# Questions tagged [utility]

For all questions involving utility functions as used in economics and decision theory, including study of their properties or how they can be used to represent preferences.

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### Question regarding Allais Paradox (I know title unspecific; Sorry!; I don't know how to specify the question other than “what am I getting wrong?”)

Reading about Decision Theory I have come about Allais Paradox to be an argument against expected utility theory. One faces the following lotteries each with 100 tickest and the following payoffs per ...
2answers
35 views

### Is the utility function $u(x)=x_1 x_2 + \gamma x_2$ concave or quasi-concave?

I want to prove, given $\gamma>0$ and $x\in \mathbb{R}^2_+$, if the utility function: $$u(x)=x_1 x_2 + \gamma x_2$$ is concave, strictly concave, quasi-concave or strictly quasi-concave. I have ...
1answer
33 views

### Finding Marshallian Demand without Lagrange?

I need to find Marshallian demand for goods x and y (in terms of $P_x, P_y,$ and $I$) with the following utility function: $$U(x,y) = x + 10y - y^2$$ and general budget constraint $$I = P_xx + P_yy$$ ...
0answers
8 views

### Bayesian estimation for partial observation

Let $B$ be the competitor's hidden bid which follows some stationary distribution $F_B$ parameterized by $\theta$, and let our bid price be denoted by $x$. We win the auction when we bid higher than ...
1answer
24 views

### How to Quantify Utility/Pleasure/Pain using the Positive Real Numbers?

I am studying about Cardinal Utility in Economics (or more generally, how to quantify pleasure and pain!) Intuitively, I assign a positive number to pleasurable experiences, and a negative number to ...
0answers
13 views

### Derive demand function from a specific quadratic utility function

Suppose that the following function is the utility function of a representative consumer: U(x1,x2,y)=a/(b−c)∗(x1+x2)−b/(2∗(b−c)2)∗(x21+x22)−c/(b2−c2)∗x1∗x2+y The budget restriction is given by p1∗x1+...
0answers
32 views

### Please help: Derive the demand function from a specific quadratic utility function

Suppose that the following function is the utility function of a representative consumer: $$U(x_1,x_2,y)=a/(b-c) *(x_1+x_2)-b/(2*(b-c)^2)*(x_1^2+x_2^2)-c/(b^2-c^2)*x_1*x_2+y$$ The budget restriction ...
0answers
15 views

### How can I implement a sigmoid function composed from three distinct phases?

I want to divide a sigmoid function to three functions, I found this function: Where The five parameters in this model have the following meaning: alpha is the initial size of y, beta represents the ...
0answers
39 views

### How can I decompose sigmoid function on three parts?

I want to create a function F(x, x1, x2, x3, c1, c2, c3), where the function F represent a segmoid function. This function defined by 3 parts [0,x1], [x1,x2] and finally [x2,x3]. Can you please help ...
0answers
15 views

### Calculate premium for claim, the principle of zero utility

$$\begin{array}{|c|c|c|c|c|} \hline X&0&200&400&800&1000&2000\\ \hline \mathbb{P}&0.4&0.2&0.1&0.1&0.1&0.1\\ \hline \end{array}$$ The principle of ...
0answers
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0answers
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### Utility maximization: two-period portfolio

Question: Utility function $U(w) = aw-bw^2$, where $a>0$, $b>0$ and wealth $w>0$ Two-period portfolio. Second-period wealth is determined with the portfolio’s return, $R^\sim$ which is a ...
0answers
36 views

### Economics-utility function

We let $g(z)$ be a strictly monotonous function so: $$\frac{dg(z)}{dz}>0$$ Consumer 1 has preferences given by the utility function $u(x_1,x_2)=ln(x_1)+2ln(x_2)$, while consumer 2 has preferences ...
0answers
19 views

### Cobb-Douglas taxes advantage mathematically

Let a utility function for a consumer be defined as $u(x_{1},x_{2})=x_{1}^{1/2} x_{2}^{1/2}$. With the budget $x_{1}p_{1}+x_{2}p_{2}=m$. With values $p_1=p_2=1, m=32$. The state now adds a tax of unit ...
0answers
6 views

1answer
48 views

### Deconvolution with respect to a particular function

Let $\mathcal L, \mathcal L^*: \Theta \times \mathcal A \to \mathbb R$ be functions. When can $\mathcal L$ be expressed as the convolution of $\mathcal L^*$ with some third function $U$? That is, when ...
0answers
39 views

### Finding FONC and Maximising a utility function

So we were discussing a utility function in class today and I'm not sure how my teacher arrived at the First Order Necessary Condition that he did (using substitution) We want to maximise the ...
1answer
55 views

### Interpretation of this Lagrange Multiplier

I have the following utility maximization problem with inequality constraints: Objective function given by $U(x_1,x_2)=\ln(x_1)+\beta \ln(x_2)$ where $0<\beta<1$, and the constraints are given ...
0answers
88 views

### How to solve a VCG auction game?

So i have this question: And these are the 5 highest marginal valuations according to the answer sheet: This is how the answer sheet defines the vcg mechanism How is the answer sheet chosing these ...
1answer
57 views

### Finding the Nash equilibria of games

So i have this question I have some learning disabilities and have no clue whatsoever how the best reply of each player is what it is or how all players will demand the values shown in the answer ...
1answer
109 views