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

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22 views

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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20 views

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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14 views

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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26 views

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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18 views

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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12 views

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 ...
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1answer
32 views

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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44 views

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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20 views

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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9 views

Continuity of utility function in normal form games

I want to characterize the utility functions of normal form games. Let $G$ be a game with a finite number of players $k$ given by the action sets $S_1,\ldots,S_k$ and utility function $u:S_1\times ...
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16 views

Right enunciation/notation in utility maximisation model

I am working on a model that can be defined as a utility optimisation problem but I'm struggling with the enunciation and notation. The model should describe how the utilities of a set of agents ...
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1answer
24 views

List an utility function's values

$S$ is a finite set, and $v: S \to\mathbb N$ is a valuation function. We have $$S := \{0,1,2\}$$ and the valuation function $v$ $$v: S \to\mathbb N\\ k \mapsto 2k+1$$ The task is to list all ...
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2answers
37 views

Utility Maximization with a transformed min function

I was just wondering what the steps one would take to maximize the utility of a function of the form U(X,Y) = min{X,Y} + X subject to income I = $p_x$X + $p_y$Y where $p_x$ is the price of X and $p_y$ ...
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34 views

Local Non-Satiation Proof for utility functions

I have been having trouble with how to go forward with a proof for about three days now. I know the basic structure of the proof, but can't seem to construct it. Basically, I am trying to do a proof ...
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30 views

Making sense of an Expected Utility of a Mixed-strategy Profile definition

I came across a definition of Expected Utility of a Mixed-strategy Profile in Brown's and Shoham's "Essentials of Game Theory: A Concise, Multidisciplinary Introduction" where: "Given a normal-form ...
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30 views

When is a strict weak order representable by a function?

When can we represent a weak ordering on a set $S$ by a function $f$? Suppose I have a set $S=[0,1]^2$ (the unit square) and a strict weak ordering ($<$). By that I mean $<$ has: For all ...
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21 views

Assign an utility function for fuzzy evaluation grades on a $[0,\infty]$ scale

I have a score $ x $ on a scale $ [0,\infty]$. I know that if $0\leq x \leq 1.3$ the fuzzy grade is "None". If $1.3\leq x \leq 2.1$ the fuzzy grade is "MILD". If $2.1\leq x \leq 3.5$ the fuzzy grade ...
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1answer
120 views

Expected Utility Method and a Repeated Game Solution [closed]

I am trying to replicate Bruce B. de Mesquita's (BDM) results on political game theory for prediction. Based on where actors stand on issues, their capabilities, salience, BDM's method attempts to ...
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1answer
94 views

Can a transitive relation be represented by a utility function?

I am currently studying for my Game Theory exam and came across a question that seems pretty basic but somehow can't wrap my head around. So if you could share some insight with me, that would be ...
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1answer
154 views

Underlying utility function behind a linear two-product demand curve

I am trying to find the underlying utility function behind a linear two-product demand model. For that, I use two methods considering the following utility function: \begin{equation} U(q_1,q_2) = ...
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1answer
43 views

Scaling in utility maximisation

If I have the wealth process $$dw_t=rw_tdt+n_tS_t(\sigma dB_t+(\mu-r)dt)-c_tdt,$$ where $n$ is number of $S_t$ and $B_t$ is Brownian motion. If we define the admissible set $A$ as follows: ...
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132 views

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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31 views

Is it a Risk-averse utility function?

I'm a little unsure whether this utility function represents a risk-averse attitude, while it's not wholly concave: Would you define it as both risk-averse and risk-neutral as it seems to have ...
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1answer
47 views

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 ...
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119 views

Ramsey-Cass-Koopmans model/Economic Growth/Phase Diagrams

I haven't had to ask for your service since my second year (I'm in my third now) of University. However, after today's seminar, which was filled with equations, terminology, and more equations, I'm ...
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1answer
66 views

Derivatives defined on a discrete state space

Ive been looking at certain economic papers, and optimal control papers. They define a state variable, $\omega$, which follows a discrete time Markov Chain. Then they define a utility function ...
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175 views

Deriving demand from quadratic utility function

How do you derive the demand for utility $u(x_1, x_2) = x_1^2 + x_2^2 $ and initial endowment is $\omega = (2,2) $? I believe this demand has three cases. Thank you
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91 views

Utility Theory: Risk Averse, which should I choose?

Question: If I am slightly risk averse which do I prefer. (Give a mathematical justification for your conclusion): [0.5, \$450; 0.5, \$400] or [0.1, \$4375; 0.9, \$0] Okay so I get that the risk ...
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1answer
43 views

Finding Preto Optimal allocation if utlities are of the form $u_1=x_{11}x_{12}$ and $u_2=2x_{21}+x_{22}$

There are two persons and two goods in an exchange economy. Initial endowment is $$ \omega = (\omega_1,\omega_2) =\left((1,0),(0,1)\right)$$ The utilities of two agents are given by: ...
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3answers
216 views

Economics, numeraire, utility, demand, marginal rate of substitution

I typed my question in Microsoft Word and printscreen it instead of typing it, this is because I don't know how to type mathematical questions here, sorry for the inconvenience caused.
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1answer
95 views

Intemporal budget by lagrange

Assume that a representative agent lives forever and receives an endowment, denoted yt, in each period. The entire endowment sequence is known with certainty on date 0. The representative agent ...
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1answer
84 views

Making a matrix full rank through affine transformations

If I have (finite) $k$ vectors, $u_1,...,u_k\in\mathbb{R}^N$ that are in general linearly dependent is it possible to take positive affine transformations of the form: $$u'_i=\alpha_i u_i ...
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1answer
126 views

Looking for resources for understanding derivation of demand from utility

I am struggling with my homework and would very much appreciate a rundown of the math or pointers to where I can find help otherwise. Quoting from the assigment: There are $n$ sectors in the ...
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2answers
64 views

Can a game with negative expectation still have a positive utility?

Intuitively, I think not. But I can't clearly prove why. Specifically, I've been thinking about lottery games, where the expectation is obviously negative. But can the utility of hitting the jackpot ...
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1answer
485 views

How to derive demand function from a utility function without any knowledge of Lagrange Multipliers?

How do I derive the demand function for a utility function of, say, $U(x,y)=\sqrt{11x+11y}$ for goods X and Y in terms of $P_x$, $P_y$, and income $I$, with basic mathematics (basic calculus, but no ...
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1k views

Utility function, plotting indifference curves

I know how to plot indifference curves; simply take the utility function and plot some level curves in $2D$. But how to plot a specific indifference curve, so all bundles on it are indifferent to a ...
2
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1answer
105 views

Solving first order constraints; lagrangian function and utility maximisation

I am supposed to find the demand curve if the following is given; $U(x,y) = xy$ price of $x * x$ + price of $y * y = m$ (so a general case, and I will be adding certain prices and income levels ...
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60 views

Utility Max Problem

I have a utility function $U(x,y)=\frac{xy}{x+y}$ and a budget of $200=2x+2y, P_x=P_y=2$. But for the first 50 units of product 1 sell for 2 dollars but for "$x>50$" the price of product 1 ...
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1answer
33 views

Multivariable Calculus Application Question: Utility and MCRS

If a student has a utility function given by $$U(x_1, x_2) = −x_1 + > 10x_ 2^2 − 2x_1x_2$$ where $X_1 = 5$ and $X_2 = 20$. If this student was to eat $5$ less hot meals per month, estimate the ...
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55 views

Infinite fourth moment and maximum entropy

Alright, I expect this is a silly question, but I don't actually know, so. Suppose there is some random variable that's distributed on the reals, and all I know about the distribution is its mean ...
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143 views

preference relation.

In the exercise below I need to check whether the relation below is a preference relation ( need to be transitive (if $x>y$ and $y>z$ then $x>z$) and connected ). But I cannot find an ...
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1answer
95 views

Counterexample in axioms of expected utility theory

This is an exercise problem. Suppose $X_1=200$ with probability $1/3$, $0$ with probability $2/3$. $X_2=200$ with probability $p$, $0$ with probability $1-p$. $X_3=200$ with probability $1-p$, ...
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1answer
66 views

Expected utility representation

I am stuck on some question on utility theory. The question is as follow: Consider $A=[0,+\infty)$, and $Q=${F-cumulative distribution function on $A: \int^{+\infty}_0 x dF(x)<\infty$}, the set of ...
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1answer
85 views

Is the expected utility function linear?

Given the definition of the mixed extension of a finite game as in the link below (only first 7 lines): How to find perfect equilibria in a finite game? We define the expected utility function in the ...
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2answers
138 views

A little question about payoff functions being continuous.

In the mixed extension of a finite game $G$, why are the payoff functions of players continuous? Does it has something to do with being von Neumann and Morgenstern utility functions? Is there other ...
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1answer
83 views

utility and uncertainty of economics

United Petroleum is operating a deep water oil rig in the Gulf of Calexico. Management have been informed that the drilling riser may be susceptible to methane build up and hence at risk of an ...
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1answer
84 views

Finding the value of $p$

I need some help with this question: Consider an individual who possesses the Bernoulli utility function of $u(x)=\dfrac{x^{1-\gamma }}{1-\gamma }$ where $\gamma>0$, $\gamma \neq 1$. Who maintains ...
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1answer
78 views

utility function for nominal attributes

I'm working in a decision making topic where a product (e.g., a hotel) is described by some attributes, that is: $p=(p_1,\ldots,p_n)$. An attribute $p_i$ can either be numeric (e.g., the room average ...
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1answer
860 views

Curvature and the Arrow Pratt Absolute Risk Coefficient

So I'm in my first year of grad school, and I'm taking a decision analysis course. One of the topics we're covering is risk aversion, and with that comes discussion of the Arrow Pratt Absolute Risk ...
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136 views

How do I optimize a function subject to a two-part constraint?

I would like to maximize the following function $$\max\; U= log(xT_o + (1-x)T_s) + log(Y)$$ by choosing levels of $T_o$, $T_s$, and $Y$, and where $x\in[0:1]$ subject to $$N = \binom{P_sT_s+Y ...