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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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 ...
0
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0answers
5 views
'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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0answers
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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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1answer
34 views
Utility function $u(x_1,x_2)=\sqrt[4]{x_1}+x_2$ [closed]
im new on this community and even on economy topics, so please help me if you can't, my microeconomics teacher really sucks and gave us a homework which i'm barely making thought it, but in this ...
1
vote
2answers
31 views
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
votes
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
votes
0answers
58 views
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.
$$
\underset{c_{t+i},h_{t+i}}{max}U_{t}^{...
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votes
1answer
39 views
Cobb-Douglas function homotheticity
I've been given the Cobb-Douglas utility function:
$\ u(q_1, q_2)=a\ln q_1+b\ln q_2=q_1^aq_2^b \ $
If I want to prove homothetic preferences, I use the following condition:
$\ u(\lambda q_1, \...
0
votes
3answers
51 views
locally nonsatiated preferences
what does this symbol mean in the discuss of locally nonsatiated preferences:
$\varepsilon > 0$ and $||y-x||<\varepsilon$.
0
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1answer
35 views
How do I derive the aggregate demand function given two utilities functions?
Assume that we have two people with the same utility function of $U_i = x^{1/2} + y^{1/2}$ where $i=1,2$ and $I_i$ is the income. Let $P_x$ denote price of good $x$ and $P_y$ denote price of good $y$.
...
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2answers
49 views
Derivation of a Demand Equation
A consumer's utility function is $U(x,y)=\sqrt x + y$. Assuming we have an interior solution, I need to show that the demand for $x$ does not depend on income.
I know that the consumer consumes where ...
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0answers
28 views
On Demand Functions and Engel Curves
A consumer has utility function $U(x,y)=(x−2)y$, where $x≥2$ and $y≥0$. The price of $x$ is $P_x$, the price of $y$ is $P_y$ and the consumer's income is $I>2P_x$. ($x$ and $y$ do not have to be ...
1
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1answer
48 views
Example of a utility maximization problem with a non-binding budget constraint
Given a utility function $U(x,y): \mathbb{R}^{2} \to \mathbb{R}$, the general utility maximization can be stated as follows:
$$
\max_{x, y} U(x,y) \text{ s.t. } p_{x}x + p_{y}y \leq m
$$
where the $...
2
votes
1answer
63 views
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 ...
1
vote
1answer
50 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 ...
2
votes
1answer
163 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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0answers
34 views
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 ...
0
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1answer
43 views
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$ ...
0
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2answers
54 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 ...
0
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0answers
33 views
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 ...
1
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0answers
36 views
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}{...
2
votes
0answers
37 views
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 ...
2
votes
1answer
179 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.
3
votes
1answer
70 views
Intertemporal choice with possibility of death
Here is the setup:
Suppose that there is an individual who lives up to two periods. He lives with absolute certainty during period $1$, and during this period his sub-utility function is given by:
$$...
1
vote
1answer
40 views
How to calculate CRRA bounds from Holt and Laury (2002) type lottery?
Lottery is between:
Option A: a certain choice of £5
Option B: £10 with probability 0.1 and £1 with probability 0.9
The probability of receiving £10 increases in each subsequent choice.
How do I ...
0
votes
2answers
79 views
How can I prove $U(x) = [𝛼_1𝑥_1^𝜌+𝛼_2𝑥_2^𝜌]^{(1/𝜌)}$ is equal to Cobb-douglas Utility function when $𝜌\rightarrow0$ [closed]
This is the question, I have problem with part b, I don't know what function should I use to reach the result
thanks in forward
0
votes
1answer
46 views
Does utility in economics also refer to producer's surplus ? How to balance the consumer surplus and producer surplus?
I am confused about the use of utility in economics and how it relates to allocative efficiency.
At 4:35 and 5:07 in this video (https://www.youtube.com/watch?v=9a3wXj1o91k) he talks about how at the ...
1
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1answer
74 views
Prove this indirect utility function is quasi-convex
The indirect utility function is as follows:
$$ v(m,p) = \frac{m}{p_{1}^{1/2} p_{2}^{1/4} p_{3}^{1/4}} $$
I need to prove that it is quasi-convex. I tried both definition of a quasiconvex function ...
1
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1answer
75 views
Why is the marginal utility of money assumed to be constant in Marshallian Theory of Consumer Behaviour
While studying the Marshallian Theory of Consumer Behaviour, I came across the assumption that the marginal utility of money is assumed to be constant. Can someone please explain why is this so?
3
votes
3answers
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Why are interpersonal utility comparisons not possible
Why is it not possible to compare utility across individuals?
Is this only impossible when we consider ordinal utility where we have no numerical unit?
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1answer
93 views
Linear Utility?
Consider a preference relation $\succeq$ on $X\subseteq\mathbb R^2$. If $\succeq$ satisifies:
$$
\begin{align}
&1.\mbox{ }(a_1,a_2)\succeq (b_1,b_2)\implies(a_1+t,a_2+s)\succeq (b_1+t,b_2+s),\...
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2answers
97 views
Prove quasi-concavity of utility function [closed]
How do you prove from definition (no Hessians) that $U(x_1,x_2)=x_1^2 x_2$ is quasi-concave?
0
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1answer
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How can I prove $∇U(x).D_m x(p,m)= \text{shadow price}$?
Why inner multiplication of the gradient of utility function in derivative of demand function with respect to income is equal to shadow price?
This is the equation which is given but I don't know ...
0
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1answer
129 views
Does quasi-concave utility function imply convex indifference curve?
It is well-known that convex indifference curve (i.e. the function is convex)/ preference would imply quasi-concave utility function. But does quasi-concave utility function imply convex indifference ...
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1answer
54 views
How to prove the relationship between the expected value of a lottery and its certainty equivalent?
Utility function $u(x)$ is monotonic. I want to prove that $u(x)$ exhibits risk aversion if and only if for all lottery $F$: $E(x) \geq CE(F,u)$ (CE is certainty equivalent).
(Definition of $CE$: the ...
5
votes
3answers
178 views
Are there any examples for $u(x_1, x_2) = \max\{x_1, x_2\}$ in real word?
I know how its graph looks like, and it's like when you want to choose between 2 inferior goods you choose the cheaper one so you can have more, but is there another examples?
1
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1answer
66 views
A question about the property of quasi-linear preference
In case of quasi-linear preference, why would one unit more of the numeraire good (good 1) give the same additional utility as spending an additional amount of wealth equal to the cost of one unit of ...
1
vote
2answers
56 views
Why is the nature of graph of utility function different from indifference curve?
I am new to Economics, but I have this doubt. The indifference curve and utility function both have the same equation, so their graph must also be similar, which is true I guess. Then why is it that ...
0
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1answer
91 views
A question about MWG Exercise 3.D.4
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 ...
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0answers
35 views
Does quasilinear preference contain rationality, monotonicity or other assumptions?
I have a question when I'm doing exercise 3.C.5(b) of MWG. The exercise asks to prove that a continuous preference on $(-\infty,\infty)\times R^{L-1}_+$ is quasilinear with respect to the first ...
9
votes
1answer
81 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 ...
0
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1answer
38 views
How to find change in the optimal choice with a utility function in general form?
Suppose the utility function is represented as $U(x_1,x_2;I)$, where $I$ is the level of information the consumer possesses.
How to find the change in the optimal choice of $x_1$ as price of $x_1$ ...
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 ...
1
vote
2answers
271 views
Finding demand functions for an unusual utility function
I have a utility function: $U = x + \min\{x,y\}$
I want to draw the indifference curve and find the demand functions. Will it be the case of the usual perfect complements?
Also, what preferences ...
0
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1answer
55 views
Why is a monotone increasing but nonlinear transformation of a utility function not represent the same preferences if the preference is complete?
According to a textbook, in the context of uncertainty (e.g. in lottery), if the preference is complete, a monotone increasing but nonlinear transformation of a utility function would not represent ...
0
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0answers
48 views
How to prove that the walrasian demand function $x(p,w)$ is continuous in $p$ and $w$?
If the utility function $u$ is continuous and satisfies local nonsatiation, and walrasian demand function $x(p, w)$ is a function (i.e. always map to only single values), how to prove that $x(p,w)$ is ...
2
votes
1answer
45 views
Why does strictly Walrasian demand with quasi-concave utility function mean that the walrasian demand having only one single consumption bundle?
In the context of Walrasian demand:
Suppose u is continuous, satisfies local nonsatiation, and is strictly quasi-concave, each $w(p, x)$ contains a single consumption bundle.
The proof I got from a ...
0
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1answer
37 views
Deriving demand function in case of multivariable utility functions with min and max structures
Suppose I have utility function like this: $u(x_1,x_2,x_3)=min\{x_1,a-x_1\}\times min\{x_2,b-x_2\}+x_3$ where a and b are real numbers and $x_1\in [0, a]$ and $x_2\in [0,b]$. What will be a procedure ...
0
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2answers
113 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.
3
votes
1answer
44 views
Why does quadratic utility function imply $\mu-\sigma$ preference?
Why does investors having quadratic utility function mean that their optimal portfolios can be chosen by only considering mean and variance of returns i.e. imply $\mu-\sigma$ preference?
