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# 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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140 views

### Order relations and preferences using logic

I want to understand order relations using their underlying implication mechanics and what this means for certain results, specifically looking at preference relations. Using the logical rules of ...
1 vote
59 views

### 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 ...
100 views

### Preference relations based on Varian

I understand that there is no universally agreed terminology for preference relations. However I need to pin down a definitive way to think about them (both for my exam, and my own sanity). Please can ...
71 views

### Assigning dollar value to intangible costs and benefits

I am trying to develop a framework that a person can use to help them decide where to live. The idea is to assign a dollar value to various attributes (e.g. work opportunities, cost of living, climate,...
60 views

### Conflicting Definitions of Weak Monotnocity (preferences)

Strong Montonicity my sources seem to agree on Strong monotonicity, i state equivalent definitions below. But weak montonicity i keep finding what appear to be conflicting definitions. In the ...
102 views

### Risk aversion and utility transformation: are preferences still the same?

If you have two utility functions $u(\cdot), \; v(\cdot)$ such that $v(x) = f(u(x))$ for some monotonic transformation $f(\cdot)$, then $u(\cdot)$ and $v(\cdot)$ represent the same preference ...
70 views

### Willingness to sell a lottery ticket vs. willingness to buy a lottery ticket

I'm struggling with this question: There is a lottery which gives you D with p = 0.25 and L with p = 0.75 while initial wealth is w (w > D > L > 0). What is the minimum price the person would ...
42 views

### Linear Engel Curve

How to prove that if the Engel curves (expenditures as a function of wealth) are linear in wealth, then the indirect utility function has the form $v_{i}(p,a_{i})=\alpha_{i}(p)+\beta(p)a_{i}$ for an ...
1 vote
29 views

### 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, ...
10 views

### How to rationalize the following behaviors using preference relations?

The producer wishes to produce at least $y^*$ units. Once he has achieved that goal, he maximizes profit. The producer maximizes profit, but already employs $a^*_1$ workers and will incur a cost c (...
16 views

### What are the conditions to determine whether demand function is rationalizable?

A consumer chooses a bundle (z, z, . . . , z) where z satisfies $z Σp_k = w$. The book (Rubinstein's) states that the demand function x(p,w) can be rationalized if there exists a preference such that ...
89 views

### What does it mean if the derivative of the Utility function (at the optimal bundle) is 0?

It states in my book that under strict monotonocity, the derivative of U(x*)=0 can be possible although it's unlikely to happen. What does this exactly mean?
39 views

### What does differentiability of Utility function at an optimal solution x* mean?

I am working with Rubinstein's book. It states there that if preferences are differentiable, then value per dollar at a bundle of a commodity is as large as value per dollar of the bundle of any other ...
1 vote
73 views

### Help with checking work for preferences over consumption and leisure question

I was wondering if anyone could help me check my work for the following question, and if I am wrong, help me correct my mistakes? Question: Work:
1 vote
34 views

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### Cost, disutility and loss aversion applied to a queuing system

I am currently working with a queueing system where customers enter a system and are served. Service takes a random amount of time $\Delta t \sim F(\cdot)$ where $F:\mathbb{R}\to[0,1]$ is a cumulative ...
106 views

### On risk aversion and validity of utility functions

Question A risk-averse, non-satiated investor has decided to use the utility function $$U(w) = w + dw^2,$$ where $$d \leq 0$$ is a constant, to describe his preferences. The investor has a current ...
1 vote
208 views

Question A risk-averse, non-satiated investor has decided to use the utility function $$U(w) = w + dw^2,$$ where $$d \leq 0$$ is a constant, to describe his preferences. Derive an upper bound for $w$, ...
355 views

### A preference relation is continuous if and if there exists a utility function that represents it

Suppose that $X \subset \mathbb{R}^n$. A preference relation $\preceq$ is reflexive, complete, transitive and continuous if and only if there exists a utility function $u:X \rightarrow \mathbb{R}$ ...
62 views

### 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 ...
33 views

### 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 ...
99 views

### Indifference curve - corner point - Q about notation

I wonder if someone can help me interpret the vertical bar notation used in the picture. From the graph, it is apparent that the consumer will consume only good $x_1$, since the indifference curve is ...
31 views

### Is it possible to have mean-variance preferences with different states of nature? Mean-Variance and Expected utility together?

I have to maximize mean-variance preferences like this (where Pi is a profit function): \begin{align} \label{eq:9} \max\limits_{Q_{F}^{\{x\}}}Z_{w}= E[\pi{\{x\}}]-\frac{A}{2}Var[\pi{\{x\}}] \nonumber\\...
298 views

### Convexity of preferences (dissimilar definitions)

Varian's Intermediate Microeconomics describes convexity as $$\text{Given } x, y \in X: x \sim y \implies \forall t \in [0,1], tx + (1-t)y \succeq x,y$$ The other definition I read everywhere is: \...
147 views

### Are these preferences locally non satiated? U(x1,x2)=(x1-1)/(2-x2)^2

I got this utility function representing certain preferences. Are these preferences locally non satiated? Can somebody please explain me with the exact definition of local non satiation why these ...
199 views

### Does Concavity or quasi-concavity imply local non satiation?

I got a utility function with convex Indifferences curves and therefore convex preferences. Convexity of preferences implies Quasi-concavity. I would like to know if there is a relation between ...
1 vote
### 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 ...