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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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
23 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 $m$ ...
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1answer
26 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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0answers
23 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 ...
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0answers
20 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
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0answers
35 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
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1answer
164 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
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1answer
68 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:
$$...
1
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1answer
34 views
How to calculate CRRA bounds from Holt and Laury (2002) type lottery?
Lottery is between:
Option A: a certain choice of £5
Option B: £10 with probability 0.1 and £1 with probability 0.9
The probability of receiving £10 increases in each subsequent choice.
How do I ...
0
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2answers
66 views
How can I prove $U(x) = [𝛼_1𝑥_1^𝜌+𝛼_2𝑥_2^𝜌]^{(1/𝜌)}$ is equal to Cobb-douglas Utility function when $𝜌\rightarrow0$ [closed]
This is the question, I have problem with part b, I don't know what function should I use to reach the result
thanks in forward
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1answer
45 views
Does utility in economics also refer to producer's surplus ? How to balance the consumer surplus and producer surplus?
I am confused about the use of utility in economics and how it relates to allocative efficiency.
At 4:35 and 5:07 in this video (https://www.youtube.com/watch?v=9a3wXj1o91k) he talks about how at the ...
1
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1answer
64 views
Prove this indirect utility function is quasi-convex
The indirect utility function is as follows:
$$ v(m,p) = \frac{m}{p_{1}^{1/2} p_{2}^{1/4} p_{3}^{1/4}} $$
I need to prove that it is quasi-convex. I tried both definition of a quasiconvex function ...
1
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1answer
40 views
Why is the marginal utility of money assumed to be constant in Marshallian Theory of Consumer Behaviour
While studying the Marshallian Theory of Consumer Behaviour, I came across the assumption that the marginal utility of money is assumed to be constant. Can someone please explain why is this so?
3
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3answers
64 views
Why are interpersonal utility comparisons not possible
Why is it not possible to compare utility across individuals?
Is this only impossible when we consider ordinal utility where we have no numerical unit?
1
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1answer
87 views
Linear Utility?
Consider a preference relation $\succeq$ on $X\subseteq\mathbb R^2$. If $\succeq$ satisifies:
$$
\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
63 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
35 views
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
87 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
49 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 ...
4
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2answers
99 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
59 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
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2answers
48 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
87 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
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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 ...
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
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2answers
253 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
53 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
43 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
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1answer
39 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
26 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
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1answer
39 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?
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2answers
113 views
Utility function_maximazation [closed]
A consumer is deciding about her hours ($h$) and consumption ($c$), her preference over bundles of work and consumption are as follows:
$U(c,h)= c + \sqrt{24-h}$
The consumer would get an hourly wage ...
3
votes
1answer
29 views
Is there any evidence for consumer utility-maximising behaviour, at individual or market level?
Even though utility maximisation is ubiquitous in economic textbooks to model consumer behaviour, its usefulness is rarely demonstrated by evidence.
Is there any evidence that some consumers do ...
1
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0answers
42 views
derive value function from utility function
We have the utility function.
$$U_{t} = \ln{c_{t}} + E_{t}\sum_{s=1}^{\infty}(\beta^{s}\ln{c_{t+s}})$$
And I am trying to find the value function.
$U$ is utility function. $c_t$ is consumption at ...
0
votes
1answer
42 views
Strictly increasing function transformation
I have utility function given by:
$U(x_1, x_2) =
\begin{cases}
x_1+x_2 & \text{if $x_1+x_2<6$} \\
6 & \text{if $6\...
1
vote
3answers
58 views
utility function always negative
In a problem set, I found a strange utility function: $U(c)=-1/2(c^* - c)^2$, where $c^* =$ positive constant level of consumption. Does this function have economic sense?
0
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0answers
29 views
Is this utility function continuous?
$u(x_1,x_2)=|x_1 −2|+x_2$
Is this function continuous?
PS: The continuity theorem I use is this: Whenever for any $x^n$, $n \in N$ with $x^n \to x$ (i.e. $\lim_{n \to \infty} x^n = x$) and for any $...
0
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1answer
47 views
Study whether $\succsim$ represented by $u(x)=\lfloor x \rfloor$ is continuous
Using the following definition of continuity: $\succsim$ is continuous if for any bundles $x,y,z$ such that x$\succ$y$\succ$z, there exists $\alpha \in (0,1)$ such that $\alpha x + (1-\alpha)z \sim y$....
0
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1answer
64 views
Who took utimatum game and dictator game as the evidence against Homo Economicus assumption of individual utility maximization?
Wikipedia and this McGill University page states that the two games "have been taken as both evidence for and against the Homo economicus assumptions of rational, utility-maximizing, individual ...
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0answers
28 views
Modeling risk aversion. Expected utility function
I want to model an Expected Utility Function for risk aversion but my problem is uncertainty in itself.
I want a function(a special case) $$f(x, y) =\left\{\begin{matrix} h(bx^{1-C}+ay^{1-C}),C\neq 1\...
1
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1answer
53 views
Framing Effect Risk-Aversion Risk-Pursuit
I am an economics' graduate seeking to study Law and I want to illustrate the importance of legal certainty. Penalties, Costs are negativelly framed.
I am trying to word.
200 dollars with 50% ...
1
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1answer
193 views
Rent dissipation meaning?
What is Rent dissipation? Please explain with an example.
I tried to search it on the internet about it. And I couldn't find anything in simple language. It was the esoteric language and was unclear. ...
1
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1answer
163 views
What would the indifference curve of min{√x,y} looks like?
The locus of kinks would follow x=y^2 but what would the arms look like?
0
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1answer
106 views
A case where the solution to Expenditure Minimisation Problem is not a solution to Utility Maximistion Problem
I am looking for a preference relation which satisfies the above property.
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2answers
384 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 ...
3
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0answers
60 views
Mean Variance Optimization in a Utility Maximization Framework
I'm struggling to gain a broad understanding of Mean-Variance utility theory as it relates to finding the efficient frontier of a group of assets which each have some return and variance.
The typical ...
2
votes
1answer
39 views
Opportunity Cost effect on benefits
My question is the following:
Let's say a person has two career choices. He would be succesful in both, but in one of them he is slightly better and thus he will do better. So let's say career A will ...
