# 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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### What is the importance of Epstein-Zin preferences?

I've heard that there is a lot of work being done recently that applies Epstein-Zin preferences. The Wikipedia page doesn't seem to be very full. Why are Epstein-Zin preferences important? How does ...
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### Lexicographic preference relation cannot be represented by a utility function

I am stuck on the following exercise, related to preference relations and von-Neumann-Morgenstern utility function. A farmer wants to dig a well in a square field $[0,1000]\times[0,1000]$. The ...
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### What is the definition of exogenous and endogenous preferences?

Wikipedia states: Exogenous Preference -- one that comes from outside the model and is unexplained by the model. Endogenous Preference -- preferences then cannot be taken as given, but are affected ...
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### What is an example of a utility function where one good is inferior?

Say the consumer has a standard convex, monotonic preference over Apples and Bananas. (Update: I'd like the preference to be as 'standard' as possible. So ideally we have diminishing MRS everywhere ...
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### What is the difference between "aggregation" and a "representative agent?"

What is the difference between "aggregation" and a "representative agent?" I'm sorry if I'm not entirely clear on this question, but that's why I ask. It seems to me as if a representative agent is ...
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### When treating a relative, normalized utility function as a pmf, what is the interpretation of Shannon entropy or Shannon information?

Suppose $\Omega$ is a set of mutually exclusive outcomes of a discrete random variable and $f$ is a utility function where $0 < f(\omega) \leq 1$, $\sum_\Omega f(\omega) = 1$, etc. When $f$ is ...
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### Has the assumption that individuals' tastes do not change over time been rigorously challenged?

In their seminal paper De Gustibus non est Disputandum, Stigler and Becker (1977) surveyed four classes of phenomena widely believed to be inconsistent with the stability of tastes: addiction, ...
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### Fair voting procedure when there are many issues

When several people have to decide about a single yes/no issue*, the natural decision rule to use is the majority rule. But when there are many issues to decide upon, the majority rule is "unfair" ...
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### What utility functions are equivalent to additive functions?

Call a utility function $u(x,y)$ additive if there exist functions $v_x,v_y$ such that: $$u(x,y)=v_x(x)+v_y(y)$$ Consider the function $u(x,y)=xy$. It is not additive, but, it can transformed using a ...
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### What are the economic benefits of SLAPP in file sharing/piracy?

Spin-off from Piracy/File sharing - Why aren't songs, movies or ebooks given for free (+ads) like TV? What are the economic benefits of SLAPP in or out of file sharing/piracy? There's a comment in ...
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### 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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### Quasiconcavification

Let $f_1, f_2$ be two smooth strictly-quasiconcave functions. Do there always exist monotone transformations $g_1,g_2$ such that the sum $g_1\circ f_1 + g_2 \circ f_2$ is ​a strictly-​...
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### Is MRS supposed to have a minus sign or not? What's there to say about convexity of preferences?

If we have a utility function $U(x_1, x_2) = x_1(x_2+1)^2$ of some consumer, then $$MRS_{x_1, x_2} = \frac{\color{red}{-}(x_2+1)}{2x_1}$$ Some books have a $\color{red}{-}$. Others and Wiki don't ...
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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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### Utility Representation of Lotteries

We went over a lemma in class leading up to a larger theorem. The Lemma states: Let $\succeq$ be a rational preference relation on $\mathscr{L}$ and let $\succeq$ admit utility representation under ...
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### Sum of Homothetic Functions

If two utility functions represent homothetic preferences, will their sum also be homothetic?
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### 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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### How can I tell if 2 different utility functions represent the same preferences?

I need to verify that $u(x,y)=x^{1/3}y^{1/3}$ represents the same preferences as $v(x,y)=x^3y^3$. Obviously these are completely different functions with different derivatives, so what am I comparing? ...
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### (Preference Relation/Set) Continuous $\succsim$ imply closedness of upper and lower contour sets

[ADDED/MODIFIED] : I have put my proof where the commodity space is simply $\mathbb{R_+}$(e.g. nonnegative reals) for simplicity below. Please share your 2 cent. I have put words to aid my own ...
Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have $$Eu(w+x) = u(w+E(x)-R).$$ The classical derivation ...