# 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.

214 questions
Filter by
Sorted by
Tagged with
1 vote
0 answers
17 views

### Isoelastic utility functions, how to calculate risk boundaries.

I am trying to replicate a calculation I found in a paper that calculates the level of risk aversion for an individual to choose one option over the other, but I am struggling to solve it. Ideally, ...
• 11
0 votes
1 answer
21 views

### A concrete example with Arrow-Pratt coefficient of absolute risk aversion

Let $u_1$ and $g$ be increasing strictly concave functions from $\mathbb{R}$ to $\mathbb{R}$. Let $u_2:=g\circ u_1$. If we regard $u_1$ and $u_2$ as utility functions of two players, this is saying ...
• 656
1 vote
0 answers
124 views

### Wealth equation for optimal consumption

Consider a market with $d = 1$ risky asset with prices $(S_n)_{n \geq 0}$ and interest rate $r$. Suppose an investor has initial wealth $X_0 > 0$, consumes $C_n$, and holds $\theta_n$ shares over ...
2 votes
0 answers
27 views

### Characterization of Optimal Payoff (under Expected Utility) via Gateaux-Derivative/Fréchet Derivative

Background: Let $(\Omega, \mathcal{F}, \mathbb{P})$ model a financial market and $T>0$. Denote by $(S_t)_{t\in[0,T]}$ the price process of the risky asset in the financial market. Assume that the ...
• 53
1 vote
1 answer
55 views

• 307
1 vote
1 answer
39 views

• 339
1 vote
0 answers
68 views

### Why does the uniform law of large numbers hold with non-i.i.d. random variables in Bayesian experimental design?

This paper, Asymptotic theory of information-theoretic experimental design, studies Bayesian experimental design where in each round $n$, the experimenter selects a stimuli $X_n$ that maximizes mutual ...
• 49
0 votes
0 answers
19 views

### What is the discounted (4%) difference in health outcomes between Treatment A and Treatment B using ICER, QALY and utility value?

I'm studying health economics and have been racking my brain trying to find the right answer to this problem, but I keep getting it wrong no matter what I do. I haven't had any trouble calculating ...
0 votes
0 answers
26 views

### Difference between Pareto optimal redistribution and strict pareto optimal redistribution

Can someone explain the difference between Pareto optimal redistribution and strict pareto optimal redistribution? Because I know the definition but I do not understand it.
• 149
0 votes
0 answers
35 views

### Pareto optimal redistribution in binary exchange economy

Consider binary exchange economy with two goods and two agents, whose preferences are defined as follows: $\textbf{x}\succ \textbf{y}$ iff $x_{1}x_{2}>0$ and $y_{1}y_{2}=0$. In Edgeworth's box ...
• 149
4 votes
1 answer
89 views

### Game holder is always losing money in the St. Petersberg Paradox?

The St. Petersberg Paradox is described as follows: A gambler pays an entry fee $M$ dollar to play the following game: A fair coin is tossed repeated until the first head occurs and you win $2^{n-1}$ ...
• 135
2 votes
1 answer
100 views

### Von Neumann–Morgenstern: compare coefficients in Archimedean axiom

Now we have: Axiom1: Completeness of $\succeq$. Axiom2: Transitivity of $\succeq$. Axiom3: Independence: For any $N$ and $p\in (0,1]$, if $L\succ M$, then $pL+(1-p)N\succ pM+(1-p)N$. Axiom4: ...
• 193
0 votes
0 answers
43 views

### Should we stay or pay the exit fee given the utility function

You have invested $10\%$ of your wealth in a hedge fund; the other $90\%$ is in cash and there is no time value of money. One year from now the hedge fund will cease operations; it will either fail ...
• 49
1 vote
1 answer
1k views

### What is α in a Cobb-Douglas utility function?

Sorry if this is not the place to ask, I'm new here. I'm studying economy but I'm struggling to understand the Cobb-Douglas utility function. If we've one such that xt is consumption in period t, and ...
• 31
2 votes
0 answers
233 views

### How can I differentiate the expected value of a utility function?

Suppose I have a maximisation problem $$\underset{0\le R(y)\le y} \max E\left\{u_B\left[ y-R( y)\right]\right\}$$ subject to$$E\left\{u_L\left[R( y)\right]\right\}\ge \bar U_L$$ $B$ and $L$ are simply ...
• 121
0 votes
1 answer
50 views

### How to solve this expectation problem?

I truly don't know how to name this question properly, and I will try my best to be more specific. And here is my problem Suppose a person has 2 choices. For choice A, he gets $Z$ guaranteed dollars; ...
• 183
3 votes
0 answers
64 views

• 15
0 votes
1 answer
31 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 ...
1 vote
0 answers
228 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 ...
0 votes
0 answers
54 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 ...
• 107
0 votes
0 answers
95 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 ...
• 1,318