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

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2
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1answer
33 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 ...
1
vote
1answer
30 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
0
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1answer
25 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 ...
0
votes
0answers
9 views

Decision Analysis, Utility Function

Tom planning to invest in the stock market. Utility function U(m) = m^2 for what values of x & y maximises utility when action a1 is applied?
1
vote
1answer
24 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: ...
1
vote
3answers
62 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.
1
vote
1answer
46 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 ...
0
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0answers
16 views

Aggregated demand function for several similar offers?

I want to generate a realistic demand function for a service, depending on the price and properties of offers. The service is passenger travel, for whatever purpose. There are several companies that ...
0
votes
1answer
35 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 ...
1
vote
1answer
62 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 ...
1
vote
2answers
26 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 ...
0
votes
1answer
205 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 ...
0
votes
1answer
118 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
votes
1answer
41 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
votes
0answers
21 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] - ...
0
votes
1answer
36 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 ...
0
votes
1answer
23 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 ...
1
vote
0answers
29 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 ...
0
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0answers
113 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 ...
0
votes
1answer
56 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 $1-p$, ...
1
vote
1answer
40 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
55 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 ...
1
vote
2answers
59 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 ...
0
votes
1answer
64 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 ...
0
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1answer
70 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 ...
0
votes
1answer
56 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 ...
3
votes
1answer
323 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 ...
0
votes
1answer
88 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 ...
-1
votes
1answer
287 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 ...
1
vote
1answer
23 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?
2
votes
1answer
62 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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vote
0answers
33 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 ...
3
votes
1answer
149 views

Mistake in 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 ...
3
votes
1answer
216 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 ...
1
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0answers
49 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: ...
0
votes
1answer
41 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?
0
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1answer
75 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 ...
0
votes
1answer
116 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 $c$ ...
4
votes
2answers
278 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 ...
2
votes
1answer
223 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, ...
2
votes
2answers
80 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 ...
0
votes
1answer
37 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 ...
0
votes
1answer
49 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] ...
0
votes
1answer
191 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 = ...
0
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2answers
524 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) = ...
1
vote
1answer
18k 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 ...
1
vote
1answer
177 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 $u:X\rightarrow R$ ...
0
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1answer
37 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 ...
2
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0answers
86 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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0answers
90 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 ...