Skip to main content

Questions tagged [choice-theory]

a conglomerate of models and results concerning the aggregation of individual choices into collective choices

Filter by
Sorted by
Tagged with
3 votes
1 answer
84 views

Question About Proof of Proposition 3.C.1 in MWG - Step 1

I have difficulties understanding the first step of the proof of Proposition 3.C.1 in MWG. Proposition 3.C.1$\quad$ Suppose that the rational preference relation $\succsim$ on $X$ is continuous. Then ...
Beerus's user avatar
  • 505
3 votes
1 answer
73 views

Understanding the definition of monotone

In Microeconomic Theory by Mas-Colell, Whinston, and Green, the definition of monotone preference relations is given as follows: Definition 3.B.2$\quad$ The preference relation $\succsim$ on $X$ is ...
Beerus's user avatar
  • 505
4 votes
1 answer
93 views

Prove: The law of demand holds if WA, Walras' law, homogeneity of degree 0, and homogeneity of degree 1 in wealth hold for Walrasian demand functions

Problem I am asked to prove the following result (MWG Exercise 2.F.5): The law of demand always holds if the walrasian demand function $x(\mathbf{p},w)$ satisfies the weak axiom of revealed ...
Beerus's user avatar
  • 505
2 votes
1 answer
58 views

Proof for Marshallian Demand function

If you have a Marshallian demand function that is strictly convex, then it satisfies WARP. How to prove this?
babededeeptido's user avatar
3 votes
1 answer
79 views

Proving the Choice with Recommendations

Suppose that there are two types of outcomes, i.e. $X=X_1 \cup X_2$ with $X_1 \cap X_2=∅$. All outcomes in $X_2$ are the same to the decision maker (he doesn't understand these kind of products). He ...
homo-economitux's user avatar
4 votes
1 answer
83 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
  • 1,916
2 votes
0 answers
29 views

Find a choice function such that WARP or SARP is violated

WARP implies choice function is raionalizable. Say we have a choice function $C(B)$, $B$ is a closed convex compact set. I am looking for a intuitive example of $C$. The $C$ is economic meaningful, ...
High GPA's user avatar
  • 1,916
0 votes
0 answers
57 views

Question About Stochastic Choice - MWG Exercise 1.D.5

I am studying microeconomic theory using MWG. I got stuck on Exercise 1.D.5, specifically part (c), but I would also like to have my part (a) and (b) checked by someone. Here is the exercise and my ...
Beerus's user avatar
  • 505
3 votes
0 answers
68 views

In Debreu's representation theorem of ordinal utility, is the assumption of "second countability" necessary?

Debreu's representation theorems Debreu 1959 states that: second countability, continuity, and weak ordering sufficiently implies the existence of real (continuous) utility function. The second and ...
High GPA's user avatar
  • 1,916
2 votes
2 answers
160 views

Minimal assumption for a “certainty equivalence” exists

Let $R$ be the set of real number. Let $N$ be an infinite set. Let utility $u:R^N\to R$. The utility function is strictly monotonic. My question is, does the certainty equivalence $CE$ exist? Do we ...
High GPA's user avatar
  • 1,916
0 votes
1 answer
29 views

Is the relation $\mathcal{R}=\{(1,2),(2,3),(1,3)\}$ on $X=\{1,2,3\}$ complete?

Is the relation $\mathcal{R}=\{(1,2),(2,3),(1,3)\}$ on $X=\{1,2,3\}$ complete? By looking at the completeness definition in preference: Definition 1.1(c), this is same as the connected relation in the ...
LJNG's user avatar
  • 143
2 votes
1 answer
294 views

Choice theory vs decision theory

I always thought that Decision Theory and Choice Theory are the same fields. But when reading the Wikipedia entry for Decision Theory recently, I read the explicit clarification: "not to be ...
Ishan Kashyap Hazarika's user avatar
1 vote
1 answer
61 views

Can the following statement be rationalized if it yields a choice function?

A person choose an alternative to maximize another person's suffering. I thought we could define a sort of relation where the person suffers more from x than y. And if we can always do this, we can ...
aliosha karamazov's user avatar
1 vote
1 answer
36 views

Can the following behavior be rationalized if it yields a choice function?

The decision maker has an ideal point in mind and chooses the alternative closest to it. I am not sure if I am right, but in order to rationalize it, we first have to construct a choice function. So, ...
aliosha karamazov's user avatar
4 votes
1 answer
108 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
2 votes
1 answer
158 views

State dependent preferences vs state independent preferences in utility theory

I am working on changes in preferences and found papers on state-independent preference. What is the difference between state-dependent and state-independent preferences and utility functions? What ...
desi arthshastri's user avatar
1 vote
1 answer
97 views

Consumer surplus in Logit model should minus actural payment?

In Logit model, as Train(2003) said in his book(page 55) said, "By definition, a person’s consumer surplus is the utility, in dollar terms, that the person receives in the choice situation. The ...
S.X's user avatar
  • 11
4 votes
1 answer
176 views

Choice Function and Empty Set [duplicate]

Can the choice function of a non-empty and finite set be the empty set? Or is this by definition of the choice function impossible? Does there need to be always at least one winner if we evaluate non-...
dewewdew's user avatar
  • 105
2 votes
0 answers
235 views

How to find the substitution and income effects?

The usual definition of Substitution Effect (pg. 30; also found in Varian) tells that the Slutsky SE is $x(p_x', I') - x(p_x,I) = x(2,15) - x(1,10) = \frac{15}{2 \cdot 2} - \frac{20}{2 \cdot 1} = -6....
Isa's user avatar
  • 87
2 votes
0 answers
184 views

Uncompensated and compensated demand functions

I came across this lecture note online and some of the points below confuse me. I have added the part that confuses me as an image and here is the lecture note for further reference, if needed. ...
Isa's user avatar
  • 87
3 votes
1 answer
413 views

Hick's and Slutsky's approaches lead to different income effects. Why?

Suppose a cup of coffee and a plate of beans are sold at € 1 and € 3 respectively during the winter. In summer, the government decides to remove the subsidy on coffee and its new price per cup goes up ...
Isa's user avatar
  • 87
1 vote
0 answers
122 views

Lump sum income grant is better than a subsidy grant

There is an exercise in a Microeconomics book that says an income grant to a person provides more utility than does a subsidy on one good that costs the same amount to the government. Something like ...
Isa's user avatar
  • 87
0 votes
0 answers
21 views

Influence on the consumption of $Y$ when the price of $X$ falls

Consider the utility function $u(x,y)$ and two budget constraints $B_1: px + qy = 1$ and $B_2 : p_1x + qy = 1$ where $p_1 < p$. If $(x^*, y^*)$ and $(x_1^*, y_1^*)$ maximize $u$ subject to $B_1$ ...
Isa's user avatar
  • 87
2 votes
1 answer
86 views

If the income increases by $\$d$, will it mean the utility at the optimal point increases by $\lambda d$?

I read that if the income increases by $\\\$d$, then the utility at the optimal point will increase by $\lambda d$. How do I get a sense of this, both mathematically and intuitively? Can we write that ...
cris's user avatar
  • 21
2 votes
1 answer
242 views

Proof of the tangency condition in UMP

When an indifference curve is tangent to the budget line such that the preferences are convex and monotone, why is the point of tangency an optimal for an UMP? Given the budget line $p_1 x + p_2 y = I$...
xyz123's user avatar
  • 23
3 votes
1 answer
395 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
2 votes
0 answers
28 views

What social aggregators are complete?

I am reading Eliaz (2004) for a general treatment of social-choice impossibilities. I am confused by the fact that it seems that we should get completeness even in situations where we should not have ...
raving-bandit's user avatar
2 votes
0 answers
267 views

Indifference curves representable by real-valued functions on $\mathbb{R}$ of a continuous preference relation

Let $X = \mathbb{R}^2$. Suppose $\succeq$ denotes a continuous preference relation. If every indifference curve can be represented by functions from $\mathbb{R}$ to $\mathbb{R}$, will it mean the ICs ...
not tdm's twin's user avatar
2 votes
2 answers
279 views

Discontinuous function $U$ with continuous preferences can be written as a composition of discontinuous & monotone function and a continuous function

Conjecture: Every discontinuous utility function $U$ representing continuous preferences can be written as $U = f \circ g$ for some continuous $g$ and discontinuous strictly monotone $f$. The goal is ...
not tdm's twin's user avatar
1 vote
0 answers
67 views

Perfect substitutes mathematical definitions not equivalent

Statement: Consider goods $X$ and $Y$ (and we denote the quantities of by the same notation) such that they are perfect substitutes with the substitution ratio $1:n$. Assume the basic axioms ...
not tdm's twin's user avatar
0 votes
1 answer
72 views

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
0 votes
0 answers
109 views

In consumer theory, shouldn't necessity good and neutral good be different ? What will be the IC and utility function for both?

Necessity good for example salt, which regardless of income has to be consumed at certain quantity. But neutral good for example is Suppliments for a healthy person which regardless of income he/she ...
ASC's user avatar
  • 1
1 vote
1 answer
741 views

Weak preferences and negative transitivity

Let $ \succ $ be a binary relationship on the set $X$ such that, given any $ x, y, z\in X $, if $x\succ y$: (Asymmetry): $\neg(y\succ x)$, (Negative transitivity): $(x\succ z) \vee (z\succ y)$. ...
antonio's user avatar
  • 113
1 vote
1 answer
40 views

In a setting with N goods how many combinatorial bits do we need to construct a preference map

I am reading this paper: https://www.researchgate.net/publication/5208445_The_market_for_preferences By P.E Earl and J.Potts On page 3 the following is written: "If we think of individual ...
ra514's user avatar
  • 13
2 votes
1 answer
92 views

Part of proof of Gibbard-Satterthwaite Theorem

I'm currently working through Nisan's Algorithmic Game Theory, Chapter 9 (Introduction to Mechanism Design). A part of the proof for the Gibbard-Satterthwaite Theorem is given as "obvious," ...
andrew's user avatar
  • 51
0 votes
0 answers
23 views

How to empirically measure the underlying utility function for a 'max EU" SWF? Stated/revealed preferences over uncertain lotteries, or?

Direct answers, as well as pointers to the best literature and textbook treatments, as well as the names of key researchers, are appreciated. Suppose we are considering policies and transfers that ...
daaronr's user avatar
  • 111
5 votes
0 answers
47 views

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 ...
cfp's user avatar
  • 252
3 votes
2 answers
162 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
  • 1,916
2 votes
0 answers
147 views

Market shares of Nested Logit demand model

Consider a Nested Logit demand model with two nests, $N_1, N_2$: $N_1$ contains the outside option only (labelled "0"), $N_2$ contains all the remaining alternatives (labelled "$j=1,...,...
Star's user avatar
  • 446
0 votes
1 answer
253 views

max{x1,x2} where P1not=p2

I have seen min{x1,x2} functions representing perfect compliments but have never seen a max{x1,x2} function anywhere in my book or lectures, I also have never seen anything about p1 not equaling p2. ...
Amin Mazooji's user avatar
2 votes
1 answer
101 views

Market with changing number of goods and services

In the General Equilibrium framework of Arrow, Debreau and others, there are a fixed number of commodities, which I feel is a valid assumption in the short run but maybe not in the long run. Over time,...
Ishan Kashyap Hazarika's user avatar
3 votes
1 answer
191 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
2 votes
1 answer
780 views

Can the Certainty Equivalent be negative?

I am questioning if the CE of a lottery can be negative? For me it doesn't make much sense by definition. I encountered this problem on the following exercise: Imagine a case where we have a lottery(...
Gonçalo Gameiro's user avatar
4 votes
1 answer
125 views

Utility representation of single peaked preferences

Is it true that a single-peaked preference (with the peak at some finite point) over the set of real numbers, always has a utility representation ?? If yes, can you please hint towards the proof or ...
Polime's user avatar
  • 71
0 votes
0 answers
70 views

Binary relation on the set $X = \{v, w, x, y , z\}$ that is asymmetric and transitive but not negatively transitive

So I am trying to find a binary relation on the set $X = \{v, w, x, y, z\}$ that is asymmetric and transitive but not negatively transitive, and is quite tricky. Will $R = (v, w)$ be asymmetric and ...
Ben Stoud's user avatar
0 votes
1 answer
168 views

Prove that Choice Coherence Implies IIA

Prove that Choice Coherence implies Independence of Irrelevant Alternatives (IIA). From the definition of choice coherence, we have this: A choice function c satisfies choice coherence if, for every ...
Anon's user avatar
  • 3
4 votes
1 answer
127 views

Doesn't the Pareto-extension rule invalidate Eliaz's (2004) unified theorem of social choice?

Eliaz (2004) uses social aggregators to provide a unique "meta-theorem" from which Arrow and Gibbard-Satterthwaite follow as corollaries. He defines social aggregators as follows. Let $\...
decisionsdecisions's user avatar
4 votes
1 answer
483 views

Difference between social choice functions and social decision functions?

A social decision function (SDF) à la Sen (1970) is defined as a collective choice rule whose range is restricted to social preference relations which generate a choice function. From Gaertner (2009), ...
decisionsdecisions's user avatar
3 votes
2 answers
90 views

Exact definition of one-player Bayesian Correlated Equilibrium

Consider a game where a decision maker (DM) has to choose action $y\in \mathcal{Y}$ possibly without being fully aware of the state of the world $V$. The state of the world has support $\mathcal{V}$. ...
Star's user avatar
  • 446
2 votes
1 answer
173 views

Why does Figure 2.F.1(b) (MWG page 30) satisfy the WARP (Definition 2.F.1)?

I can see that Figure 2.F.1(a) satisfies the WARP (Definition 2.F.1) in MWG (page 30). However, as the choice $x(p',w')$ is only feasible under the price-income level $(p',w')$ and $x(p'',w'')$ is ...
Yun's user avatar
  • 101