Archimedean but not mixture continuous

In the context of preferences on a set of lotteries on a finite set $X$, what is an example of a preference that is independent, Archimedean but not mixture continuous? I know the mixture continuous ...
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1answer
55 views

Does Preference have a Hierarchy? A Silly Question

I have what is probably a very silly question, but I have gone down the rabbit hole and can’t get back out..... Is there is a hierarchy of preference, and within each level of choice do we reset the ...
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1answer
42 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 ...
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1answer
80 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?
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87 views

Quasi-linear Optimal Consumption Bundle

I have a question involving optimal consumption bundles for quasi-linear preferences. Utility is given by $$U(x_1,x_2) = 16\sqrt{x_1} + 2x_2$$ and $p_1 = 8, p_2 = 4, I = 30$. What I have so far ...
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1answer
69 views

Prove that $u$ is a utility function for $\succsim$

If X is finite, define this function $u : X \rightarrow \mathbb{R}$ by $u(x) = |\{z\in X:z \prec x \}|$. Prove that $u$ is a utility function for $\succsim$. Is it sufficient to prove that the ...
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2answers
74 views

Does $U(x,y) = x^2 + y^2 + 2xy$ represent transitive, monotonic preferences?

I'm a monitor for a microeconomics course and a student came up with this question. That this utility function represents monotonic preferences I think it's clear. Both goods have positive and ...
3
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1answer
103 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 ...
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2answers
73 views

Doubt about equivalence relation

In class I was taking notes about equivalence relations defined as: Given a generic relation $R$ on $X$, $xIy$ if both $xRy$ and $yRx$ Now, I don't really understand the following proposition: ...
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1answer
45 views

If $\succsim$ is transitive but irreflexive, then it is asymmetric, proof

If $\succsim$ is transitive but irreflexive, then it is asymmetric. this is my proof: Suppose $\succsim$ is not asymmetric, which means that for any $x,y \in X$ $x\succsim y \rightarrow y \succsim ...
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0answers
48 views

Revealed preference if we know that the decisionmaker is rational?

In standard revealed preference, we don't assume that the agent has rational preferences over a choice set $X$, and we can then ask: under what conditions can $X$ be rationalized by a rational ...
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1answer
73 views

Slutsky Decomposition from Indirect Utility Function [closed]

Given the indirect utility function: V={M^2}/{4P1P2}, how do we establish the Slutsky Decomposition? I used Roy's Identity to get the Demand, but I'm stuck with the other components of the Slutsky ...
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2answers
34 views

Efficient revealed preference check of whether two preferences over lotteries are the same?

I want to find conditions under which two utility functions can be known to be linear transformations of each other. Consider a (possibly finite) arbitrary set of outcomes $X$ (Not necessarily ...
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1answer
162 views

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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2answers
79 views

preference relations and monotonic transformations of utillity functions

Given a choice set $X$ (NOT assumed to be a commodity set...), and utility functions $u,u'$ on $X$, it is clear that if $u'$ is a strictly monotonic transformation of $u$ then they induce the same ...
3
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1answer
36 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 ...
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0answers
35 views

The use of preference relations in choice theory and the $\succsim$ symbol

At least as from Edgeworth and Pareto we think about utility in mathematical terms. My question twofold (i) about the start of the usage of binary relations to model preferences in economics, and ...
2
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1answer
65 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 ...
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2answers
135 views

preference relations

Can anybody give an intuitively explanation for the following problem? Let $\succeq$ be a preference relation on a set X. Define I(x) to be the set of all y ∈ X for which y ∼ x. Show that the ...
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1answer
89 views

Compare utility functions

I recently joined an econ class. I am so lost on how to prove their equality. As a math standpoint, these are completely different equations. Please help! ...
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1answer
507 views

Unusual perfect complements utility function min{ax+y, x+2y} [closed]

What's the graph for this utility function? How can it be represented graphically? Is this function perfect complements? I do not fully understand that in the question attached in the picture, the ...
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2answers
287 views

Relationship between convexity and a perfect complements type utility function

Consider someone who consume two goods and hates them both. Given the utility function: U(x,y)= -max{x,y} 1.What would be the shape of the indifference curve? 2.Why are these preferences weakly ...
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0answers
20 views

Can a GARP-satisfied observation set also be rationalized by a **convex** utility function?

Afriat's theorem states that a set of price-consumption observations that satisfies GARP, can be rationalized by a concave increasing utility function. However, does this mean that GARP precludes ...
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1answer
322 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 ...
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1answer
665 views

Inferior and normal good and the change in price of those goods

In general, We know that if a good is normal, then as your income increases, then demand of that good increases as well as price is fixed. Similarly, if a good is inferior, then as your income ...
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1answer
50 views

Indiference between two lotteries

Suppose that a binary relation satisfies only: Independence axiom: $L≿L′⟺α\circ L+(1−α)\circ L′′≿α\circ L′+(1−α) \circ L′′$ Reduction to simple lotteries: For all $g$, $g~g'$, $g'$ is the simple ...
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1answer
88 views

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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1answer
143 views

Why does the violation of a preference axiom not invalidate the discipline of economics?

There are many examples of the preference axioms of consumer theory being violated. I feel like there are very few cases where at least one of these axioms isn't broken, so is any theory or model ...
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0answers
32 views

Literature on Recursive Preferences and Time-Additive Expected Utility

In Chapter 20 of the book Economic Dynamics in Discrete Time, named "Recursive Utility", the author asserts that the Time-Additive Expected Utility Model (TAEU) has some shortcomings when applied to ...
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34 views

A model for the transmission of preferences

Say we have an $m\times n$ grid with three types of agents, $A$, $B$ and $C$. At time $t$ there are $a_t$, $b_t$ and $c_t$ agents of each type, and $z_t$ blank cells. Agents of the $A$ type like ...
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2answers
134 views

Problem with a Hal Varian Question from chapter 5

Remember our friend Ralph Rigid from Chapter 3? His favorite diner, Food for Thought, has adopted the following policy to reduce the crowds at lunch time: if you show up for lunch t hours before or ...
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1answer
457 views

MRS for quasi-linear preferences

I'm having difficultly understanding what my professor taught in class. I thought, like cobb-douglas, when finding $U_1$ we take partial derivative with respect to $q_1$ and hold everything else ...
3
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1answer
37 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 ...
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1answer
234 views

Continuity of preference relation (iff?)

I have a question about the following definition of a continuous preference relation. I apologize for not providing a reference and will try to add one as soon as I can find one. Definition: A ...
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2answers
2k 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 $px^* = m$...
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142 views

Why is local nonsatiation an essential precondition for these identities?

There are four identities regarding expenditure function and utility maximization: ...
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2answers
470 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 ...
2
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1answer
569 views

Weak axiom of Revealed Preference application

The following is a problem I am dealing with related to Weak Axiom of Revealed Preference. I have given my solution below to the situation. What I am not getting is how is WARP not violated? A law ...
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1answer
252 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 ...
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4answers
2k views

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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2answers
858 views

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 ...
2
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1answer
114 views

Stone-Geary preferences and competitive equilibrium

Does anybody know if a competitive equilibrium obtains under Stone-Geary preferences; are there multiple equilibria problems; do such preferences admit an analysis with more than one type of ...
1
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1answer
154 views

Properties of preference relation

Let $\succeq$ be a preference relation on $X$. Is it true that $x \succeq y$ if and only if $\lnot (y \succ x)$? I think it is true and my proof is as follows. To prove $\implies$ direction, we have ...
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1answer
2k 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 ...
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2answers
121 views

Equivalence of definitions of continuity [closed]

One of the definitions of continuity is that the Upper Contour Set and the Lower Contour Set are closed. I am trying to show that if preference is continuous and $x>y>z$, then there is some $\...
2
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1answer
104 views

What does non degeneracy mean for a preference?

I saw a non-degeneracy assumption in Gilboa and Schmeidler's paper (maxmin expected utility with non-unique prior). The statement is "Not for all $f$ and $g$ in $L$, $f \geq g$". So can you explain ...
2
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1answer
846 views

How to prove convexity + quasilinear preferences imply concave utility?

Let $\succsim$ be a strictly convex and quasilinear preference relation. It's defined over, say, $\mathbb{R}^2_{+}$ and is quasilinear on good 1. So, $U(x_{1},x_{2}) = x_{1} + f(x_{2})$. How to prove ...
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1answer
34 views

Revealed preferance: elementary question

When the market prices are Rs 5 per apple and Rs 6 per orange a person buys 16 apples and 28 oranges. When the prices are Rs 4.4 per apple and Rs 6.4 per orange ,the person buys 20 apples and 25 ...