# Questions tagged [utility]

For all questions involving utility functions as used in economics and decision theory, including study of their properties or how they can be used to represent preferences.

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### Proving a function is quasi-concave

This is from economics, but I think there's a lot of math involved and I want to make sure I didn't mess anything up. There is a utility function U = $x_1$ + $\ln(x_2)$ such that $x_1$ and $x_2$ are ...
• 31
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### Compute a definite integral that involves exponentials and trigonometric functions.

Let $r > 0$ and let $\vec{\gamma} = (\gamma_i)_{i=1}^2$ such that $\gamma_{1} > 0$, $\gamma_2 > 0$ and such that $\gamma_1 + \gamma_2 < 1$. We consider the following integral: \begin{...
• 9,073
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### Convexity of CES functions

I'm asked to confirm if the CES utility function is convex, and I know it is, I just don't understand why :( My function is: $$U(x_1,x_2)=(αx_1^ρ+(1-α)x_2^ρ)^{1/ρ}$$ pictured here I've seen ...
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### Existence of Maximum and Minimum (Utility Functions)

I'm given the following question: Show that any utility function on a finite set of alternatives attains maximum and minimum values by using Bolzano-Weierstrass Thm. Well, if it were the case that we ...
• 467
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### maximizing using lagrangian

So I have a question from my quiz. I don't want a specific answer but a help or guidence. My objective function is F(x,y)=x+4y and my subject is I-Pxx-Pyy=0 where I,Px and Py are both positive ...
1 vote
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### The Arroyo Game versus The Pasadena Game

This choice problem builds on St. Petersburg’s Paradox. Part 7 of this SEP article indicates the problem. Question For all integers $n\geq1$, the Arroyo game pays $X$ where \text{P}\left(X=(-1)^{...
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### Utility function square root [closed]

Could somebody tell my how to calculate $EU(X+2)$, where $U(X)={\sqrt X}$ and X is distributed evenly over the interval $[a,b]$?
105 views

### Maximizing the probability of choosing a ball from two boxes

I am new here but I have a question that I would like to ask. If any body is in the know, kindly assist. The problem is from Berger (1985) statistical decision theory and Bayesian Analysis Exercise No....
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### Total Utility Value Composition of Different Utility Functions

Let's suppose we have a variable $x$ with a domain $X \in [0,1000]$ and two utility functions $uf_1(x)$ and $uf_2(x)$ that describe the utility of $x$ with respect to two different properties. We ...
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### Under which conditions is the expected value of a function a (strictly-quasi) convex function?

I have an indirect utility function - $P(a,b ;\theta)$ - where $a$ and $b$ are positive, deterministic parameters and $\theta$ is a random variable. I would like to study the properties of the ...
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1 vote
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### Intuition for complete monotne functions

While reading papers about utility theory, I've stumbled upon a definition of a completely monotone function (AKA proper), which is a function with $u'>0$, $u''<0$, $u'''>0$ and so on. See ...
• 4,309
1 vote
The choices are of the form $(x; y)$ where $x$ represents the amount of time you have left to live, say anywhere from $0$ to $50$ years, and $y$ represents the amount of time you have left to work, ...