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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90 views

WARP implies SARP: A 2 Good Case

I am considering an example where there are two goods and three budget sets $(\mathbf{p}^{(n)},w^{(n)}),n=1,2,3$. If we assume $\mathbf{p}^{(n)} \cdot \mathbf{x}(\mathbf{p}^{(n+1)},w^{(n+1)}) \leq w^{(...
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46 views

Is this Incomplete or Indifferent? [closed]

Given X = {1,2,..., 100}. For x, y in X, define x # y if and only if x - y is a positive prime number. Is the # relation incomplete? I don't particularly understand the reasoning as of yet, and though ...
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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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2answers
242 views

Are Indifference Curve graphs continuous given the preferential definition of continuity?

Assume the relation $\succeq$ is continuous (by the preferential definition). Does this mean the graph of Indifference Curves are continuous? Since $\sim$ satisfies the definition for $\succeq$, we ...
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1answer
84 views

Understanding the Continuity axiom of preference

Let $x^{1}, x^{2}, \cdots \to x$ where each $x^{i}$ and $x$ are elements of the set of consumption bundle or the choice set $X$. If $x^{i} \succeq y$ for each $i \geq 1$ then $x \succeq y$. This is ...
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71 views

Do the continuity axiom and transitivity axiom justify non-satiation?

Let's assume on the contrary that the indifference curve is "thick" or crosses. We can only assume the four axioms: completeness, transitivity, reflexivity and continuity. We do not assume ...
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55 views

King–Plosser–Rebelo Preferences and Additively Separable

The wiki of King–Plosser–Rebelo preferences says that the utility function has the multiplicatively separable form $$u(C, L)=\frac{1}{1-\sigma_{c}} C^{1-\sigma_{c}} v(L)$$ and "in the limit case ...
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1answer
55 views

How are weak preferences different to strict preferences/indifference?

Given a utility function $u(\cdot)$ and two bundles $x$ and $y$. Assuming $u(x)=u(y)$. I am to prove or disprove that $x \succcurlyeq y$. Now I'm confused by this. We say $x$ is strictly preferred to $...
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1answer
68 views

The Price and Demand Index in Homothetic Kimball Utility

Suppose with Kimball preferences, utility $Q$ from consuming $\left\{q_{\omega}\right\}_{\omega \in \Omega}$ is implicitly given by $$\int_{\omega \in \Omega} Y\left(\frac{q_{\omega}}{Q}\right) d \...
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1answer
77 views

The Intuition of CES Utility

Suppose a (symmetric) CES utility function $$U(\mathbf{x})=\left[\int_{\Omega}\left(x_{\omega}\right)^{\frac{\sigma-1}{\sigma}} d \omega\right]^{\frac{\sigma}{\sigma-1}}, \sigma>1$$ 1 The indirect ...
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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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Social welfare in terms of preferences

How does one define a social welfare in terms of individuals’ preferences $\succeq_i$? If we have utility functions $u_i$ then a social welfare maximizing outcome $x$ is simply one that maximizes $\...
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119 views

Convex rationalization when the budget sets are segments?

Backgroud: SARP can be defined on general budget set. SARP: Assume for all $B$ the choice $c(B)$ is only one element. If $x_i,x_{i+1}\in B_i$, and $x_i = c(B_i)$, for all $i\in \{1,N-1\}$, then $x_1=...
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1answer
260 views

How to prove that a utility function U(x,y)=min(x,2y) is quasiconcave?

I have a question that asks: "Let there be two goods 1 and 2.Let $x$ and $y$ denote their respective quantities.$(x,y)$ represents a bundle. Suppose a consumer’s preferences over bundles in $R^2_+...
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1answer
143 views

Necessary and sufficient conditions for the existence of a utility function

I was reading Jehle and Reny, Advanced Microeconomic Theory, where they discuss in detail, the choice problem of a consumer. The Consumption Set (or Choice Set) $X$ is a subset of $R_+^n$, is closed ...
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1answer
71 views

Local nonsatiation

Suppose that $x^*$ satisfies $x^*\succsim x$ for $\forall x\in\{{x∈X|p·x\leq m}\}$. How can we prove that $x\succsim x^*$ $\Rightarrow$ $p·x≥m$ if $\succsim$ is locally nonsatiated? My idea for this ...
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44 views

What is the usefulness of Cobb Douglas functions? Why do we use them so often?

Hard to find much explanation as to why we generally use CD functions so often. My understanding is that it is usually well behaved when used for utility functions and preferances, since it is convex,...
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44 views

Assumptions on preference relation

This question is from Harvard seminar problem set (Q-3 part b) https://www.studocu.com/en-us/document/harvard-university/economics/mandatory-assignments/econ2020a-14-ps01-please-give-as-much-...
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1answer
74 views

max{x1,x2} where P1not=p2

I have seen min{x1,x2} functions representing perfect compliments but have never seen a max{x1,x2} function anywhere in my book or lectures, I also have never seen anything about p1 not equaling p2. ...
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2answers
129 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
86 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
72 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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59 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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27 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
48 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 ...
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47 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 ...
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1answer
78 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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53 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.
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192 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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95 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
242 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 ...
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1answer
124 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 ...
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1answer
36 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
33 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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2k 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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407 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/...
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1answer
102 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
113 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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94 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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86 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 ...
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1answer
50 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
45 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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48 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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45 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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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
314 views

Convex Preference but Convex Utility

Can preference be convex when utility is not a concave function (e.g. $U=x_1^2 + x_2^2$)?
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115 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 ...
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3answers
817 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
33 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
275 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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