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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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 ...
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Consumption-Leisure Elasticity

The macro-literature insists on a consumption-leisure elasticity of 0 to match the balanced growth fact of constant labor supply. Is there any paper that tries to evaluate this elasticity using ...
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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: $\...
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Does consumer demand in the secondhand market actually affect the firsthand market for high-cost goods

In the 21st Century, there is an increasing consumer awareness of the externalities of manufacturing and along with it a stronger consumer preference to buying used goods rather than new. My question ...
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How to solve a general equilibrium problem with lexicographic preferences?

I have been unable to find a good example of this type of GE problem in our textbooks, and our professor has indicated that something like this may appear on our exam. So, here is a hypothetical ...
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MATLAB code: Plot utility function and budget constraint

how do i plot these? i have this utility function: $$U(x_1,x_2)=\log(x_1)+\beta \log(x_2)$$ and this budget constraint: $$p_1 x_1+p_2 x_2=R$$ where $R=3, p_1=0.5, p_2=0.5$ i dont know how to plot ...
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What is the observable definition of "preference" by Frisch?

To make things weird, although Frisch was fully aware of the importance of random distribution in economics relations, he never mention the randomness in binary preference relations! How to define ...
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MWG_3D4_C, why the solution seems in reverse?

I'm doing exercises of Chapter3 of MWG, there's a problem that I don't understand (I didn't figure out the solution manual either...). It is about exercise 3.D.4, the full statement of the exercise is ...
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Does quasilinear preference contain rationality, monotonicity or other assumptions?

I have a question when I'm doing exercise 3.C.5(b) of MWG. The exercise asks to prove that a continuous preference on $(-\infty,\infty)\times R^{L-1}_+$ is quasilinear with respect to the first ...
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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 ...
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Preference aggregation rules that satisfy the property that the most frequent best alternative is the collective best alternative?

Let $X$ be the set of alternatives, and $(R_i)_{i\in N}$ a profile of partial orders for $n= \#N$ individuals. I make the assumption that those partial orders are so that they all give rise to one ...
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labor leisure model, quasilinear preferences

There is a quasilinear utility function $u= (1-t)wl - p(l)$, where $l$ is labor supply. I don't quite understand what happens, if the budget changes (due to $w$ or $t$) since it is quasilinear. Does ...
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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 ...
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Non-homothetic CES preferences: demand derivation

I am struggling a little with the derivation of the goods demand and price index when preferences are CES and not homothetic. I am optimising the allocation of a Dixit-Stiglitz aggregator, so the ...
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What is a utility function rationalizes these preferences?

For a consumer deciding between goods A and B, with a budget of w: If A and B are the same price (or if A is cheaper), the consumer will spend their entire budget on A. As the relative price of A ...
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Considering there are four different goods {w,x,y,z}, how many different relations can be defined using all goods

In this problem, you can either prefer a good to another, disprefer a good to another or be indifferent between the two goods. While I have been able to do it mechanically, I am very confused as to ...
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Stock market existence and saving money

I have a generic question that perhaps has more to do with psychology than with anything else. The question is, how effective is the stock market's existence in being effective in making people save ...
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Proof for convex preference relation

⪰ is a strictly convex preference relation on a set X which is the set of all N-tuples of nonnegative real numbers. Further are x,y,z element of this set X and i have the preferences x ≻ y ≻ z given. ...
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What was the study that shows peoples' tax preferences shift when they get more information about their income?

I am trying to find a study I read a few years ago, but I forgot the names of the authors and the title of the study. I have already tried to search for the study on Google Scholar without much luck. ...
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Is it possible to get back the consumer’s utility function from their demand functions?

I am curious about if it’s possible to reverse the utility maximization process, i.e. given the consumer’s Marshallian demand functions, find their utility function. I was thinking of trying to find ...
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What is the difference between preferences of the producer vs the consumer?

The book I am working with (Rubinstein) states that in the case of the profit-maximizing producer, preferences are linear and the constraint is a convex set. Meanwhile, in the consumer model, ...
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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 ...
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Representation theorem for $\succsim\supset>\cup\sim$

On $\mathbb R^2$, define $x=(x_1,x_2)>(y_1,y_2)=y$ if $x_i\geq y_i$ for all $i$ and $x_j>y_j$ for some $j$. Let $\sim $ be an equivalence relation that $x\sim y$ implies $x\not> y$. Define ...
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Say a preference is "constant“, by analogy with a constant function

Let $f$ be a function with range of $\{-1,1\}$ and $f(x,y)=-f(y,x)$. Let the preference $\succ\subset X\times X$ where $x\succ y \iff f(x,y)=1$. In math we can define $f$ to be a constant function on ...
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Risk Premium for Prospect Theory-like value function

I am curious how to calculate the following risk premium for a utility function that is not linear in $w$. What i'm asking is the following: Consider an agent with utility function $u$, initial wealth ...
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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 ...
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How to measure utility functions in the stock market

i am looking for some articles on how to identify and estimate utility functions in the stock market. My own search results yielded some papers by Blackburn and Ukhov https://www.researchgate.net/...
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Asking for reference of trading strategy without inherent preference?

Han et. al.,2021 mentioned that So in contrast with traditional behavioral finance models, active strategies tend to spread through the population even if investors have no inherent preference for ...
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Definition of strictly convex preference

Let $x,y\in X$. Does strictly convex preference (which implies that the utility is strictly quasiconcave) mean that: $x\succsim y$ implies $\alpha x+(1-\alpha)y\succ y$ for any $\alpha\in (0,1)$?
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Show that if $\succsim$ is continous on $X$, then the sets $ \precsim (x^0)$ and $\succsim (x^0)$ are closed

For a set to be continuous, it's contour sets must be closed. Since we can define $$ \succsim x^0 = \{x, x^0 \in X: x \succsim x^0 \} $$ and $$ \precsim x^0 = \{x, x^0 \in X: x \precsim x^0\}$$ it ...
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Is it possible and logical to have an upwards sloping budget line?

The question I have is, for example, say Garry has two goods, cookies he pays 1 to consume a cookie and a maximum of 10 can be consumed, whilst he gets PAID 2 to consume vegetables. Garry is also ...
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Reference request: modeling firms that act to create demand for their products

(I don't have an economics background; apologies if my terminology is confusing.) It seems like there is often a situation where a firm can take actions to create demand that did not already exist. ...
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Completeness Axiom in Preference Relation

My textbook, Microeconomic Theory by Mas-Colell, Whinston, and Green states that given a preference relation $\succsim$ on $X$, Strict preference relation $\succ$ is defined by $ x \succ y \iff ...
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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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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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First Reference Leontief/Perfect Complements

I googled a lot and I'm still to find: 1. In which paper/book/reference do Leontief [production] functions make their first appearance? Similarly 2. In which paper/book/reference do perfect ...
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Uniqueness of Competitive Equilibrium Conditions

I know that if a consumer has strictly convex preferences it may not guarantee uniqueness of CE. I believe that we need monotonicity of preferences as well but would like to hear any thoughts of this ...
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Convex consumer preferences

Man has blue and red marbles. If he has more red marbles then blue one he wants to exchange one red for two blue($1R:2B$). If otherwise (more blue then red)he wants to exchange one blue for two red($...
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Equivalent assumptions in Revealed Preference and Classical Preference Theories

I have read that there are dualities between Revealed Preference Theory and Classical Preference Theory. Suppose, I have $X$ as the set of all conceivable choices, and $\mathscr{B} \subseteq 2^X$ the ...
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Varian Analysis Non satiation question

Consider preferences defined over the nonnegative orthant by (xl,x2)> (yl,y2) if X1 + X2 < y1+ y2. Do these preferences exhibit local nonsatiation? If these are the only two consumption goods ...
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What does GARP in revealed preferences mean and how to regocnize it graphically?

I have a froblem understanding GARP in revealed preferences. I know what WARP means, and that SARP adds transivity such that it allows for indirect preferences, but what about GARP? How can you ...
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How do I prove 2 indifference curves have the same properties?

I understand questions a) but I'm completely stumped at c). What do they mean by U'=1 having same properties as U=10?? And w,for questions b and c, what are they asking by "general expression for ...
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Properties of Consumer Preferences - Monotonicity

Was reviewing topics and I came across this question. I am confused because there is no reference to strict or weak monotonicity in this case. I first thought that monotonicity is violated b/c an ...
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Convexity preferences

What is the difference between convexity and strict convexity preferences? What is the difference between quasi-concavity and quasi-convexity? And is MRS still true in concave preferences?
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McKelvey-Schofield Chaos Theorem Without Agenda Setter

The McKelvey-Schofield Chaos Theorem states that in a multidimensional preference space, it is almost always possible to reverse engineer the implementation of your desired policy by constructing an ...
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Strict monotonicity and strict convexity - prefences

I've just encountered the following exercise from GEOFFREY A. JEHLE micro's book Strict monotonicity comes from the fact that any increase in $x_1$ or $x_2$ increases utility, and strict convexity ...
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Indifference curves drawing

Can indifference curves be drawn when we know only preference relation that defined below? To be precise about condition given: $[x_1 > x_2] or [x_1 = y_1$ and $ x_2 ≥ y_2]$ I’ve tried to find an ...
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strict monotonicity definition in Reny textbook and strong monotonicity

Reny-advanced microeconomic theory-page 10 wiki-monotonicity preference This capture is the definition of strict monotonicity in Reny's textbook, and I've compare it with wikipedia also other ...
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In Austrian economics, do producers have an ordering of preferences similar to consumers?

I watched a video from the Mises Institute where the lecturer mentioned that in Austrian economics, the consumer behavior that is observed is a result of their perception of the utility of the ...
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Proving that Every preference relation can be represented by utility function

Im looking the prove the following: every preference relation ⪰ over finite/countable set X can be represented as a utility function u such that ...
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