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

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difference between utility curve?

A consumer's preferences give me the indifference curves for bundle (a,b) = 16/x for bundle (c,d) = 24/x and another consumer's preferences give me the indifference curves for bundle (e,f) = 26/x ...
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2answers
23 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
156 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
26 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 ...
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1answer
19 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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0answers
12 views

Maximizing utility function equivalence

Let's denote our expected utility $U_{\pi} = \int ((1-e^{-kx}) \frac{1}{\sqrt{2\pi}\sigma}e^{-(x-z)^2/2\sigma^2} dx$ I'd like to show that maximizing this is equivalent to maximizing $E[X] - ...
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1answer
29 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
20 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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27 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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0answers
109 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
33 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
31 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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0answers
47 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
51 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
59 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
67 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
53 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
165 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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1answer
84 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 ...
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1answer
222 views

Expected utility and St. Petersburg paradox

Can someone explain to me how they get the $10.94$ at the Expected utility theory section of the solutions to the St. Petersburg paradox? My problem is that they use a formula to calculate the ...
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1answer
20 views

Markov Decision Process - Optimal policy invariance to scaling in the Utility Function

The title says it all. If i use a discounted Utility Function, why is the optimal policy invariant with respect tot the scaling of the Utility Function by a positive Factor?
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1answer
52 views

Optimal Price for Monopolist

I want to find the total demand for good r and the optimal price p for a monopolist using the following information: Marginal cost per good = $c$ (constant) All consumers have the following utility ...
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32 views

How to define a utility of an information source?

This is a more specific (and, hopefully, clearer version of a previous question). The utility of discovering the value of a random variable $X$ can be defined to be its information content. When ...
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1answer
115 views

Mistake wikipedia article on St petersburg paradox?

I suspect that there is a mistake in the wikipedia article on the St petersburg paradox, and I would like to see if I am right before modifying the article. In the section "Solving the paradox", the ...
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1answer
159 views

Maximum amount willing to gamble given utility function $U(W)=\ln(W)$ and $W=1000000$ in the game referred to in St. Petersberg's Paradox?

The game works as such: I flip a fair coin until it lands on tails. $h$ is the number of heads obtained until the first tail occurs and the game stops. My payoff from this game is: $\hat G=2^{h}$ I ...
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0answers
47 views

How to derive recursive equation for expected discounted utility function?

I am trying to mathematically represent expected discounted utilities when the length of a lifetime is uncertain. $V_0$ is the expected discounted utility at $t=0$ and can be represented as such: ...
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1answer
38 views

What type of utility function is this?

I'm a little unsure about what kind of utility function this is? u(x1, x2)=x1*x2+x1 Is it correct that this is a Cobb-Douglas function?
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1answer
73 views

What causes the change in the expected value of the product of random variables?

The following question is part of a homework exercise on portfolio theory that I have to do. Suppose that $Y$ is a random variable representing the returns on an investment. Now, let $f$ be a ...
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1answer
102 views

Functional equation for scale invariant utility functions

Two utility functions $u,v:\mathbb{R}_{>0}\rightarrow\mathbb{R}$ (giving the utility of, say, an amount of money) are considered equivalent if $u(x)$ is given by $m\,v(x)+c$, for some constants $c$ ...
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2answers
230 views

What does Arrow's theorem say about Kaldor-Hicks social welfare functions with von Neumann-Morgenstern utility?

Let $A$ be the set of all possible states of the world, let $G(A)$ be the set of all "lotteries" or "gambles", i.e. the set of all probability distributions over $A$. Now consider an individual with ...
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1answer
215 views

How can a social welfare function be a linear combination of von Neumann-Morgenstern utility functions?

The von Neumann-Morgenstern axioms were an attempt to characterize rational decision-making in the presence of risk. The von Neumann-Morgenstern utility theorem says that if someone is vNM-rational, ...
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2answers
71 views

“intertwined” subset in linearly ordered set

I am trying to solve an exercise in utility representation theory which leads me to the following question. Take any (nonempty) linearly ordered set $(X,\succeq)$. Can we construct a set $Y\subset ...
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1answer
36 views

Insurance Premium that covers only the loss and not the profit

For example: The utility function is ln(W), where W refers to the Wealth level. The initial wealth is $10,000 $ and you have a equal chance of winning and losing $1000. What if the insurance policy ...
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1answer
46 views

Probability Density Function to Cumulative Density Function

I am reading on Stochastic Dominance (http://en.wikipedia.org/wiki/Stochastic_dominance) and few questions on PDF and CDF. The paragraph I am looking at this: Why is that $P[A\ge x] \ge P[B \ge x] ...
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1answer
151 views

Mathematical Economics - Utility maximization

I am thankful to any hints: What I have: Simple log-utility form: $u = \log c_1 + \beta \log c_2$ Budget constraints: $c_1 + s \leq w$ $c_2 \leq R\; s$ Problem: For utility maximization: $s = ...
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2answers
386 views

Endowments & Utility Function to get Demand Function

We have two people, $A$ and $B$, A has $200$ units each of both good $X$ and $Y$ and $B$ has $100$ units each of both good $X$ and $Y$. $A$ has tastes providing a utility function such that $u(X,Y) = ...
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1answer
13k views

Deriving demand functions given utility

A consumer purchases food $X$ and clothing $Y$. Her utility function is given by: $U(X,Y) = XY +10Y$, income is $\$100$ the price of food is $\$1$ and the price of clothing is $P_y$. Derive the ...
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1answer
150 views

Preference Relation and Utility Function - Problem with inductive proof

I have a problem with an inductive proof of the following result. Theorem: If $X$ is a finite set, a binary relation $\succ$ is a preference relation iff there exist a function $u:X\rightarrow R$ ...
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1answer
36 views

Utility Question

You produce an information product (IdeazTM) that you produce on a weekly basis (each one is different but you sell the same product to everyone during that week). Historically you have been ...
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80 views

stochastic dominance

A group of people are choosing between two investments A and B. Both have these payoff distributions: A: $$\langle.2, .1, .2, .4, .1 \mid 1, 2, 3, 4, 5\rangle$$ B: ...
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85 views

Game theory question- information quality maximisation, opinions of the question

I am developing a game theory question to help in deconstructing situations where information quality is comprimised and requires valuation against a set of criteria. I would be interested to know any ...
2
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1answer
228 views

Elasticity of Substitution (CES)

This appears to be a nice forum. I just registered since I have a question... I have a CES aggregator-function $$ f(c,q) = (r c^{a} + b q^{a})^{1/a}. $$ It is postulated that it can be rewritten as ...
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2answers
368 views

Game theory: Nash equilibrium in asymetric payoff matrix

I have a utility function describing the desirability of an outcome state. I weigh the expected utility with the probability of the outcome state occuring. I find the expected utility of an action, a, ...
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207 views

derive demand function of $u(x,y)=log(x+3y)$

I tried by using lagrangian method $$ \mathrm{Max}\; u(x,y) \quad\text{where}\quad px=m $$ F.O.C. results in $3Px=Py$ and put it into the $px=m$ then $Px(x+3y)=m$. I cannot derive the form $x(p,m)$ ...
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1answer
147 views

How to prove that there exist a concave function and $\gamma\in[0,1]$ and some other numbers which satisfy an inequality

I'm working on an economics paper, and in the model I've made I've basically gotten myself a little bit stuck. I need to show that there exists a nondecreasing concave function $u$ and numbers $P$ and ...
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2answers
224 views

Knapsack with non-trivial “utility” function

The standard knapsack problem imagines a thief trying to stick the most items in his knapsack as possible. It assumes that having, say, two Picasso paintings is twice as good as having one. We might ...
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1answer
82 views

Authoritative measure for rating photos in a photo contest - practical issue

I am trying to find a good algorithm that would serve as an authoritative way to assess pictures provided for a photo contest. There is a bunch of photos that came for the contest. Each person from a ...
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1answer
1k views

Simple math formula to calculate average

I am making a software that deals with employee trust. I am trying to make a math formula (no need to tell that I am bad in math :) ). Here is the scenario: ...