Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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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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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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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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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 $$(x_1,y_1)\mathcal{R}(x_2,y_2)\iff |x_1|\geq|...
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Proof: Risk averse; Certainty Equivalent smaller than expected value
I would like to show for a randomly distributed variable $x$ with CDF $F(\cdot)$ , given a Bernoulli utility function $u(x)$ the following property holds:
The certainty equivalent, $CE(\cdot)$, is ...
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The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them?
I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality.
But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
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Rotation of Quasilinear Utility
Let $u(x,y)=f(x)+y$ be a quasilinear utility. Now we rotate it by 45 degrees, (such that the $x-$axis becomes the direction of $(1,1)$)
$v(x,y)=f(x-y)+x+y$. Is $v$ also a quasilinear utility? What is ...
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Linear Homothetic Utility
A Homothetic Utility is where
$$
\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 ...
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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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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 ...
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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:...
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1answer
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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 ...
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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 ...
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59 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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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?
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28 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/...
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58 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
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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 ...
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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 ...
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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 ...
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1answer
50 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 ...
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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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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 ...
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1answer
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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 ...
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1answer
125 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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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 ...
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1answer
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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
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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 ...
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What is the assumption behind “indifference curve does not cross”?
If only weak-ordering and continuity is assumed, "ICs" can definitely intersect.
If we assume Monotonicity or convexity in addition to weak-ordering, then we can get "no cross of IC".
But those two ...
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Question about an economy with 3 components household, firm and government with functions given
I've spent considerable amount of time on this question, in vain. It is from one of the competitive exams for admission to a grad econ program. Help would be tremendously appreciated. Thanks.
An ...
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Quasi-Linear Functions
I understand that quasi-linear functions have a general form
$U(x_1,x_2,...,x_n,y) = f(x_1,x_2,...,x_n) + y$
and that for a quasi-linear function, the income effect with respect to the other ...
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1answer
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Solution to maximization not Pareto efficient
In my economics class, we saw a proof that if an allocation $ ((\hat x_h), (\hat y_f)), h\in H$ (the set of households), $f\in F$ (the set of firms) is Pareto optimal/efficient, it must necessarily be ...
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Imperfect Substitutes and Utility Funcitions
The utility function for perfect substitutes is defined as U(X,Y) = aX + bY. If the two goods X&Y are imperfect substitutes what would be their utility function?
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What was “Pareto's proof of the immeasurability of utility”?
Wong (1978, 2002, Foundations of Paul Samuelson's Revealed Preference Theory), repeatedly refers to "Pareto’s proof of the immeasurability of utility". What was this proof?
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What are the definitions of the terms value, wealth, and utility in economics?
Are there any definitions for the following three terms that are widely agreed upon in economics?
Value
Wealth
Utility
In particular, are these terms identical? If not, what differentiates them?
I ...
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Optimal spending over several periods with log utility and uncertain lifetime
If someone has probability p(n) of being alive after n periods and p(n) is known with p(n) = 0 for n >= m, and if he has log utility of consumption, and his utilities are additive over time, and ...
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How can two different utility functions represent the same preferences?
I have this question for microecon that asks do the following utility functions represent the same preferences:
$u(x_1, x_2) = x1 \cdot x2, \; v(x_1, x_2) = \ln x_1 + \ln x_2$
$u(x_1, x_2) = x1 \cdot ...
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Why do we have to normalize the income of consumers when working with an Edgeworth Box in a simple trade model with Pareto optima?
I was studying microeconomics and I confess I am not the brightest person for maths and sorry if this is very dumb but I get that we CAN normalize the income and I get where it comes from and how it ...
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indifference curve slope from utility function
in the economics book that I'm reading right now it is written that this utility function:
$$u(x_1,x_2) = 2x_1 + x_2$$
yields indifference curves with a slope of $−2$.
Could someone please explain me ...
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Purpose of a monotonic transformations in utility functions
Based on my economics book, monotonic transformations for a utility function can look something like this:
$f(u) = u + 17 $ or even like this: $f(u) = u^3$
That being said what it purpose in the ...
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Is there a possibility to have an inferior good (x) in a utility function where x & y have 0 cross elasticity?
A question I got on an exam that I think I messed up on:
If we have cross elasticity of 0 (x & y are independent), can x be an inferior good? I answered with a yes. Am I wrong?
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Demand equation with demographics
I am trying to reconcile the derivation of a demand equation with what I actually run in an OLS model. After solving $$max_{x_1,x_2}U(x_1,x_2)= \alpha ln(x_1) + \beta ln(x_2)$$ subject to $$p_1x_1+...
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1answer
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If a utility function is quasi-concave, can we say that the IC curve associated with it is convex?
Let's say we have an utility function, $ U(x,y) = \sqrt{x \cdot y} $. The indifference curve associated with this is convex, while the function itself is quasi concave (because it satisfies $ f_{xx} ...
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2answers
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When can I say that a utility function has constant marginal utility?
Does this utility function have increasing/decreasing or constant marginal utility?
$ U(x,y) = x^2 y^2 $
Now, $ f_x = 2xy^2 $, $ f_{xx} = 2y^2 $, $ f_y = 2yx^2 $, $f_{yy} = 2x^2 $
$ f_{xx} $ has no ...
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1answer
63 views
A utility function that gives a regressive tax rate [closed]
I see some discussion that the reasoning for the construction of a tax rate function is the utility function. Whould $u=\ln\ln w$ function where $u$ is the utility and $w$ the wealth give a regressive ...
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Who was the inventor of Utility function?
To my knowledge, the idea of representing weak-order with a function dates back to Cantor. So my questions are:
1) Was Cantor the first person to rigorize these kinds of representation?
2) Were ...
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Which utility function yields following demand $\alpha p^{\epsilon}$ [duplicate]
I am looking for a utility function that will lead to the following demand
$$\alpha p^{\epsilon}$$.
I know it is most likely a CES utility since the elasticity of demand is constant and this is ...
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1answer
51 views
In law of DMU statement what is meant by “keeping other commodities”?
Law of Diminishing Marginal Utility states that marginal utility from consuming each additional unit of a commodity declines as its consumption increases, while keeping consumption of other ...
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How to calculate marginal utility with two goods?
I'm just getting started as an amateur into microeconomics and I really can't understand this thing about marginal utility when more than one good is involved:
Let's say I have the utility function U ...
