# 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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### Intuition behind the Compensating Variation!

In Economics, we can calculate the compensating variation (CV), which (to my understanding) is the amount of money we would need to give back to a consumer to keep them at the same level of Utility ...
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### Define a cost function for an agent walking on a 3-parts segment.

Let us consider an agent that can walk along a one-dimensional room (i.e. along a segment). The segment is split into three equal parts and we assume the agent is in the middle piece of the segment, ...
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### Concave Utility function

I'm trying to solve the following question in the book Optimal Statistical Decision: Question: Consider two boxes each of which contains both red balls and green balls. It is known that one-half the ...
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### Why does the uniform law of large numbers hold with non-i.i.d. random variables in Bayesian experimental design?

This paper, Asymptotic theory of information-theoretic experimental design, studies Bayesian experimental design where in each round $n$, the experimenter selects a stimuli $X_n$ that maximizes mutual ...
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### What is the discounted (4%) difference in health outcomes between Treatment A and Treatment B using ICER, QALY and utility value?

I'm studying health economics and have been racking my brain trying to find the right answer to this problem, but I keep getting it wrong no matter what I do. I haven't had any trouble calculating ...
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### Difference between Pareto optimal redistribution and strict pareto optimal redistribution

Can someone explain the difference between Pareto optimal redistribution and strict pareto optimal redistribution? Because I know the definition but I do not understand it.
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### Pareto optimal redistribution in binary exchange economy

Consider binary exchange economy with two goods and two agents, whose preferences are defined as follows: $\textbf{x}\succ \textbf{y}$ iff $x_{1}x_{2}>0$ and $y_{1}y_{2}=0$. In Edgeworth's box ...
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### Game holder is always losing money in the St. Petersberg Paradox?

The St. Petersberg Paradox is described as follows: A gambler pays an entry fee $M$ dollar to play the following game: A fair coin is tossed repeated until the first head occurs and you win $2^{n-1}$ ...
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### Von Neumann–Morgenstern: compare coefficients in Archimedean axiom

Now we have: Axiom1: Completeness of $\succeq$. Axiom2: Transitivity of $\succeq$. Axiom3: Independence: For any $N$ and $p\in (0,1]$, if $L\succ M$, then $pL+(1-p)N\succ pM+(1-p)N$. Axiom4: ...
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### Should we stay or pay the exit fee given the utility function

You have invested $10\%$ of your wealth in a hedge fund; the other $90\%$ is in cash and there is no time value of money. One year from now the hedge fund will cease operations; it will either fail ...
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### What is α in a Cobb-Douglas utility function?

Sorry if this is not the place to ask, I'm new here. I'm studying economy but I'm struggling to understand the Cobb-Douglas utility function. If we've one such that xt is consumption in period t, and ...
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### How can I differentiate the expected value of a utility function?

Suppose I have a maximisation problem $$\underset{0\le R(y)\le y} \max E\left\{u_B\left[ y-R( y)\right]\right\}$$ subject to$$E\left\{u_L\left[R( y)\right]\right\}\ge \bar U_L$$ $B$ and $L$ are simply ...
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### How to solve this expectation problem?

I truly don't know how to name this question properly, and I will try my best to be more specific. And here is my problem Suppose a person has 2 choices. For choice A, he gets $Z$ guaranteed dollars; ...
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### Philosophically motivated risk metrics

During a random process over a sample space $\Omega$, an agent incurs a cost (say, in money) given by a random variable $Z:\Omega \rightarrow R$, which is determined by the agent's action. The agent ...
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### Assume the marginal utility of $u(w)$ is $\alpha e^{-\alpha w}$, $\alpha > 0$ i.e. $u'(w)=\alpha e^{-\alpha w}$, $\alpha>0$.

Assume the marginal utility of $u(w)$ is $\alpha e^{-\alpha w}$, $\alpha > 0$ i.e. $u'(w)=\alpha e^{-\alpha w}$, $\alpha>0$. a) Compute the utility function $u(w).$ b) Let $X_1$ and $X_2$ be two ...
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### Find the optimal weighting distribution for a die given a set prize values

Say you have $B$ boxes, each of which contains a prize of value $v_b$. You have a $B$-sided die, and you win the value of box $b$ by rolling $b$. You get $R$ rolls, and so can collect multiple prizes, ...
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### What is the probability of being selected for execution? [closed]

Thirty Arkton hostages in a Brumton prison in occupied Arkland need to select three of them to be executed by their captives in retribution to the killing of three Brums by the Ark army. They tear ...
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### Problem using Lagrange Multipliers in Utility function

I am to optimize utility given the utility function $$u(c,l):=c-\frac{\eta}{\eta+1}(24-l)^{\frac{\eta+1}{\eta}},$$ where $c$ represents consumption and $l$ represents leisure. The budget constraint ...
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### The indifference curve of $U(x,y)=\min(x,y)^2+\max(x,y)$
I am trying to draw the indifference curves for $U(x,y)=\min(x,y)^2+\max(x,y)$. It should not come as a straight line, right? I tried to calculate it by setting one variable $= 0$ and the other ...