Questions tagged [choice-theory]

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

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64 views

Boots' Theory by Pratchett

Consider the following quote from the book, $\textit{Men at Arms}$ by Terry Pratchett. “The reason that the rich were so rich, Vimes reasoned, was because they managed to spend less money. ...
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51 views

The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them?

I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality. But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
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Afriat theorem for negative goods

GARP and Afrait theorem assume that the alternative $x\in\mathbb R_+$ is always positive. In some economic contexts, such as financial choices, the attribute can be negative. I wonder if we can ...
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36 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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37 views

What does irrationality mean under the notion of revealed preferences? An example with terrorism.

I am currently studying for an economics of conflict exam and one of the potential questions is likely to be in the vein of "Are Terrorists Rational - Discuss". However how would rationality be ...
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29 views

Is WARP the same of consistent choice?

Is there any difference between WARP satisfaction and consistent choice? I'll explain my case better. Assume we have the consumer choosing $x_1=(2,1)$ at prices $p_1 = (1,2)$ and choosing $x_2=(1,2)$ ...
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2answers
129 views

a risk lover agent preferences and the preference of risk natural agent may be the same

Consider two lotteries $N$ and $M$. Agent $i$ is risk-averse and prefers $N$. Agent $j$ is risk-neutral and prefers $M$. Would any risk-loving agent $k$ also prefer $M$? That is, would $j$ and $k$ ...
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181 views

Choice correspondence notation

My question is about the following notation: I have noticed in several places (for example here (page 15) and here (page 1)) that different authors use different notations for choice correspondences....
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196 views

Envelope theorem for discrete choice sets?

If we have a function $$f(x)=\max_yg(x,y)$$ Then we can find the derivative $d/dx \ f(x)$ by realizing that $$(1): \quad \frac {\partial }{\partial y}g(x,y^*)=0$$ because of the first order ...
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234 views

What is the economic incentive to cheat? How does an experiment capture exogenous deviations?

In my undergraduate career an economic experiment was conducted on my class: one class was the control two classes were the experimental (I was in an experimental class) The basic premise was a ...
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1answer
50 views

Is this proof correct?

i'm new at this, so i´m really sorry sorry if i do something wrong. The problem is this: A choice function satisfies condition α if whenever $x = C(A)$ and $x ∈ B ⊂ A$, it follows that $x = C(B)$ as ...
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256 views

Choice rule and path independence

Question: A choice rule $C$ satisfies path independence if for all $A, B \in 2^X \setminus \emptyset$, $C(A \cup B) = C(C(A) \cup C(B))$. Prove that if $C$ is nonempty and rationalizable, then $C$ ...
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38 views

Vocabulary/Name for Utility of a Set of Choices

I am trying to find if there is some litterature or definition of the concept of the Utility of a set of choices. My google searches return nothing, and I expect it is because I do not know the right ...
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1answer
69 views

What is one dimensional, ordered type?

I am reading papers about moral hazard. What is one dimensional, ordered type $\theta\in\Theta$? What is one dimensional, not ordered type $\theta\in\Theta$? Could you please give an example? ...
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1answer
239 views

Inc Linear Transformation of Bernoulli Utility

According to MWG Proposition 6.B.2, it illustrates that the expected utility form is preserved only by increasing linear transformation. What is the significance of this proposition? The part I ...
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1answer
71 views

Consequentialist View of Risk

In MWG, the authors introduce the consequentialist view of risk by assuming for any risky alternative, only the reduced lottery over final outcome matters to decision maker. From philosophical view, ...
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183 views

Troubleshooting Utility Maximization with the Lagrange Method

I'm trying to solve a utility maximization problem through the Lagrange method. The utility function is something like $u(x,y)=x+B(y-a)$. However, I'm running into problems as x and y do not come up ...
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2answers
5k 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: ...
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612 views

Whom would you consider to be the father of rational choice theory? [closed]

Whom would you consider to be the father of rational choice theory? My suggestions that would qualify for major publications: Arrow (1959), Economica Homans (1961) Becker (1976) Sugden (1991), ...
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1answer
185 views

Consumer demand: a function of present endowment?

I don't know about you, but each time I go shopping for groceries, my purchasing decision takes into account what I already have at home. I don't make only one demand decision for my entire life the ...
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108 views

Can there be sensible choice behavior that violates the Weak Axiom of Revealed Preference?

Following the notation of Mas-Collel, Whinston, and Green, consider a family of budget sets $\mathcal{B}=\{\{x,y\},\{x,y,z\}\}$. To make the example concrete, let's let $x$ be a book $y$ be a left ...
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618 views

My Challenge in Econ 101 explanation of Marginal Benefit = Marginal Cost

In Econ 101 textbooks, there are lots of examples and emphasis on marginal analysis leading to the greatest equation of all, $MB=MC$. My challenge is the following and wonder if anyone had a similar ...
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72 views

Weierstrass Thm: Continuous Fn Attaining Extrema on Compact Domain $u:\mathbb{R^L}\rightarrow\mathbb{R}$

This is just semantics, but MWG doesn't use the Weierstrass Theorem in its Math Appendix when using the fact that a continuous function always has a max value on any compact set. Some books appeal ...
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1k views

Why is Price Vector Orthogonal to Vector connecting two bundles on Budget Hyperplane

Here is my revised version/understanding why price vector is orthogonal to any vector from a bundle on the budget hyperplane to another bundle on the hyperplane: (see below for original question) ...
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317 views

Continuous Preference Relation Imply Continuous Utility Fn Existence

I am reading MWG's explanation in Chapter 3 when showing continuous preference relation implies the existence of continuous utility function. First, the authors show $u(.)$ is continuous by using the ...
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2k views

(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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701 views

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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3answers
1k views

What is the point of the indirect utility function?

Where does this have application? I understand how the demand function may be arrived at using the utility maximization problem but I don't understand where the indirect utility function is used and I ...
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323 views

The 'Economic Man' (Reference Request)

We are writing a paper about the 'economic man.' By this, we mean that the choices he makes epitomize a rational economic thinker. However, we also acknowledge the fact that there are other, non-...
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282 views

performance as utility function / price?

I am trying to define a 'model' for the perceived performance of a product based on this definition: Presumably, customers take both price and quality into account as they form an overall ...
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1k views

Are terrorists rational?

Terrorism in general, and suicidal terrorism in particular, is popularly seen as “irrational,” but many economists and political scientists argue otherwise. This quote is from Terrorism: The ...
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420 views

Prove that a continuous $\succsim$ is quasilinear

This question is closely related to Mas-colell, Whinston, Green: Microeconomic Theory, Question 3.C.5b Let $\succsim$ be a strictly monotone, continuous, and rational preference relation on $(-\...
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What is the difference between “Social Choice Theory”, “Public Choice Theory”, and "Collective decision-making?

I need to know the difference between Social Choice, Public Choice and collective decision-making. Also, Is public choice, social choice the same as collective choice? Thank you
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How to derive formula for marginal probability of choosing nest in nested logit model?

I am trying to understand all the details of the nested logit and what confuses me is the formula for marginal probability of choosing the nest. In more details: the joint probability of individual n ...
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1k views

Weak axiom of revealed preference and choice coherence - how to show they are equivalent

$B$ and $B'$ are elements of the family of subsets of $X$ WARP For every pair $x,y \in B \cap B' $ and if $x \in c(B)$ , then if $y \in c(B'), x$ must $\in c(B').$ Choice Coherence For very pair $x,...
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116 views

Proof of Proposition 1.4 from Microfoundations I by Kreps

Regardless of the size of X (set of all possible objects), if a preference relation which is complete and transitive is defined on it, then the corresponding choice function generated by it will ...
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992 views

Condorcet's paradox: Is the majority rule transitive?

From this wikipedia link I would say that the majority rule is not transitive. Also I'm not sure I understand exactly what is transitivity in this situation... With a usual preference relation $x\...
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2k views

intertemporal utility function usage : calculating consumption

I have encountered this a lot in my exams and can not seem to understand how to use these functions here is an easy exemple : A consumer who will only live 2 periods receives 1000€ in the first ...
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255 views

Microeconomic foundation of discrete choice model

(1) Does the following result in a "valid" (in the sense of being consistent with the economic theory) market demand function? A consumer $i$ maximizes a utility $u_{ij}$ in choosing one of J ...
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1k views

What is an example of a choice which is not necessitated by scarcity?

I am first year economics student and for the past month we have had it constantly drilled into us that all choices have an opportunity cost and thus they are all necessitated by scarcity. Thus when I ...