Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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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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1answer
32 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:...
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How to identify substitutes and complements?
For this utility question; it asks whether x and y are substitutes or complements. They specify it is either net or gross but I find it hard to distinguish between the two since they depend on income ...
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1answer
16 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
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1answer
33 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 ...
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1answer
50 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
20 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?
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1answer
25 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
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1answer
51 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 ...
2
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1answer
17 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
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2answers
75 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 ...
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Microeconomic Theory and Utility/General Equilibrium
I am working on this problem and struggling... as in I don't even know where to begin. Please help! It would be greatly appreciated!
(Reference: Mas-Collel et.al (1995, section 3E)) Let u : X → R be ...
2
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1answer
49 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 ...
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1answer
45 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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2answers
67 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
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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 ...
3
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1answer
104 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 ...
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1answer
107 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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2answers
69 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 ...
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1answer
44 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
60 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 ...
2
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1answer
61 views
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 ...
4
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1answer
104 views
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 ...
0
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1answer
52 views
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 ...
2
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1answer
173 views
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?
3
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1answer
54 views
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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0answers
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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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1answer
17 views
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 ...
2
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1answer
68 views
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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1answer
32 views
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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2answers
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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 ...
4
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2answers
83 views
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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0answers
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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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0answers
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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 $$p_1x_1+...
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1answer
86 views
If a utility function is quasi-concave, can we say that the IC curve associated with it is convex?
Let's say we have an utility function, $ U(x,y) = \sqrt{x \cdot y} $. The indifference curve associated with this is convex, while the function itself is quasi concave (because it satisfies $ f_{xx} ...
2
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2answers
62 views
When can I say that a utility function has constant marginal utility?
Does this utility function have increasing/decreasing or constant marginal utility?
$ U(x,y) = x^2 y^2 $
Now, $ f_x = 2xy^2 $, $ f_{xx} = 2y^2 $, $ f_y = 2yx^2 $, $f_{yy} = 2x^2 $
$ f_{xx} $ has no ...
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1answer
59 views
A utility function that gives a regressive tax rate [closed]
I see some discussion that the reasoning for the construction of a tax rate function is the utility function. Whould $u=\ln\ln w$ function where $u$ is the utility and $w$ the wealth give a regressive ...
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2answers
64 views
Who was the inventor of Utility function?
To my knowledge, the idea of representing weak-order with a function dates back to Cantor. So my questions are:
1) Was Cantor the first person to rigorize these kinds of representation?
2) Were ...
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0answers
34 views
Which utility function yields following demand $\alpha p^{\epsilon}$ [duplicate]
I am looking for a utility function that will lead to the following demand
$$\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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1answer
115 views
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 ...
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2answers
161 views
Any interior solution for $u(x,y) = min\left \{ x,y \right \}^{2} + max\left \{ x,y \right \}$?
Will all the solutions be in the corner or will the cusp in the middle give us any interior solution? This is by the intersection of the budget line.
I am getting this type of a shape:
But I am not ...
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1answer
34 views
Theories that complement/contradict prospect theory?
Kahneman and Tversky's prospect theory, which they developed to contradict expected utility theory, is obviously an interesting result.
But, after their experiments has anyone tried to completement ...
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2answers
167 views
Is utility in neoclassical economics a circular argument/concept?
Neoclassical economics as a utility function that represents a consumer's preference ordering over a choice set.
Joan Robinson criticized utility for being a circular concept:
"Utility is the ...
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0answers
53 views
Three consumers three goods competitive equilibrium
I have the economy described by the three consumers above with their respective preferences and endowments. I'm not so sure about how to proceed towards the competitive equilibrium...
3
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2answers
66 views
Linking top-down and bottom-up models for analyzing electricity price-based demand response: Expenditure constraint is violated?
I have a question about the contents of this paper*, which links a building energy model and a utility-maximization component. In it, the author tests several electricity prices using a Cobb-Douglas ...
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2answers
417 views
Strongly and strictly increasing utility functions
What's the difference between Strongly and strictly increasing utility functions?
What I know is that if $x'>>x $ where $x'$ has all elements strictly greater than $x$ then $U(x')>U(x)$, I ...
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1answer
43 views
What is the difference between solving for utility maximization separately or aggregately?
I derived the Walrasian equilibrium for an economy of two consumers with their respective utility functions (u1, u2) and initial endowments but later on I am asked to maximize (u1+u2).
Does anyone ...
0
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1answer
61 views
How to draw the indifference curves for [closed]
$u(x,y) = min(2x,y)+ y?$
I don't understand how we can plot it. I know that there's going to be minimum so I am familiar with the cusp shape of perfect complements. But this looks like a quasilinear ...
