Questions tagged [utility]

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

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10
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2answers
17k views

Lexicographic preference relation cannot be represented by a utility function

I am stuck on the following exercise, related to preference relations and von-Neumann-Morgenstern utility function. A farmer wants to dig a well in a square field $[0,1000]\times[0,1000]$. The ...
8
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1answer
13k views

Finding demand function given a utility min(x,y) function

I am confused about a particular point regarding finding a demand function. All the problems in this practice set I am doing have involved applying the method of Lagrangian multipliers. But I am ...
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5answers
806 views

Are there Utility Monsters in Economics?

Economics, especially in the modern school is broadly influenced by the utilitarian concept of utility. More so since the labor theory of value has been broadly replaced by the theory of marginal ...
14
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12answers
12k views

If I gain, then someone else loses. Correct?

On a very small scale, it's certainly true that if I gain, somebody else might lose. If I take away my brother's chocolate, then he will lose it, and will most probably not get anything comparable. ...
11
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3answers
13k views

What is an example of a utility function where one good is inferior?

Say the consumer has a standard convex, monotonic preference over Apples and Bananas. (Update: I'd like the preference to be as 'standard' as possible. So ideally we have diminishing MRS everywhere ...
6
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2answers
3k views

Local Non-Satiation Proof

I have been having trouble with how to go forward with a proof for about three days now. I know the basic structure of the proof, but can't seem to construct it. Basically, I am trying to do a proof ...
5
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3answers
1k views

Question about the Ellsberg Paradox in Expected Utility Theory

The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...
9
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2answers
993 views

When can one safely talk about decreasing marginal utility?

One thing I hear a lot is talk of decreasing marginal utility—the idea being that additional units of a good become progressively less attractive the more units of that good one has already. However, ...
9
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3answers
11k views

How to show that a homothetic utility function has demand functions which are linear in income

A homothetic utility function is one which is a monotonic transformation of a homogeneous utility function. I am asked to show that if a utility function is homothetic then the associated demand ...
7
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2answers
3k views

Which utility function yields a constant price elasticity of demand function?

How do I know which utility function I can use to find an isoelastic demand function, e.g., $x(p)=Ap^a$? And similarly, which cost function can I use to find an isoelastic supply function? Does it ...
6
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1answer
1k views

Homothetic preferences and utility functions

I know that if you have homothetic preferences and a utility function that represents it, then this utility function must present constant Marginal Rate of Substitution (MRS). My question is whether ...
5
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3answers
456 views

Preferences where wealth effect dominates

King-Plosser-Rebelo preferences satisfy balanced growth requirements, we have that income and substitution effects of labor cancel. Labor does not respond to a change in the wage level. Greenwood-...
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1answer
3k views

Linear Expenditure System of Demands, Derivation Help

This problem I am working on comes out of--surprise--the Mas-Colell book for graduate micro (3.D.6). I think I have correctly used the FOC of the Lagrangian of the utility maximization problem to ...
3
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1answer
6k views

Monotone transformation of utility

We have learned that any "strictly positive monotonous transformation" of utility functions is okay, as long as they preserve the ranking of choices implied by the underlying preferences. Consider $U(...
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1answer
66 views

Would a very cheap renewable energy source be harmful economically?

This question is not on whether these devices work or not but so much as if they did work. What if electricity can be made so cheap that everyone could afford it ti the point there was no demand for ...
14
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2answers
12k views

The relationship between the expenditure function and many others!

I dont understand the relationships between Hicksian demand, walrasian demand (marshallian), the expenditure function and the indirect utility function (including the value function V(b)). I have ...
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3answers
1k views

Does risk aversion cause diminishing marginal utility, or vice versa?

Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. ...
14
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3answers
187 views

Current knowledge about the empirics of consumer theory

I would like to get up to speed on the current state of empirical work done to test the assumptions and predictions of consumer theory (think Chapters 1, 2, 3, and 6 of Mas-Colell et al.). Can anyone ...
5
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2answers
756 views

Calculate the elasticity of substitution of Epstein-Zin preferences

$$ \newcommand{\E}{\mathbb{E}} $$ Let a consumption sequence be given $C=(C_0, C_1,...)$ and let $C_t^+ = (C_t, C_{t+1}, ...)$. Now, suppose I have Epstein-Zin preferences, \begin{align*} U_t(C_t^+) &...
4
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2answers
7k views

How to derive utility possibility frontier?

I'm trying to derive the utility possibility frontier of a economy whose consumption contract curve is $$y_A = \frac {y} {x} x_A$$ and $$y_B = \frac {y} {x} x_B$$where $x_A + x_B = x$ and $y_A + y_B= ...
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1answer
257 views

Question on consumer theory

The story of my question is I have multiple question. (1) when John doesn’t work in the underground economy at all , t=0, how can I find the optimal value of $l$ and consumption bundle and his ...
5
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1answer
200 views

Generalized KPR: Frisch Elasticity

Consider the following version of KPR preferences (with $l$ being leisure): $$ U(c,l) = \left(\left(c\right)^\gamma l^\omega\right)^{1-\sigma}$$ I'm after the Frisch elasticity: $$ \frac{\partial(1-...
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3answers
338 views

Consumer preferences

I want to know under what preferences relation will I not want to consume all of my budget. Because if my preferences are strictly monotonic, strictly convex or convex, even LNS or continuous. I would ...
2
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1answer
246 views

What is the assumption behind “indifference curve does not cross”?

If only weak-ordering and continuity is assumed, "ICs" can definitely intersect. If we assume Monotonicity or convexity in addition to weak-ordering, then we can get "no cross of IC". But those two ...
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1answer
462 views

Question about budget constraint and utility maximization [closed]

I have also following budget set $$B=\{x=(x_1,x_2)\in R^2_+ \mid 2\sqrt{x_1}+x_2\le y\}$$ where y is income. Assume that there are two stories. The agent can shop in both of them. The first store ...
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2answers
904 views

Why do so many models assume homothetic preferences?

...when Engels Law, backed by a good amount empirical evidence, demonstrates that overall consumer preferences are not homothetic. See for example, Jorgenson (1997)
4
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1answer
941 views

Is the Cobb-Douglas Utility Function Locally Non-Satiated at (0,0)?

My understanding of local non-satiation is that increasing your allocation of one good by a marginal amount increases utility. Suppose your utility takes the following form: $$U(x,y)=x^\alpha y^\beta$$...
4
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2answers
2k views

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 ...
4
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2answers
11k views

Cobb-Douglas and Logarithm Utility Functions

Suppose I have a consumer with a utility function $U(x,y) = x^\alpha y ^{1-\alpha} $ where $a \in (0,1)$. Suppose this consumer has wealth $w$ and the prices for $x$ and $y$ are $p_x$ and $p_y$ ...
3
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0answers
90 views

Fixes of quadratic utility when probability of decreasing utility is large

In finance and specifically portfolio theory, a popular utility function is quadratic utility $$ u(x)=x-\frac{\lambda}{2}(x-\mu_x)^2 $$ where $x$ is wealth and $\lambda$ is the parameter of risk ...
3
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1answer
64 views

What was “Pareto's proof of the immeasurability of utility”?

Wong (1978, 2002, Foundations of Paul Samuelson's Revealed Preference Theory), repeatedly refers to "Pareto’s proof of the immeasurability of utility". What was this proof?
3
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2answers
224 views

Ruling out boundary solutions in Utility Maximization

Solving the basic Utility Maximization Problem, i.e. \begin{align} max_{x\geq 0} u(x) \\ s.t. \,\,\, p^Tx\leq w \end{align} we get the Kuhn-Tucker first order condition \begin{gather} \frac{\...
3
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1answer
2k views

Positive Monotonic Transformations and Nested Functions

Suppose there is an economic agent with the utility function $u(x,y)$. A second agent has the utility function $h(g(f(u(x,y))))$. Am I correct in thinking that if $f'(x)>0$, $g'(x)>0$, and $h'(...
2
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1answer
180 views

Utility theory and portfolio optimization: utility of what exactly?

In finance, a common problem is selection of an optimal portfolio given some constraints (e.g. budget constraint and perhaps nonnegative allocation constraint). One can define the optimization problem ...
1
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1answer
296 views

What is the concept of ordinal utility?

I have read in many books that since utility cannot be measured - so ordinal concept or comparison concept is used. If that is so, how can one define a mathematical function for utility which gives a ...
1
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1answer
384 views

Ordinal utility and monotonic transformations

If u(x) is an ordinal utility function that represents the (weak) preference relation R, then (a) any strictly monotonic transformation of u(x) also represents $R$, or (b) any monotonic transformation ...
0
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2answers
120 views

Algebraic approach towards convexity

I have a function: $ u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}$. How do we algebraically show if it's convex or not? Also, what would be the general way to show if any given function is convex.
0
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1answer
38 views

Why might a monotone increasing but nonlinear transformation of a utility function not represent the same preferences?

According to a textbook, a monotone increasing but nonlinear transformation of a utility function might not represent the same preferences. Why is it so? An example of such preference would be ...