Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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questions
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Comparing utility functions
I'm doing an econ course after not having any math or micro for a few years, now I'm totally missing the basics again.
I'm wondering how to show that utility functions are an equivalent to each other:
...
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1answer
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Strictly increasing but not convex preferences
Is it possible to have preferences that is strictly increasing but not convex?
Will perfect substitutes indifference curves show strictly increasing but not convex preferences? I am confused, as won't ...
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Present value concept in Utility Maximization
We can use the utility function as U(Ct) = Ct since logCt is just a monotonic transformation but still, I can't get the answer.
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1answer
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The efficient frontier in mean variance criterion
The efficient frontier is the portfolios with the minimum of variance ($V$) at a given mean ($E$) or a maximum of mean at a given variance，Why do the optimal portfolios in the effcient frontier, is ...
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1answer
25 views
Proving that Marshallian demand is of the form: $x_i^*(p,I) = \hat{x}_i^*(p)I$ with certain conditions
Can I please have some feedback/help proving the following. My proof is below but I am quite uncertain as to whether my solution is efficient. Thank you.
If $u(x)$ is a homothetic utility, then show ...
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32 views
Quasi-linear utility. Deriving demand
I was trying to derive a general demand for the good $x$ for this quasi-linear function $u(x,y) = y + 2\sqrt{x}$ subject to standard budget constraint $p_x x + p_y y \leq M$
Using Kuhn-Tucker ...
2
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0answers
35 views
MWG_3D4_C, why the solution seems in reverse?
I'm doing exercises of Chapter3 of MWG, there's a problem that I don't understand (I didn't figure out the solution manual either...).
It is about exercise 3.D.4, the full statement of the exercise is ...
3
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1answer
93 views
Convex Preference but Convex Utility
Can preference be convex when utility is not a concave function (e.g. $U=x_1^2 + x_2^2$)?
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Marginal rate of substitution interpretation
I am trying to interpret the marginal rate of substitution stidied in an article. The article in question is Burbidge, J. B., Robb, A. L., 1980. Pensions and retirement behaviour. The Canadian Journal ...
2
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1answer
55 views
When the global optimal is outside of the constraint set, what will be the demand?
$u:\mathbb R^n\to\mathbb R$ is a quasi-concave utility function so the indifference curves are convex.
$a,b\in\mathbb R^n$ are two points. Our budget set is the (one-dimensional) segment $[a,b]$ that ...
4
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2answers
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What are the correct utility functions?
It is common to talk about utility functions. For example in a universe with only two goods, we might assume each person (or group of people) carries a function $u(x,y)$ in their heads. When offered ...
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How do I figure out whether the ICs are convex or concave?
Question: Randy Ratpack hates studying both economics and history. The more time he spends studying either subject, the less happy he is. But Randy has strictly convex preferences.
(a) Sketch an ...
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0answers
9 views
Effect of a productivity shock on the real exchange rate within a two period model
So if we have a two period model, tradable goods and nontradable goods, where consumers tend to maximize utility, then we have the following Euler equation:
$$\frac{ u' (c_1) }{P_1} = (1+r)\beta \frac{...
2
votes
3answers
105 views
Relation between demands of $x, y$ and $z$
Question: Consider a consumer with utility function $U(x,y,z)=y\min\{x,z\}$. The prices of all three goods are the same. The consumer has $100 to spend on these three goods.The demands will be such ...
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0answers
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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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2answers
104 views
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 ...
2
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2answers
331 views
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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1answer
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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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2answers
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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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2answers
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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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2answers
34 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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1answer
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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:
$...
0
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1answer
30 views
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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1answer
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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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1answer
102 views
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 ...
3
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2answers
110 views
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 ...
0
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0answers
23 views
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 ...
0
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1answer
31 views
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
...
4
votes
1answer
216 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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0answers
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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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1answer
86 views
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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0answers
9 views
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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0answers
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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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0answers
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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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1answer
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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 + ...
3
votes
2answers
369 views
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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1answer
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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 ...
0
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1answer
33 views
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 ...
3
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1answer
49 views
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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1answer
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 ...
1
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1answer
56 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 ...
5
votes
1answer
80 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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0answers
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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 ...
0
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1answer
35 views
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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2answers
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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
$ ...
24
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9answers
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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 ...
2
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0answers
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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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1answer
56 views
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, \...
0
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3answers
61 views
locally nonsatiated preferences
what does this symbol mean in the discuss of locally nonsatiated preferences:
$\varepsilon > 0$ and $||y-x||<\varepsilon$.
