# Tagged Questions

A tag for all questions involving a type of utility function.

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### Risk tolerance and expected utility function

Question: Consider the following crime utility function: EUcrime = pu2 + (1-p)u1 where u1 is return from illegitimate activity and u2 is return if punished and p is the probability of conviction. Let ...
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### Risk seeking utility

I am stuck on a question in an archived course on BerkeleyX's CS188x Artificial Intelligence. Which of the following would be a utility function for a risk-seeking preference? That is, for which ...
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### Preference relations that are order-separable

This question concerns dense order relations and separability of orders. This question has changed radically since the first version. Hence the first two answers below now look strange because they ...
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### Negative Utility Function

I'm using a negative utility function to compute portfolio allocation, $u(x) = -p_1e^{-X/T} + -p_2e^{-Y/T} + -p_3e^{-Z/T}$ where $p_1 + p_2 + p_3 = 1$ Certainty equivalence of this I get through, ...
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### Constrained maximization of …

I have to maximize $U(x,y)= Min(ax+y, by+x)$ s.a $p_{1}x +p_{2}y =m$. I try the traditional solution for a leontieff $(ax_{1}+y= by_{1}+x)$ function but I'm not sure.. beacause exist regions where one ...
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### Problem with code for numerical integration in matlab.

Hi I have problem with calculating this expected utility with means of numerical integration, using matlab. The matrix stock data is a 1000x8 matrix with columns representing 7 stocks (columns 2-8, ...
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### What are some techniques of constructing a good utility matrix?

A utility matrix is considered to be subjective and arbitrarily defined. Therefore, we run the risk of over-emphasizing or under-emphasizing the possible alternatives. Are there ways to design an ...
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### what is a ordinally quadratic function？

A function is ordinal equivalent to another means there exist a (unique) monotonic transformation between wiki definition of ordinal utility. I am a little confused, a function is ordinally quadratic ...
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### Are these preferences rational according to utility theory?

I have this question about whether preferences satisfy the $6$ properties of utility, and am particularly stuck on the boundness, coherence and continuity conditions. Here is the problem: If one ...
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### Does there exist a utility function for these gambles and preferences?

Suppose that you prefer a gamble which pays $£100$ with probability $0.5$ and $£10$ with probability $0.5$ to a gamble which pays $£200$ with probability $0.25$, $£50$ with probability $0.25$ and $£10$...
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### Arrow's theorem, strategic thinking and utilitarianism

I have this problem as part of a course on Decision Theory, and was not sure about question a (4th condition of Arrow's theorem) and question dii (utilitarianism). I have provided the whole question ...
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### LEN-Model equivalency

Starting position is a principal-agent-model with incomplete information (moral hazard) and the following properties: Agent utility: $u(z)=-e^{(-r_az)}$ Principal utility: $B(z)=-e^{(-r_pz)}$ Effort ...
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### Creating utility function with certain properties

This is a fun little task I need help completing. Im creating a game-theoretical model for the utility a government get from labour rights (R) and FDI (F), and I need a utility function to have ...
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### Optimal Insurance Coverage - risk neutral and risk loving consumers

I'm struggling with understanding a problem in finance: We have 2 states: $S_1$: bad state $Y-K = 2000$; probability $\pi$ = 10% $S_2$: normal state $Y = 5000$; probability $1-\pi$ = 90 ...
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### Stochastic dominance characterization

Consider two probability measures on $\Bbb R$ given by $\mu$ and $\nu$. We write $\mu\leq \nu$ if there exists a joint distribution $P$ with the latter marginals such that $P(x\leq y) = 1$. In ...