Questions tagged [utility]

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

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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. ...
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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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5answers
758 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 ...
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3answers
173 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 ...
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Help understanding Lagrangian multipliers?

I am trying to understand Lagrangian multipliers and using an example problem I found online. Problem Set Up: Consider a consumer with utility function $u(x,y) = x^{\alpha} y^{1-\alpha}$, where $\...
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2answers
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Intuition behind risk premium

In Lecture 20 of MIT's Microeconomics course, a situation is proposed where a 50/50 bet will either result in losing \$100 or gaining \$125 with a starting wealth of \$100. It is stated that a person ...
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3answers
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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 ...
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1answer
535 views

Is it possible to derive indifference curves given marshallian demand function?

In a two good world, will a marshallian demand function the likes of D(p,m) where p is the price of one good and m the income yield a utility function or ...
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3answers
805 views

When treating a relative, normalized utility function as a pmf, what is the interpretation of Shannon entropy or Shannon information?

Suppose $\Omega$ is a set of mutually exclusive outcomes of a discrete random variable and $f$ is a utility function where $0 < f(\omega) \leq 1$, $\sum_\Omega f(\omega) = 1$, etc. When $f$ is ...
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1answer
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Homogenous of degree one in utility function.

Question My solution is as follows. Please check my solution. If I make a mistake, please tell. I am really not sure about my solution. Thank you U(x) is homogenous of degree one i.e. u(...
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16k 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 ...
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864 views

Thin indifference curves

If a consumer follows the rationality axiom of continuity (i.e. no jumps in his preferences), the indifference curves of a utility function are said to be thin. Why does continuity ($x \succeq y \...
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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 ...
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1answer
78 views

Weakly monotone preferences with singleton indifference curves: do any of them admit a utility representation?

Inspired by this question. The original question was answered by Amit with some nice examples. I would like to know the generalized answer: Suppose we have a preference ordering $\succeq$, which is ...
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692 views

How do I compute the relative risk aversion of Epstein-Zin preferences?

$$ \newcommand{\E}{\mathbb{E}} $$ Preface This question is related to this one about the elasticity of intertemporal substitution and this one about the definition of absolute risk aversion. (It's ...
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Why couldn't the Karush-Kuhn-Tucker optimization find the solution?

I have the following utility maximization problem: $$\max (xy)$$ $$(x+y-2)^2 \leq 0$$ Conditions: $$y-2\lambda (x+y-2) =0$$ $$x-2\lambda (x+y-2) =0$$ $$\lambda(x+y-2)^2=0$$ When I set $\lambda>0$, ...
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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 $A$. ...
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1answer
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Gross substitutes vs. net substitutes

Wikipedia explains the difference between products that are "gross substitutes" and products that are "net substitutes". However, the mathematical explanation doesn't give much intuition about these ...
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2answers
940 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, ...
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1answer
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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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1answer
5k views

Leontief preferences

I can solve most utility maximization problems using my mathematical knowledge .... but not when it comes to Leontief preferences. I do not have a book to lean on (am self-studying), so would really ...
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1answer
200 views

On the Ms. Exponential vs Ms. Hyperbolic vignette

I've come across this little parable purporting to show why exponential discounting is superior to hyperbolic discounting1: The greater bowing [of the hyperbolic discount curve] means that if a ...
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Can A Utility Function Take On Negative Values?

Can someone provide a rigorous definition of a utility function? I had thought that a utility function only needs to the preserve the order of preferences. Thus a utility function can take on negative ...
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735 views

Doesnt convexity prevent thick indifference curves aswell?

It is standard in many micro textbooks when analyzing the relationship between preference axioms and the shape of the utility function (and consequently the shape of indifference curves), to ...
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385 views

Doesn't the concept of marginal utility speak to a cardinal utility function?

When we differentiate the utility function with respect to some input $x_i$, we get a number that tells us how "fast" the utility function is changing at some point with respect to $x_i$. Doesn't that ...
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813 views

Constant Elasticity of Substitution: Special Cases

Take an $n$-commodity constant elasticity of substitution utility function, $$U = \left[\sum^n_{i=1} \alpha_i x^\rho_i \right]^\frac{1}{\rho}$$ How do we show the following: Show that as $\rho \...
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Utility function types - request for review

I am working on a Wikipedia page that compares several common utility functions. Although I found some information about these topics on the web, I didn't find it all in one place, and often got ...
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Convexity of the Market Demand Function

The market demand function can be either concave or convex. I am looking for conditions under which a general market demand function can be considered convex. For example would convex preferences or a ...
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948 views

Calibration of utility function parameters controlling labor disutility

Consider the very basic utility function $$ u(c, n) = \log (c) - \alpha \frac{n^{1 + \frac{1}{\nu}}}{1 + \frac{1}{\nu}}$$ Where $c$ is consumption and $n$ is working hours. As the Frisch elasticity ...
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1answer
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Why is CRRA utility often used in macroeconomics DSGE model?

As title says, why is CRRA utility often used in macroeconomics DSGE model? That is, the form of $$u(c_t) = \frac{c_t^{1-\sigma}}{1-\sigma}$$ I cannot find any theoretical background around this........
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343 views

Why should the statistical value of life exist?

In areas such as insurance pricing and government policy analysis, it is often necessary to assign human life a monetary amount in order to compare it with other monetary amounts. So economists have ...
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1answer
108 views

What are good dataset alternatives to estimate value functions?

Suppose we want to estimate for many goods in the economy (or classifications thereof) the preferences of each household for these goods. We may want to restrict the analysis to specific utility ...
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2answers
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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 ...
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1answer
319 views

Selecting the best utility function for households

I have little to no background in micro, but I'm learning about utility functions. It seems that there are many forms of utility functions for households. In general terms, how does one go on to ...
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1answer
100 views

Mythbusters - Determine optimal boarding strategy based on time and satisfaction score

Most airlines board passengers starting from the back of the plane and then working their way towards the front (after boarding priority classes and passengers). In an episode of Mythbusters, Adam ...
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4answers
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Existence of utility representation of a rational but discontinuous preference

This is related to Do discontinuous preferences imply no continuous utility function? I think the title of the above-linked question is phrased in such a way that obscures a subtly different but more ...
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4answers
166 views

Examples of behavioural breakdowns in game theory?

I'm trying to compile multiple scenarios of the breakdown of game theory. Specifically, I'm looking for scenarios where game theory predicts certain behaviours, but in real-world scenarios or ...
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2answers
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Empirical estimates of CRRA and CARA utility

I am working on macroeconomic model and I need to calibrate it. I am looking primarily for a statistically-founded estimate for the coefficient of relative risk aversion in the CRRA utility function ...
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1answer
508 views

If all indifference curves are parallel lines, then preference has linear representation

Given a continuous preference relation $\succeq$ over $X=\mathbb{R}^2_{+}$ where all sets: $$ I_x\equiv\{y\in X:y\sim x\} $$ are lines on $X,\forall x\in X$, and are parallel to $I_y,\forall y\notin ...
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1answer
284 views

How is labor disutility modeled in Arrow-Debreu model?

In DSGE models, utility function contains labor disutility components. But I cannot not see how labor disutility is incorporated in Arrow-Debreu-Mackenzie model.
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1answer
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Meaning of $dF(z)$ in expected utility framework

Background: from a Microeconomics course, $F$ is a cdf. In other words, if $F$ has a density function $f$, then $$F(z)={\int_{-\infty}^z f(x) dx} $$ Write the Bernoulli utility function $u:...
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1answer
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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 ...
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2answers
857 views

Is risk aversion bounded in CRRA utility?

For instance, Cagetti (2003) estimates ρ > 2 by targeting the median wealth of households, Gourinchas and Parker (2002) find ρ < 2 by targeting the mean consumption of households, Chetty (2006), ...
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What is the point of the indirect utility function?

Where does this have application? I understand how the demand function may be arrived at using the utility maximization problem but I don't understand where the indirect utility function is used and I ...
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2answers
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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 ...
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1answer
206 views

Shopping example in Kőszegi / Rabin (2006)

In "Section IV Shopping" of Kőszegi / Rabin (A model of reference-dependent preferences, QJE 2006), the example of consumer buying a pair of shoes is given. They claim that "her disutility from ...
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Quasilinear Utility Functions

We know if the utility function is quasilinear (QL) w.r.t good 1, then the demand for other goods is independent of income (no income effect for goods $(2,\dots, N)$). But is the reverse implication ...
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1answer
245 views

Nash social welfare function with negative exponential utilities

I got one question about the Nash-SWF. Typically it is defined as the product of individual utilities, ie. $$ NSWF:=u_1(x_1) \cdot u_2(x_2) \cdot u_3(x_3) \cdot ... $$ For this to make sense, ...
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1answer
235 views

Optimization of Households' utility in “ Rule-of-Thumb Consumers and the Design of Interest Rate Rules ” (Gali et al., 2004)

I can't figure out how the calculation of first order conditions was carried out. I can't figure out where the stochastic discount factor came from.
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854 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)