Questions tagged [utility]

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

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Calculating risk interest rate within a two period model

I am trying to calculate how to determine the interest rate ( = risk free rate + premium) within the following model where a consumer decides to invest in a safe asset or in a risky asset. The utility ...
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How do I solve the Envelope Theorem condition in Microeconomics?

I am preparing myself for a MSc in Economics and don't understand why, according to the Envelope Theorem, when deriving a utility function $ u(θ, q(θ), r(θ)) = B(q-r) - C(\frac{q}{θ})$, its derivative ...
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Why do many papers not write the actual utility function?

Why do many papers write the intertemporal maximisation problem for the household as \begin{equation}E_{0} \sum_{t=0}^{\infty} \beta^{t} U\left(C_{t}, N_{t}\right)\end{equation} and then do not write ...
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Expenditure function. Prove that this set is bounded

I need to prove that the following set is bounded in order to derive the expenditure function: $e(p,v)=min_x px$ ST $\{x \in R^n_+$ such that $U(x)\geq v\}$. Knowing that $U(x):R^n \longrightarrow R$ ...
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Is it considered acceptable or unacceptable to use currency as a measure of utility?

There will always exist at least one economist who condones measuring utility in US dollars and another who does not. However, I am wondering which way the majority of contemporary economists lean. ...
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Prove that budget constraint is Lower Hemi Continuos (LHC)

I need to prove that the following constraint is LHC. $B=\{x \in R^n : px\leqslant pw)$ But Im not capable of finding and sequence $\{x_n\}$ such that $x_n \in B(p_n,w_n) \forall n$ and that $x_n\...
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32 views

Remove Linear Good From Quasi-linear Utility Function

Given a quasi-linear utility function: $u(x_1, x_2) = f(x_1) + \beta x_2$, $\beta > 0 $ What would happen if good 2 ($x_2$) is removed from the market? Would the new utility function be: $u(x_1) =...
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How is the defintion of the mean preserving spread (MPS) not too general?

The mean preserving spread is defined as follows: Consider two lotteries g and h. Let $x_g$ und $x_h$ denote the corresponding random variables. Then h is a mean preserving spread (MPS) of g, if: $...
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Does the duality of utility maximization and cost minimization hold in practice?

I recently learned about the relationship between utilization maximization and cost minimization. Are there studies on whether this duality holds in real life? Any information on this topic for a ...
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Differentiability of the utility function and indifference curves

Comment on the following affirmative: In the traditional consumer model, the hypothesis of differentiability of the utility function and of convexity of preferences, assure the indifference curves ...
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Mathematics of the income and substitution effects

I have recently been learning about the concept of utility and the indifference curve. I am having some problems understanding the effects on consumption of two goods $X$ and $Y$ of a change in the ...
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Additional components in utility functions (behavioral economics)

I am looking for a term describing the second part of a utility function in behavioral economics and related disciplines. For example, Thaler (1983) describes a utility function that could be ...
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What would we say on the utility of risk and its consequences?

Anything has its risks and anything has its utility or desutility. The risk aversion causes a looking for safer alternatives in the market which maximizes utility in a trading off between risk and ...
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Why doesnt Law of Diminishing Marginal Utility not affect price effect?

Ok so in my textbook, it is given that the downward slope of the demand-price curve is justified by three factors: Law of Diminishing Marginal Utility Income Effect(Real income) Substitution effect ...
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212 views

Price-consumption curve

Suppose a consumer whose income is $b$ has a utility function given by $U(x,y) = 2xy+y^2$ with the price of $x$ being $p_x$ and the price of $y$ being $p_y$. Draw the price-consumption curve assuming ...
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making a utility model for CO2 compensating travel demand

I'm trying to make a model which is build around the idea of carbon offsetting fuel (the consumer pays an extra fee per litre fuel for the compensation of the emitted CO2). The goal here is to make a ...
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Name of this $u\left(x_{1}, x_{2}\right)=x_{1}+\alpha x_{2}+\beta \sqrt{x_{1} x_{2}}$ utility function?

I have seen this $u\left(x_{1}, x_{2}\right)=x_{1}+\alpha x_{2}+\beta \sqrt{x_{1} x_{2}}$ a numbers of time now. I wonder whether it is somehow special and therefore has it's own name? Kind regards,
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How to find the Utility Possibility Frontier when there are Perfect Substitutes?

I am trying to derive the Utility Possibility Frontier (UPF) when both utility functions display perfect substitutes (in an Edgeworth economy with to consumers and two goods). The specific problem: $...
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Equivalent Variation of Price Change

If Bernice (whose utility function is min {x; y} where x is her consumption of earrings and y is money left for other stuff ) had an income of \$12 and was paying a price of \$3 for earrings when the ...
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Aggregate CES Cobb-Douglas utility over different individuals

Suppose I have a CES Cobb-Douglas Utility function: $$U_i=X^{\alpha_i} Y^{1-\alpha_i}$$ Can I add utilities of different individuals meaningfully? I.e, where people have different $\alpha_i$. $$\...
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Monotonic transformation of utility functions [duplicate]

Why taking monotonic transformation of a utility function does not change marginal rate of substitution?
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Two interpretations of the Lagrange Multiplier

A question about the second answer on this thread: Help understanding Lagrangian multipliers? If we have a standard utility maximizing problem $$ \max_{x,y} U(x,y) $$ with the constraint $p_{x}x + ...
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Difference between direct and indirect utility

What is the difference between direct and indirect utility? Following the advanced microeconomics textbook Jehle and Reny I can not understand either the intuition or the math definition. It confuses ...
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Demand functions homogeneous of degree zero in prices and income - how this relates to budget exhaustion (solving a consumer's problem)

I have the following demand system: It appears to me that each demand function is homogeneous of degree zero in prices and income as: Why would this demand system not satisfy the following budget ...
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Utility Theory/Marginal Rate of Substitution: Can the marginal rate of substitution be calculated for a point of the budget line?

This a person's budget line with various points, and their consumption, C*, and their endowment e, which is worth $5000 (unimportant). Also shows is their initial indifference curve. The difference ...
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Concavity of Cobb-Douglass Utility Function on Non-Open set

My textbook argues that the Cobb-Douglass utility function $u=(x1)^a(x2)^b$ with $a,b>0$ and $a+b<1$ is concave on $R2+$ by computing the Hessian and showing it to be negative semidefinite for ...
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39 views

How to describe a utility function in words?

Suppose I have a utility function of Cobb-Douglas form $$U(x, y) =x^{0.2}*y^{0.8}$$ I want to describe it in words. I would say like: The utility of consumer is captured by number of good x and ...
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48 views

Max Utility Function and Finding associated demand curve

I have a max utility function, therefore; U(x,y)= max(2x,y) and I am trying to find the demand function x = x(𝑝x , 𝑝y , 𝑀), note this function cannot be differentiated. I am familiar that the ...
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58 views

Deriving a demand curve from a Cobb-Douglas utility

Probably a daft question but I derived an equation for a demand curve from a general Cobb-Douglas utility function $$U(x,y)=\beta x^{\alpha}y^{1-\alpha}$$ given a budget constraint $$M=xP_x+yP_y$$ and ...
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'Constrained optimisation' for mutually exclusive goods?

Taking the standard approach to constrained optimisation, where we maximise utility subject to a budget constraint with some allocation on the consumption of two goods, does it make apply the same ...
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Specification of the parameters of this utility function [Behavioral Economics]

This is from page 274 of "Advances in Behavioural Economics" by Camerer, Rabin, Loewenstein. This chapter of the book is entitled "A theory about fairness, competition, and cooperation". I have ...
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Marginal rate of substitution notation:

I am having a dumb doubt in writing some slides for an undergraduate class. I want to be consistent with the use in microeconomics but this easy thing is really bugging me: Mas-colell pag. 54 $ ...
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What are examples for the phenomenon that more (or better) information makes everybody worse off?

More information is usually considered "better". Let's say a rational agent chooses optimally given his information on the circumstances of a particular decision problem. Then providing him with more ...
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Deriving FOC in OLG model with Cobb Douglas utility

I'm trying to derive the first order condition in a partial equilibrium overlapping generations model. The setup contains both consumption and housing goods. $$ \underset{c_{t+i},h_{t+i}}{max}U_{t}^{...
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Cobb-Douglas function homotheticity

I've been given the Cobb-Douglas utility function: $\ u(q_1, q_2)=a\ln q_1+b\ln q_2=q_1^aq_2^b \ $ If I want to prove homothetic preferences, I use the following condition: $\ u(\lambda q_1, \...
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locally nonsatiated preferences

what does this symbol mean in the discuss of locally nonsatiated preferences: $\varepsilon > 0$ and $||y-x||<\varepsilon$.
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How do I derive the aggregate demand function given two utilities functions?

Assume that we have two people with the same utility function of $U_i = x^{1/2} + y^{1/2}$ where $i=1,2$ and $I_i$ is the income. Let $P_x$ denote price of good $x$ and $P_y$ denote price of good $y$. ...
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Derivation of a Demand Equation

A consumer's utility function is $U(x,y)=\sqrt x + y$. Assuming we have an interior solution, I need to show that the demand for $x$ does not depend on income. I know that the consumer consumes where ...
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On Demand Functions and Engel Curves

A consumer has utility function $U(x,y)=(x−2)y$, where $x≥2$ and $y≥0$. The price of $x$ is $P_x$, the price of $y$ is $P_y$ and the consumer's income is $I>2P_x$. ($x$ and $y$ do not have to be ...
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Example of a utility maximization problem with a non-binding budget constraint

Given a utility function $U(x,y): \mathbb{R}^{2} \to \mathbb{R}$, the general utility maximization can be stated as follows: $$ \max_{x, y} U(x,y) \text{ s.t. } p_{x}x + p_{y}y \leq m $$ where the $...
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Diminishing mariginal utility and risk preferences

Diminishing marginal utility is a concept only in cardinal utility theory rather than ordinal utility theory. As diminishing marginal utility implies a concave shape of the utility function, does it ...
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58 views

Why can utility functions be continuous, and what does this imply for marginal utility?

I am studying microeconomics at the introductory undergraduate level and two related but distinct questions are puzzling me. First, my textbooks express utility functions as continuous functions by ...
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181 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 ...
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Shortcuts for elasticity of substitution

How can I find the elasticity of substitution (I know the definition) if I know the utility function $u(x,y)$? I know its increasing in $x$ and $y$, etcetera, and has everything else you want from a ...
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Budget Constraint in Utility Maximisation Problem with Lagrange Multipliers

Lets say we have a utility function $U: \mathbb{R}^{2} \to \mathbb{R}$ given by $U(x,y)$ and a binding budget constraint $p_{x} x + p_{y} y = m$, where $p_{x}, p_{y}$ are prices of goods $x,y$ and $m$ ...
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58 views

For the case of two goods, give an example of preferences that are represnted by a continuous utility function that allows for fat indifference curves

The question in the title sounds like a trick question, due to the monotonicity property that indifference curves have, such that for two goods x and y, strong monotonicity implies y > x. Possible ...
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How to prove monotonic transformation of the function and equivalence?

At the microeconomics course I have to prove monotonic transformation of the function U(x,y) = A(x^a)(y^b) into U(x,y) = (x^0.5)(y^0.5) Since the MRS are ay/bx and x/y resp. I can obviously only ...
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Determine if goods are substitutes or Complements based on demand function

So I have a consumer with a utility function of the Cobb-Douglas form $v(x_1,x_2)=x^{\frac{1}{2}}_1x^{\frac{1}{2}}_2$. From that I constructed the demand function for good 1 and good 2: $x_1=\frac{1}{...
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utility from providing public good as explained in Hindriks textbook

I think I understood the highlighted part: basically, by increasing $g^1$ my utility increases because more public good is being provided but at the same time it decreases because I have less money to ...
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216 views

Why is the risk premium always positive for risk averse individuals?

I think this has to do with the definition of concavity and the fact that a risk averse person has a concave utility function, but I'm not sure how that helps.

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