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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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 ...
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0answers
14 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
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1answer
28 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\...
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3answers
46 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?
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25 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
29 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 $\alpha x + (1-\alpha)z \sim y$....
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1answer
54 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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20 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\...
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1answer
51 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% ...
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1answer
52 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. ...
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1answer
129 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?
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1answer
83 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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350 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
50 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 ...
4
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0answers
57 views
utility maximization with nested Cobb–Douglas–CES preferences
I'm trying to understand the following paper: Hsieh & Ossa: A global view of productivity growth in China (2016). The pdf can be found here: https://faculty.chicagobooth.edu/chang-tai.hsieh/...
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Fixes of quadratic utility when probability of decreasing utility is large
In finance and specifically portfolio theory, a popular utility function is quadratic utility
$$
u(x)=x-\frac{\lambda}{2}(x-\mu_x)^2
$$
where $x$ is wealth and $\lambda$ is the parameter of risk ...
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0answers
32 views
Moral hazard, bubbles, and economies of scale in limited companies and organizations
http://eprints.lse.ac.uk/100058/1/Goodhart_CEPR_DP13494.pdf
What would be the disadvantage of limiting the liability to the product of the proportion of the company and the debt(a person with 2% of a ...
3
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0answers
52 views
Log-linearizing a non-separable utility function around the steady state
I've started reading Jordi Galí's Monetary Policy, Inflation and the Business Cycle (2nd ed., 2015). In section 2.5.2, Galí considers an example with the following non-separable period utility ...
1
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2answers
59 views
Maximin utility function
If someone has the attitude that they want to maximize their worst possible outcome (so they are maximally risk-averse), what does the utility function for that look like? Can this attitude be ...
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0answers
32 views
Are marginal utilities or utilities compared?
Consider decision making in an economic model. Suppose that there is some utility and it is a function of consumption and leisure where leisure is full-time work, part-time work, or full-time ...
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0answers
40 views
What is the trade-off between? Consumption and Leisure or Income and Leisure?
When first presenting the utility function and its arguments, textbooks typically start by stating that utility is a function of consumption and leisure. See for example https://sites.hks.harvard.edu/...
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Are there examples of Cost Benefit Analysis using diminishing marginal utility of income?
In Cost Benefit Analysis (CBA) constant Marginal Utility of Income (MUI) is usually assumed. This implies that a dollar received/earned is the same at low and high levels of income. In Social CBA, ...
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1answer
43 views
Change in the marginal utility of leisure with respect to a change in consumption
I am reading a paper that derives a theoretical retirement model. There is a utility function and a budget constraint forming an optimal control problem. The solution to this problem states that
\...
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0answers
38 views
Is a combination of Political economics and Game theory possible and beneficial?
By Political economics I do not mean the "economical" advice given by some people(see the Wealth of Nations by Adam Smith) but rather the heavily mathematized subfield of Economics studying and trying ...
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2answers
76 views
Showing that a preference relation admits a utility function representation
Setting: We have two choices of goods $(x_1,y_1)$ and $(x_2,y_2)$ from the set of choices $[-1,1]^2$. Moreover, we have the following preference relation $$(x_1,y_1)\mathcal{R}(x_2,y_2)\iff |x_1|\geq|...
0
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1answer
38 views
Proof: Risk averse; Certainty Equivalent smaller than expected value
I would like to show for a randomly distributed variable $x$ with CDF $F(\cdot)$ , given a Bernoulli utility function $u(x)$ the following property holds:
The certainty equivalent, $CE(\cdot)$, is ...
0
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2answers
62 views
The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them?
I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality.
But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
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0answers
31 views
Rotation of Quasilinear Utility
Let $u(x,y)=f(x)+y$ be a quasilinear utility. Now we rotate it by 45 degrees, (such that the $x-$axis becomes the direction of $(1,1)$)
$v(x,y)=f(x-y)+x+y$. Is $v$ also a quasilinear utility? What is ...
3
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0answers
73 views
Linear Homothetic Utility
A Homothetic Utility is where
$$
\forall x,y, \forall a \in \mathbb{R}_+: \ u(ax,ay)=au(x,y)
$$ (or its monotonic transformation).
A linear Homothetic utility is defined as $$
\forall x,y, \forall ...
0
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1answer
44 views
If an ordinal-scaled utility function is defined via strictly increasing transformation, how can it represent a case of indifference?
Problem: According to Wulf Gaertner’s (2009, p. 13) A Primer in Social Choice Theory, any strictly increasing transformation of an individual’s ordinal utility function is informationally equivalent. ...
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1answer
62 views
Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?
$\succsim$ is a weak order over $\mathbb R^L$.
For a closed budget set $B\subset\mathbb R^L$, define demand correspondence: $$D(B)=\{x\in B|x\succsim y\forall y\in B\}$$.
We know that $D$ is always ...
6
votes
1answer
53 views
Meaning of $dF(z)$ in expected utility framework
Background: from a Microeconomics course,
$F$ is a cdf. In other words, if $F$ has a density function $f$, then
$$F(z)={\int_{-\infty}^z f(x) dx} $$
Write the Bernoulli utility function $u:...
0
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1answer
19 views
Gapminder's Dollar Street and the role of self-supply
I find it quite hard to get a clear picture of what the income numbers in Gapminder's Dollar Street tell. How to compare \$27 in Burundi with \$10,098 in China? What would it mean that the family in ...
2
votes
1answer
34 views
Obligations of a company
Any company may "feel" obligated towards several parties at once:
its shareholders
its employees
its customers
its partner companies (sub-contractors and suppliers)
its country and social environment ...
0
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2answers
140 views
robinson economy with production
Facing a little bit of a problem with this questions, did a similar one BUT the utility function was not linear and got MRS dependent on goods (was not just a number) - here I am at a loss.
The ...
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1answer
23 views
How does the notion of utility differ from that of value?
Is utility merely the notion of value in the subjectivist/marginalist (aka neoclassical) school?
0
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1answer
35 views
Aggregated demand of households given utility function
I have an utility function given,
$\ u_j(q_{j1},q_{j2} )=q^{3/4}_{1j}*q^{1/4}_{2j} $
$\ s.t.: y=p_1*q_{1i} +p_2*q_{2i}$
I do know that the for $\ q_{1j}$ the marginal prospensity to consume is 3/...
2
votes
1answer
128 views
WARP implies completeness, transitivity and thus rationalizability. What is wrong with the statement?
Let $A$ be a menu and $R$ be a complete and transitive binary relation. Define choice correspondence generated by $R$:
$$c_R(A)=\{x\in A|| xRy \ \forall y\in A\}.$$
Theorem (from Kreps 1988): for ...
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1answer
35 views
Is anyone familiar with the following basic resource sharing model?
Here is a resource sharing model, I do not remember where I came across it, I am wondering if this is well known in econometrics.
Let $T > 0$ be the total quantity of resources. For example, ad ...
4
votes
2answers
83 views
What are the units of utility?
I'm trying to show a result that involves utility and money (the latter is in dollars). I would like to know if it is safe to assume that the units of utility is dollars? After all, in auction ...
2
votes
1answer
90 views
Proof of monotonocity of preferences
Question from Intermediate Microeconomics by Hal Varian:
"We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve ...
1
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1answer
52 views
Utility maximization in a 2-good scenario with an option to buy a combo of the two
I am solving the following question:
Suppose that we live in a two good world, books (x) and movies (y), with utility function given by $u(x,y)=min(x+2y,2x+y)$. Prices of books and movies are 25 and ...
3
votes
2answers
87 views
Preference relations defined by $x_1^n + x_2^n$ converge to $\max\{x_1, x_2\}$
In the problem set 2 of Rubinsteins Microeconomics (btw is there a comparably nice written book on macroeconomics?) there is the following question:
Let $\succ_n$ be the preference relations defined ...
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2answers
63 views
How is the Euler Equation for Consumption derived from from intertemporal budget constraint and lifetime utility function in basic macroeconomics
I suspect that what I'm actually asking here is just a basic calculus question, which I have overwrought, but I wanted to ask it here to make sure before taking it to SEMaths.
In the Jones ...
3
votes
1answer
385 views
Demand derived from Cobb-Douglas utility, interpretation, check
I derived demand, given a Cobb-Douglas utility function but I am not really sure if I did it correctly. I am especially struggling with the sum signs and the subscripts of $i$ & $j$. It would be ...
1
vote
1answer
176 views
Utility maximimization for unusual Leontief utility function
The problem is basic utility maximization subject to a budget constraint with
$$u(x,y) = min\{x+y,4\sqrt{x},4\sqrt{y}\}$$
$$p_x = 1, p_y = 1, M = 4$$
I will have to first plot the Indifference ...
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vote
2answers
72 views
Proof of Choice Coherence in Kreps (2013)
In the first chapter of Kreps (2013), there is a proof that the choice function satisfies choice coherence. Kreps writes:
I do not understand how the third sentence of (b) logically follows from the ...
0
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1answer
50 views
Optimal choice for a weird leontief function
Compute the optimal choice for a consumer with the following utility function:
$$u(x_1, x_2) =\max \{\min(2x_1, x_2), \min(x_1, 2x_2)\}$$
I'm familiar with computing optimal choice for perfect ...
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1answer
121 views
Solving for Pareto Efficient Utility Possibility Frontier using constrained optimisation
The economy is a one-good two individual endowment economy in which individual $i’s$ preferences are given by $𝑈_𝑖(𝑥_𝑖)=𝑥_𝑖$, for 𝑖∈1,2, and the feasibility constraint on the amount of x ...
