# Questions tagged [utility]

Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.

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### Do discontinuous preferences imply no continuous utility function?

I am trying to think of a preference relation that can be represented by a utility function but such that there does not exist a continuous utility function. I know that you can represent continuous ...
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### Proving that constant absolute risk aversion and relative risk aversion implies independence of initial wealth

I was able to prove that for a portfolio with one risk-free asset and one risky asset, if the Arrow-Pratt measure of absolute risk aversion is constant (i.e., constant absolute risk aversion, CARA), ...
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### Preorder and multi-utility function

Let $\succeq$ be a preorder, i.e., it is reflexive and transitive on $X$. Prove that there exists an index set $N$ and a multi-utility function $u:X \rightarrow \mathbb{R}^N$ such that $x \succeq y$ ...
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### Consumer utility optimization question

I am having diffculty with this question: Can we proceed using Lagrange here since the utility function is convex, or do we have to treat them as perfect substitutes? If latter or any other method, ...
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### CRRA utility function with a scale parameter

I am wondering if it is possible to write down a following CRRA utility function ; $$u\left(c(t)\right)=a\frac{c\left(t\right)^{1-\sigma}}{1-\sigma}$$ where $a>0$ is a constant scale parameter. I ...
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### Are Cobb-Douglas preferences homothetic?

Our lecture defined a preference to be homothetic, if the following is true: $$(x_1, x_2) \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$ Cobb-Douglas preferences can be ...
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### Interpretation of utility function

I am reading Lucas (1980) and I am a bit confused about the way he formulates the utility function. So there is one non-storable good that comes in $n$ colours and one unit of labor produces $y$ ...
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### Specification form for household utility function

What determines the choice of the functional form to be adopted for the household CRRA utility function, when utility depends on consumption and leisure? For examples, we have these three functional ...
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### What is one dimensional, ordered type?

I am reading papers about moral hazard. What is one dimensional, ordered type $\theta\in\Theta$? What is one dimensional, not ordered type $\theta\in\Theta$? Could you please give an example? ...
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### how to raise utility of an individual having min utility function

I was doing an exercise of utility and got confused with a min utility function. endowments can redistribute among individuals. How am i supposed to increase his utility. Can i simply reduce the ...
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### Revealed preferance: elementary question

When the market prices are Rs 5 per apple and Rs 6 per orange a person buys 16 apples and 28 oranges. When the prices are Rs 4.4 per apple and Rs 6.4 per orange ,the person buys 20 apples and 25 ...
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### Troubleshooting Utility Maximization with the Lagrange Method

I'm trying to solve a utility maximization problem through the Lagrange method. The utility function is something like $u(x,y)=x+B(y-a)$. However, I'm running into problems as x and y do not come up ...
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