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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2answers
90 views

Utility function for introductory microeconomics

What are the utility functions standardly used in introductory microeconomics courses. My own list would include Perfect substitutes: $U(x,y) = ax+by$ Perfect complements: $U(x,y) = \min(ax,by)$ Cobb ...
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1answer
81 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,...
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1answer
58 views

Marshall demand for simple CES utility

Assume that preferences are given by a utility function is given $$u(x_1,x_2) = (x_1^\rho + x_2^\rho)^{1/\rho}$$ what then are the Marshall demand given budget constraint $$p_1x_1 + p_2x_2 \leq I$$
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1answer
50 views

preference convexity and existence of equilbria

Consider a production economy with $L$ goods, a single consumer and a single producer whose production set are given by $Y\subset R^L$. Question is to find the existence condition of equilibria of ...
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1answer
21 views

Question regarding preferences in Gale and Shapley (1962)

Is it correct to say that preferences in the classic Gale and Shapley College Admissions problem are quasi-linear? Or is this something thats introduced later in the literature, vis a vis Shapley and ...
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1answer
37 views

Can you please help me find this topic in Mechanism design/Rational choice theory?

When I was in university, I remember studying some kind of topic in adv microeconomics where someone gives you three options, where one is obviously worse and is put there just to deceive you so that ...
3
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1answer
35 views

If a rational preference relation over simple lotteries $\succsim$ are convex then they satisfy independence?

Let´s say there is an uncertain situation with $N$ possible consequences $C = \{C_1, . . . C_N\}$. Assume that there is a rational preference relation $\succsim$ over simple lotteries. I know that if ...
2
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1answer
59 views

Quadratic utility: monotonicity and risk aversion

I am taking macro class this fall. One of the problems asks whether decreasing absolute risk-aversion and ever-increasing consumption are two unattractive implications of the quadractic utility ...
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1answer
48 views

A question from MWG 2F12

This question is from MWG if walrasian demand function is generated by a rational preference relation then it must satisfy weak axiom. I cannot prove this statement. How can I do?Thanks alot.
2
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2answers
160 views

which type of goods maximum utility function represent?

I am not sure, which type of goods does the maximum utility function represent i.e., $U(X_1, X_2) =\max(X_1, X_2)$. As the $U(X_1, X_2) =\min(X_1, X_2)$ represent the complementary goods, and $U(X_1, ...
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0answers
43 views

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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1answer
228 views

Rational preferences/individual decision-making theory

I am taking advanced micro course this semester. In one of the problems we need to determine whether the preference relation is rational (i.e. complete and transitive). Since we have not really ...
2
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1answer
46 views

Proof on weak axiom of revealed preferences

I read the following statement. “ A utility maximizer with strictly convex and strongly monotonic preferences satisfies weak axiom of revealed preferences.” How can I prove or show this? I cannot ...
2
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1answer
28 views

Measuring and assigning utility numbers

I was recently introduced to the concept of cardinal utility. In real life, how do we assign these utility levels? For example if i wanted to assign numbers to my own utility indifference curve for ...
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1answer
28 views

Does transitivity qualify as a reason for Indifference curves intersecting each other?

Transitivity in preferences seems as a flawed concept because there might be a situation where A>B, B>C but A<C. Going by this analogy it seems that it does not qualify as a reason for ...
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1answer
176 views

what is monotonicity and strict monotonicity in preferences?

I am really confused between monotonic preferences and strictly monotonic preferences, I saw some video and read certain answer where it is mentioned that the When preferences are monotone / weak ...
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2answers
206 views

Showing utility function gives preferences that are rational and convex

Consider a consumer with preferences relation $\succsim$ over non-negative commodities $x_1$ and $x_2$ such that their utility U = $x_1$ + $\ln(x_2)$ Are these preferences rational and are they convex/...
3
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1answer
80 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. ...
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1answer
69 views

HARA preferences details

I am searching for some exntensive details about HARA preferences. Where could I find some extensive details for HARA preferences? Something like a textbook or notes
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1answer
59 views

Could lexicographic preferences on N^2 be represented by a utility function u: $N^2$ to $Z$?

I got this question on a homework: Could lexicographic preferences on $N^2$ be represented by a utility function u: $N^2$ to $Z$? I've heard countless times that lexicographic preferences can't be ...
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0answers
75 views

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 ...
3
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1answer
34 views

Question about Strict Preference Relation

Strict Preference usually states that x is strictly preferred to y if : < x is weakly preferred to y and not y is weakly preferred to x >. Let me split the < > part into two segments: x ...
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1answer
31 views

Strictly increasing but not convex preferences

Is it possible to have preferences that is strictly increasing but not convex? Will perfect substitutes indifference curves show strictly increasing but not convex preferences? I am confused, as won't ...
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45 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 ...
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1answer
25 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 ...
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0answers
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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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1answer
178 views

Convex Preference but Convex Utility

Can preference be convex when utility is not a concave function (e.g. $U=x_1^2 + x_2^2$)?
4
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2answers
91 views

What are the correct utility functions?

It is common to talk about utility functions. For example in a universe with only two goods, we might assume each person (or group of people) carries a function $u(x,y)$ in their heads. When offered ...
3
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3answers
489 views

Are Cobb-Douglas preferences monotone according to the marginal utility condition?

I understand that Cobb-Douglas preferences represented by $U(x,y)=x^ay^b$ are strictly monotonic, because increasing at least one of the goods in the bundle increases utility. However, another ...
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1answer
27 views

Expenditure function. Prove that this set is bounded

I need to prove that the following set is bounded in order to derive the expenditure function: $e(p,v)=min_x px$ ST $\{x \in R^n_+$ such that $U(x)\geq v\}$. Knowing that $U(x):R^n \longrightarrow R$ ...
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1answer
92 views

Examples of risk-neutral firms or people in business

I am looking for examples of approximately risk-neutral firms or people in business. Is there an industry where risk-neutrality is common for some agents (firms or people)? Are there perhaps time ...
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2answers
41 views

Remove Linear Good From Quasi-linear Utility Function

Given a quasi-linear utility function: $u(x_1, x_2) = f(x_1) + \beta x_2$, $\beta > 0 $ What would happen if good 2 ($x_2$) is removed from the market? Would the new utility function be: $u(x_1) =...
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1answer
80 views

Differentiability of the utility function and indifference curves

Comment on the following affirmative: In the traditional consumer model, the hypothesis of differentiability of the utility function and of convexity of preferences, assure the indifference curves ...
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0answers
25 views

Ordering of bundles for which the axioms of transitivity, continuity, strong monotonicity and convexity are valid

Let there be two bundles which are obtained from the sequences $x^n = (x_1,x_2)= \left( 2 + \frac{1}{n},5 \right)$ and $y^n = (y_1,y_2) = \left(4 + \frac{2}{n}, 5 \right)$. Is it possible to obtain an ...
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0answers
50 views

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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1answer
133 views

Strong monotonicity and weak monotonicity

We say $\succsim$ represents weak monotonic preferences if $$x,y \in X, \,\, y >> x \implies y \succ x $$ where $y >> x$ means that every element of $y$ is greater than every element of $...
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1answer
29 views

Completeness of the strict binary relation

How do I show that considering the preference relation $\succsim$, then $\succ$ is not complete? I tried the following (which I don't know if it's right) but I'd also like to know if it's possible ...
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1answer
55 views

Is the satisficing choice function rationalizable if the ordering isn't observable?

Edited: Say an observer observes only the choices made by the decision maker (and the sets from which these choices are made), but does not know the ordering. Then would the decision maker's choices ...
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1answer
47 views

How to describe a utility function in words?

Suppose I have a utility function of Cobb-Douglas form $$U(x, y) =x^{0.2}*y^{0.8}$$ I want to describe it in words. I would say like: The utility of consumer is captured by number of good x and ...
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0answers
39 views

$a\geq 0$, $x\succsim y$ implies $x+a\succsim y+a$ so the preference is linear?

$\succsim$ is a continuous and local non-satiate weak order. $x,y,a$ 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 (...
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1answer
89 views

Continuity of preferences

Let $\succsim$ be a transitive and reflexive relation on a metric space $X$ with closed upper and lower contour sets. If $\succsim$ is not complete, does it hold that: for all converging sequences ...
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1answer
63 views

$a\geq 0$, $x\sim y$ implies $x+a\sim y+a$ so the preference is linear?

$\succsim$ is a countinuous and convex weak order. $x,y,a$ 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 ...
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0answers
34 views

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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1answer
45 views

$x\sim y$ 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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1answer
77 views

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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0answers
46 views

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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1answer
377 views

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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1answer
85 views

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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3answers
69 views

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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2answers
68 views

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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