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Where does Arrow’s Impossibility Theorem standard proof rely on the existence of at least three alternatives?

I am trying to understand the proof of the world-famous Arrow’s Impossibility Theorem. To do that, I have been relying on Wikipedia’s proof by decisive coalition, as well as on the proof provided by ...
EoDmnFOr3q's user avatar
1 vote
0 answers
37 views

Kohlberg-Mertens theorem

I am trying to understand the Kohlberg-Mertens theorem. Here is the context and the theorem. We fix $N$ a set of players and $S_i$ the finite set of actions of each players with $\lvert S_i\rvert =m_i$...
G2MWF's user avatar
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4 votes
1 answer
64 views

Random Utility Model Multiple Choice Question. Which one is correct?

In this random utility model, which of the five statements is true? I've been thinking about this question ever since the exam... I said (B).
Martin's user avatar
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1 vote
1 answer
83 views

What are the most common axioms to define a strict preference relation?

I am wondering which are the standard axioms with which indifference and (particularly) strict preference are usually defined. Normally, a weak preference relation for agent $i$ on a set $X$, denoted $...
EoDmnFOr3q's user avatar
2 votes
0 answers
37 views

Axiomatic characterisations of dictatorial social choice/welfare functions?

I am looking for axiomatic characterisations of dictatorial social choice/welfare functions; where a dictatorial social choice function is one that always picks the dictator’s favourite outcome, and a ...
EoDmnFOr3q's user avatar
6 votes
1 answer
67 views

Question About Proving $\alpha(\cdot)$ is Continuous in the Proof of Proposition 3.C.1 from MWG

See Proposition 3.C.1 from MWG Continue from this post, Microeconomic Theory by Mas-Colell et al. book said the following: What remains is to establish that all convergent subsequences of $\{\alpha(x^...
Champa's user avatar
  • 167
3 votes
1 answer
77 views

Proof: Let $\epsilon>0$ and $x'\in\mathbb{R}^L_+$ be such that $\|x'-x\|\geq\epsilon$. Then $\alpha(x')$ belongs to some $[\alpha_0,\alpha_1]$

See Proposition 3.C.1 from MWG Continue from this post, the book (MWG) then started the proof that $\alpha(x)$ is a continuous function: We now argue that $\alpha(x)$ is a continuous function at all $...
Champa's user avatar
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5 votes
1 answer
73 views

Question About the Step Proving $\alpha(x)$ Represents Preferences in the Proof of Proposition 3.C.1 from MWG

Continue from this question, the book Microeconomic Theory by Mas-Colell et al. said We now take $\alpha(x)$ as our utility function; that is, we assign a utility value $u(x)=\alpha(x)$ to every $x$. ...
Champa's user avatar
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2 votes
0 answers
50 views

Question About the Step Involving the Connectedness of $\mathbb{R}_+$ in the Proof of Proposition 3.C.1 from MWG

This is a small issue, but it confuses me. In the proof of Proposition 3.C.1 of Microeconomic Theory by Mas-Colell et al, the book said ... $\mathbb{R}_+\subset (A^+\bigcup A^-)$. The nonemptiness ...
Champa's user avatar
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2 answers
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Does duality hold for u(x, y) = x^2 + y^2? (Corner solution)

Could you please help me evaluate this logic? I've been told that "if preferences are strongly monotonic, duality holds." In the case of utility u(x,y) = x^2 + y^2, we will get a corner ...
Martin's user avatar
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2 votes
0 answers
84 views

Prove that any lexicographic preference $(u_1,u_2)$ must be complete and transitive

Let $\succsim$ be a lexicographic preference represented with $(u_1,u_2)$. $x\succsim y$ if $u_1(x)>u_1(y)$ OR $u_1(x)=u_1(y)$ and $u_2(x)\geq u_2(y)$. Is it obvious that $\succsim$ must be both ...
dodo's user avatar
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1 vote
0 answers
43 views

What economic theory models describe a financial regulator's decision to monitor a company?

Let's consider an example (that may not describe how these entities actually work, but humor me): You are the Financial Stability Board (FSB), you need to designate systemically important financial ...
cgmil's user avatar
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40 views

some question on Buera and Nicolini (2004)

I am struggling with understanding one result in Buera and Nicolini (2004) published in JME. In page 538, they write $$A_t(h^t) b_{t-1}(h^{t-1}) = Z_t(h^{t-1})$$ where $A_t(h^t)$ is a $N \times J$ ...
shk910's user avatar
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1 vote
1 answer
70 views

How to force two utility functions representing the same preference to generate expected utility functions representing the same order on lotteries?

Let $i$ be an agent, and let $A=\{x,y,z\}$ be a set of three alternatives. Then, suppose that player $i$’s linear order (i.e., complete, transitive, antisymmetric and reflexive binary relation) on $A$,...
EoDmnFOr3q's user avatar
2 votes
1 answer
108 views

MWG Exercise 2.E.5

Exercise Suppose that $x(\mathbf{p},w)$ is a demand function which is homogeneous of degree one with respect to $w$ and satisfies Walras' law and homogeneity of degree zero. Suppose also that all the ...
Shenron's user avatar
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1 vote
1 answer
33 views

Spiraling decline in labour supply due to small initial wage decreases

I was asked the following by a student (I work in mathematics/complex systems, my student in econometrics): In econometric studies that measure the elasticity of labor supply and inform policymakers ...
apg's user avatar
  • 123
2 votes
1 answer
61 views

Mixed gambles and risk aversion

The 1997 Quarterly Journal of Economics (QJE) paper titled "The Effect of Myopia and Loss Aversion on Risk Taking: An Experimental Test" by Thaler, Tversky, Kahneman and Schwartz, says that ...
Ramandeep's user avatar
1 vote
0 answers
134 views

questions about basic supply and demand curve theory

I've been getting into mathematics for its own sake and finding the same type of math can be applied across various fields and diverse domains (physics, engineering, data science, ecology, economics, ...
lddovgex's user avatar
0 votes
1 answer
32 views

Goods for resale are considered as producer goods?

I was looking for the definition of producer goods and this was the first result producer goods, also called intermediate goods, in economics, goods manufactured and used in further manufacturing, ...
GrandeKnight's user avatar
0 votes
1 answer
32 views

Can FOSD-transitivity replace the transitivity in utility representation theorem?

Let $\succsim$ be a complete, non transitivity preference relation. I wonder if FOSD-transitivity implies transitivity. The primitive is the space of lotteries $p_1,p_2,p_3,...$. We say the preference ...
High GPA's user avatar
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0 votes
1 answer
31 views

Is my understanding of Arrow's dictatorship correct? The dictator is free to update her preference and the social choice will always follow her taste

Suppose $R$ is a social ordering, $f$ is the social choice function, and $R_i$ is an individual preference. A profile of individual preference is $<R_i>$. $f(<R_i>)=R$ Suppose $i=1$ is ...
dodo's user avatar
  • 293
0 votes
0 answers
17 views

How could a market be designed to prevent hoarding?

Imagine that someone has been put in charge of creating a new market for some kind of commodity. They have ultimate regulatory power. What kind of market mechanisms could they put in place to ...
Crashworks's user avatar
0 votes
0 answers
42 views

Water Economic Metaphor - Evaporation / Condensation

I was considering economics, and how a lot of economics tends to use a water metaphor as a descriptive mechanism. Ex: market liquidity, "investment evaporated", "market flows around ...
G. Putnam's user avatar
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0 answers
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Design of a money skew economy (target: museums/libraries loan rotation sharing)

I was thinking about libraries and museums, and began wondering how such institutions might institute what I would describe as a "money skew economy." Skew in the math sense, of two lines ...
G. Putnam's user avatar
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0 votes
2 answers
57 views

Debreu's ordinal representation theorem is unique up to a positive monotonic transformation, what is the source?

In Debreu's 1954 ordinal utility representation theorem, the utility is unique up to a positive monotonic transformation. While the uniqueness result is well-known, I fail to find a proper reference. ...
dodo's user avatar
  • 293
3 votes
1 answer
56 views

$H$ is a constant? Maximizing: $\int _0^Te^{-t}f(x,u)dt$ st $x_t=g(t,x,u)$ and $g$ is independent of $t$

$\max_{x(t),u(t)}\int _0^Te^{-t}f(x(t),u(t))dt$, st derivative $x_t=g(t,x(t),u(t))$. Prove that $H$ is constant. My try2: consider the Hamiltonian $$ H(x(t), u(t)) = e^{-t}f(x(t), u(t)) + \lambda(t) g(...
dodo's user avatar
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1 vote
1 answer
48 views

Give bundles $x,y\in \mathbb R^n$, there must exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?

For a problem in revealed preference. Give bundles $x,y\in \mathbb R^n$, must there exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$? Intuitively, this mean that we have two bundles, and ...
dodo's user avatar
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3 votes
0 answers
69 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
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2 votes
1 answer
98 views

Two step Generalized Method of Moments (Newey 1994). $\hat{W}$ matrix depending on the nuisance parameter

Suppose that I am working in a model containing a nuisance parameter $h$ and a finite dimensional parameter of interest $\theta$, whose true values are $h_0$ and $\theta_0$, respectively. Newey (1994) ...
mich95's user avatar
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3 votes
0 answers
103 views

Generalization of Debreu's additive utility function $\sum_nu_n(x_n)$ with infinite number of commodities

I want to generalize: $\sum_nu_n(x_n)$. Here $x_1,x_2,..,x_n,...$ are commodities. There are infinite number of commodities: $n\in\mathbb N$ or $n\in \mathbb R_+$ The following not a candidate: $\...
High GPA's user avatar
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1 vote
1 answer
46 views

Reference for monotonicity: $x\geq y\implies x\succsim y$ and $x>y\implies x\succ y$

I've seen this definition for monotonicity many times on different papers and on this site: $x\geq y\implies x\succsim y$ and $x>>y\implies x\succ y$. However, what I read on MWG's ...
High GPA's user avatar
  • 1,916
4 votes
1 answer
171 views

Inductive proofs in economics

Are there any thorems in economics which use proof by mathematical induction to prove them? I've noticed that there is nothing (to my knowledge) from a standard PhD microeconomic theory sequence which ...
EconJohn's user avatar
  • 8,407
1 vote
1 answer
165 views

Approximate Pareto efficiency with ordinal preferences

Pareto-efficiency is a very important property, but in some cases it cannot be attained (for example, when agents play a game such as the Prisonner's Dilemma). In such cases, it can be useful to ...
Erel Segal-Halevi's user avatar
3 votes
0 answers
33 views

Screening models with multiple goods and interacting costs

I'm looking for a reference in the literature on monopolistic screening/mechanism design, where there are multiple allocative variables and these interact in the agent's utility function. For example, ...
econ1324's user avatar
1 vote
1 answer
34 views

Factor changes in Melitz (2003) model

What would be the effect of changes in factor supplies, for example labor, on the open economy equilibrium?
Papayapap's user avatar
  • 1,843
6 votes
1 answer
161 views

Does the Rybczynski theorem also hold in modern trade theory models?

Does the Rybczynski theorem also hold for modern Melitz (2003) type trade models?
Papayapap's user avatar
  • 1,843
2 votes
0 answers
63 views

Time series question from book (ma)

I'm trying to understand this subject and I'm stuck in a question found in a book. I understand white noise characterization, but I'm having some problems with this... maybe it's too much theory? I ...
Blipo's user avatar
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2 votes
0 answers
88 views

Questions regarding Solving Melitz (2003) model

I am editing my question regarding solving the model in order to be more specific. Regarding the demand side, In the beginning of the model, we have a CES utility function over a continuum of goods ...
zmhs's user avatar
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1 vote
1 answer
106 views

Pareto optimal allocations with uncountably many agents

Consider an economy with some $n$ agents with continuous utility functions $u_1,\ldots,u_n$. It is easy to prove that a Pareto-optimal allocation exists: define the welfare of an allocation $x$ as: $W(...
Erel Segal-Halevi's user avatar
0 votes
1 answer
64 views

Is there a theory in economics about how companies have to withhold surplus goods or services for strategic reasons, creating artificial scarcity? [closed]

I have been thinking about how hotels and hostels have available rooms / beds, but they don’t give them away for free or a heavily discounted price; or how grocery stores and restaurants throw out ...
Julius Hamilton's user avatar
0 votes
0 answers
62 views

Non Continuous Walrasian Demand Function

I have a silly question. I’m trying to solve some exercises that have to do with the walrasian demand function $x(p,w)$ and excess demand function $z$. More especifically, I’m asked to show that there ...
Martin 's user avatar
0 votes
0 answers
27 views

Forgetting name of influential paper on evolution applied to corporations

There is a paper that I would like to cite because I remember what it said except that I am forgetting who wrote it and what its title was. Basically people were skeptical that corporations could ...
user84614's user avatar
1 vote
1 answer
25 views

Name of concept where having someone negotiate on your behalf gives you an advantage?

I had a discussion with an Amazon customer service rep yesterday. I asked for something, and they replied "we cannot do that". Amazon was, of course, perfectly capable of doing what I asked. ...
ccleve's user avatar
  • 111
5 votes
2 answers
247 views

Language of theoretical economic papers

Could anyone explain, or provide a good source to, the language used in theoretical economic papers? For example, the difference between an assumption, proposition, postulation, theorem, lemma, axiom,...
Eli J's user avatar
  • 409
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
1 vote
0 answers
75 views

Can the topological assumption in Debreu's representation theorem of cardinal utility be altered from "connected separable" to "second countable"?

Theorem (Debreu 1959 page 9, 10) Let $X$ be connected separable topological space endowed with product topology. If $\succsim$ is independent and at least three factors are essential, then there exist ...
High GPA's user avatar
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3 votes
4 answers
250 views

What does omitting capital from production function assume about capital?

We have two production functions, one $F(L)$ with labor as only factor of production, the other also includes capital $F(L,K)$. What do we assume about capital in the first case when we omit it from ...
Papayapap's user avatar
  • 1,843
4 votes
1 answer
280 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
  • 1,916
5 votes
1 answer
193 views

Looking for a paper on game theory as a beautiful thing, not needing immediate purpose

I am looking for a paper I am sure to have read a while ago, but cannot recall its title. The message was that we should not judge game theory (or economic theory in general?) by its ability as an &...
Bernd's user avatar
  • 151
3 votes
1 answer
178 views

Does continuous preference imply upper-hemi continuous demand correspondence?

Let alternative $x,y,z\in R^N$. $\succsim$ is convex, rational, monotonic, and continuous. Let $B=[y,z]$ be a budget segment. Let demand correspondence be $D[y,z]=\{x\in B||x\succsim B\}$ $D[y,z]$ is ...
High GPA's user avatar
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