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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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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$x\sim y$ implies $x+a\sim y+a$ for any $a\geq0$ and $x,y\in\mathbb R^n$, then the preference is linear?
$x,y,a$ are vectors in $\mathbb R^n$
We say $a\geq0$ if all directions of the vector $a$ is greater or equal to zero.
We want to prove (or disprove by counterexample) that:
Suppose $x\sim y$ ...
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Prove that a preference is linear
Given the following two conditions:
$x\succ y$ implies $x+a\succsim y+a$,
And,
$x\prec y$ implies $x+a\precsim y+a$
We want to prove that $\succsim$ is a linear preference.
One of the ...
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Relationship between strictly convex preference and convex preference
Let X be a convex subset of linear topological space and let binary relation >=
be a complete preordering.
prove: If preference relation is strictly convex and continuous, then it is convex.
Since ...
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Axiom: More is Better; But when is more better?
I'm taking an introductory microeconomics course and have been introduced to the 3 axioms of economic preferences. These include
Completeness
Transitivity
Non-satiation
My understanding of non-...
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Cobb-Douglas function homotheticity
I've been given the Cobb-Douglas utility function:
$\ u(q_1, q_2)=a\ln q_1+b\ln q_2=q_1^aq_2^b \ $
If I want to prove homothetic preferences, I use the following condition:
$\ u(\lambda q_1, \...
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locally nonsatiated preferences
what does this symbol mean in the discuss of locally nonsatiated preferences:
$\varepsilon > 0$ and $||y-x||<\varepsilon$.
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For the case of two goods, give an example of preferences that are represnted by a continuous utility function that allows for fat indifference curves
The question in the title sounds like a trick question, due to the monotonicity property that indifference curves have, such that for two goods x and y, strong monotonicity implies y > x.
Possible ...
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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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Why are indifference curves (often) of infinite length?
Indifference curves are often of infinite length.
Is this implied by monotonicity or non-satiation?
If not, what is/are some condition(s) that are sufficient for indifference curves to have infinite ...
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Are revealed preferences normative or positive notion?
I always thought from my understanding of the terms normative and positive that revealed preferences are a positive concept. For example, saying Anakin prefers grass to sand (i.e. $U(g)\succ U(s)$) is ...
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Can we have a Non-Reflexive Preference Relation?
I've been thinking about preferences alot recently and have been specifically thinking about the reflexivity requirement.
That is:
$$x \succsim x$$
Though this is apparent and obvious, I have been ...
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Linear Utility?
Consider a preference relation $\succeq$ on $X\subseteq\mathbb R^2$. If $\succeq$ satisifies:
$$
\begin{align}
&1.\mbox{ }(a_1,a_2)\succeq (b_1,b_2)\implies(a_1+t,a_2+s)\succeq (b_1+t,b_2+s),\...
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Question about the relationship between Weak Axiom and Slutsky Matrix
We know that if a differentiable Walrasian demand function $x(p,w)$ satisfies Walras' law ($p^Tx=w$), homogeneity of degree zero ($x(\alpha p,\alpha w)=x(p,w)$), and the weak axiom of revealed ...
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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 ...
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A question about the property of quasi-linear preference
In case of quasi-linear preference, why would one unit more of the numeraire good (good 1) give the same additional utility as spending an additional amount of wealth equal to the cost of one unit of ...
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Why is the nature of graph of utility function different from indifference curve?
I am new to Economics, but I have this doubt. The indifference curve and utility function both have the same equation, so their graph must also be similar, which is true I guess. Then why is it that ...
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Heckscher-Ohlin with non homothetic preferences [duplicate]
Can someone tell me how I can show with an example that the Heckscher-Ohlin result does not necessarily hold when preferences are not homothetic.
I was asked if it similar as a case in which the ...
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Heckscher-Ohlin with heterogeneous preferences
could someone really help me out I would need to show a situation in which the Heckscher-Ohlin result does not necessarily hold when preferences are heterogeneous.
Does someone have an idea how I ...
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A question about MWG Exercise 3.D.4
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 ...
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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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Weakly monotone preferences with singleton indifference curves: do any of them admit a utility representation?
Inspired by this question. The original question was answered by Amit with some nice examples. I would like to know the generalized answer:
Suppose we have a preference ordering $\succeq$, which is ...
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Why might a monotone increasing but nonlinear transformation of a utility function not represent the same preferences?
According to a textbook, a monotone increasing but nonlinear transformation of a utility function might not represent the same preferences. Why is it so?
An example of such preference would be ...
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Why is a monotone increasing but nonlinear transformation of a utility function not represent the same preferences if the preference is complete?
According to a textbook, in the context of uncertainty (e.g. in lottery), if the preference is complete, a monotone increasing but nonlinear transformation of a utility function would not represent ...
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Does non-monotonicity imply non-satiation always? Why or why not?
I understand that monotonic preferences imply non-satiation. But I am not sure 100% if non-monotonic functions always have satiation. An intuitive and mathematical explanation would be very helpful.
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Why does quadratic utility function imply $\mu-\sigma$ preference?
Why does investors having quadratic utility function mean that their optimal portfolios can be chosen by only considering mean and variance of returns i.e. imply $\mu-\sigma$ preference?
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Net Preference Relations
Let say the electorate consists of three segments of voters: 1, 2, and 3 with corresponding weak preference relations defined over the candidates. Let the preferences be given by --
Segment 1: Biden >...
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Given a rational $\succsim$ over a finite set $X$, show that there exists $x \in X$ such that $x \succsim y, \forall y \in X$
I have been able to show this constructively, but would like to prove it by induction. However, I am stuck with the induction step:
Consider $\succsim$ defined over $X=\{x_1,...,x_n\}$ and where ...
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Study whether $\succsim$ represented by $u(x)=\lfloor x \rfloor$ is continuous [closed]
Using the following definition of continuity: $\succsim$ is continuous if for any bundles $x,y,z$ such that x$\succ$y$\succ$z, there exists $\alpha \in (0,1)$ such that $\alpha x + (1-\alpha)z \sim y$....
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A preference relation $\succ$ is defined as $(x_1,y_1)\succ (x_2,y_2)$ if $x_1>x_2$ and $y_1> y_2$ [duplicate]
Does this satisfy completeness property? I need an intuitive explanation of this preference relation as well.
I am confused about the way how this relation is defined. The commodity Y in the first ...
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Framing Effect Risk-Aversion Risk-Pursuit
I am an economics' graduate seeking to study Law and I want to illustrate the importance of legal certainty. Penalties, Costs are negativelly framed.
I am trying to word.
200 dollars with 50% ...
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Assumption of sufficient wealth in quasi-linear preferences
Whenever we talk about quasi-linear preferences, we assume that the consumer is sufficiently wealthy. As far as I understand is that we need that assumption in order to obtain an interior solution.
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Representing preference orderings over a finite set of outcomes by two payoffs
I have read the following statement and I am having difficulty understanding the second part:
Any set of preference orderings over a finite set of outcomes can be represented either by ...
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Showing that a preference relation admits a utility function representation
Setting: We have two choices of goods $(x_1,y_1)$ and $(x_2,y_2)$ from the set of choices $[-1,1]^2$. Moreover, we have the following preference relation $$(x_1,y_1)\mathcal{R}(x_2,y_2)\iff |x_1|\geq|...
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Preference: Convexity and Monotonicity
I need an example of a
Convex, non-monotonic preference
Non-convex, monotonic preference
I figured that an example of non-convex, monotonic utility preference could be $U(x,y)=x^2+y^2$.
For convex, ...
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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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Everyone has the same marginal rate of substitution
I'm currently reading Varian's Intermediate Microeconomics and what struck me, is this statement on page 89 of the 8th edition.
If everyone faces the same prices for the two goods, then everyone ...
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Linear Homothetic Utility
A Homothetic Utility is where
$$
\forall x,y, \forall a \in \mathbb{R}_+: \ u(ax,ay)=au(x,y)
$$ (or its monotonic transformation).
A linear Homothetic utility is defined as $$
\forall x,y, \forall a \...
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If an ordinal-scaled utility function is defined via strictly increasing transformation, how can it represent a case of indifference?
Problem: According to Wulf Gaertner’s (2009, p. 13) A Primer in Social Choice Theory, any strictly increasing transformation of an individual’s ordinal utility function is informationally equivalent. ...
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Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?
$\succsim$ is a weak order over $\mathbb R^L$.
For a closed budget set $B\subset\mathbb R^L$, define demand correspondence: $$D(B)=\{x\in B|x\succsim y\forall y\in B\}$$.
We know that $D$ is always ...
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Obligations of a company
Any company may "feel" obligated towards several parties at once:
its shareholders
its employees
its customers
its partner companies (sub-contractors and suppliers)
its country and social environment ...
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WARP implies completeness, transitivity and thus rationalizability. What is wrong with the statement?
Let $A$ be a menu and $R$ be a complete and transitive binary relation. Define choice correspondence generated by $R$:
$$c_R(A)=\{x\in A|| xRy \ \forall y\in A\}.$$
Theorem (from Kreps 1988): for ...
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Substitution effect when price of both goods change by the same percentage
I am trying to grasp the concept of income- and substitution effects.
The way, I've understood it, the decomposition bundle is found, at the original indifference curve, where the slope equals that ...
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How are preferences related to relative prices?
For instance, across regions of a country or between countries.
Is that different preferences for food lead to distinct relative prices in different regions or countries? Or is it the other way ...
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GARP and SARP assumed mononticity?
Monotonicity means the decision maker prefer more goods than less. It is not mentioned in textbook that SARP and GARP preasumed monotonicity, implicitly.
GARP: if $a$ is indirectly revealed preferred ...
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Is GARP trivially satisfied with only 1 good?
As with all revealed preference work, when the number of goods is greater than 1, then GARP (Generalised Axiom of Revealed Preference) is not always trivially satisfied. However, is it always the case ...
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Proof of monotonocity of preferences
Question from Intermediate Microeconomics by Hal Varian:
"We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve ...
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An example of preferences over a countable set that cannot be represented by a utility function
Give an example of preferences over a countable set in which the preferences cannot be represented by a utility function that returns only integers as values.
I know a utility function exist that ...
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Preference relations defined by $x_1^n + x_2^n$ converge to $\max\{x_1, x_2\}$
In the problem set 2 of Rubinsteins Microeconomics (btw is there a comparably nice written book on macroeconomics?) there is the following question:
Let $\succ_n$ be the preference relations defined ...
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Finding Optimal Bundle and Change in Satisfaction after Changes in Budget Constraint
I am looking at the following exercise and struggling with the solution proposed by my microeconomics book.
A consumer spends all his income on two goods, X and Y. The prices he paid and the ...
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