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

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0answers
39 views

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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1answer
26 views

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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3answers
90 views

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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2answers
37 views

Utility of a lottery

The sentence of a problem from a book: Tickets to a lottery cost \$1. There are two possible prizes: a \$10 payoff with probability 1/50, and a \$1,000,000 payoff with probability 1/2,000,000. ...
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0answers
22 views

linear utility function 3 variables [closed]

I am trying to solve the following exercise (from chapter risk management) But I don't understand what is indifferences.. Let be a utility function $u(x1,x2,x3) = x1 + a*x2 + b*x3$ There are the ...
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0answers
15 views

Second order chain rule with bi-variate function

I am building an utility model, and I am confused how to make assumptions about second order equations. The First order condition is simple, it is the problem of $$\max_{M} u(H(M),M)$$ where $H(M)$ ...
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0answers
52 views

what does this integral stand for?

i would really appreciate some advice concerning a paper i'm reading: http://pages.stern.nyu.edu/~dbackus/GE_asset_pricing/disasters/Leland%20port%20ins%20JF%2080.pdf on page 586, there is a problem ...
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0answers
31 views

Why is maximising expected monetary value not plausible for large amounts of money?

My teacher asked us which of these gambles do you prefer: $g_1=£500,000$ $g_2=0.1£2,500,000 \oplus 0.89£500,000 \oplus 0.01£0$ The EMV for each gamble is £500,000 and £695,000 respectively, ...
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0answers
8 views

An inequality involving expectation and a concave function

I have a real-valued random variable $X$ and a function defined on the real line $x \mapsto U(x)$ which is concave and strictly increasing. What I am wondering is whether the following is true. For ...
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0answers
55 views

Utility maximization problem

I tried to search through the site and couldn't find a similar example. The task is to solve the utility maximization problem to identify the inverse demand for e(electricity). The utility function: $...
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0answers
20 views

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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1answer
25 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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0answers
26 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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0answers
18 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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0answers
28 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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0answers
20 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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0answers
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 $£10$...
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1answer
37 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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0answers
46 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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0answers
22 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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0answers
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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0answers
17 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 A={1,...
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1answer
26 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
41 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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0answers
41 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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0answers
33 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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0answers
32 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 $x$,...
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0answers
22 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
135 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
99 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
168 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
44 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: $(n_t,c_t)\...
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0answers
147 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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1answer
48 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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0answers
125 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
67 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 U($\...
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1answer
188 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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1answer
114 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: $$\begin{cases}...
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3answers
246 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
104 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
91 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 +\beta_i\...
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1answer
128 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
67 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
512 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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1answer
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
110 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 ...
0
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1answer
64 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
34 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 $\...