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Questions tagged [utility]

Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.

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Maximising utility function

Not sure how to maximise a cobb Douglass utility function? Hope you could tell me whether I’m right or wrong.
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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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91 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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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
28 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 ...
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1answer
46 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 ...
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1answer
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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
28 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 ...
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1answer
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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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1answer
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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: (a) u(x1,x2)=x1x2,v(x1,x2)=lnx1 + lnx2 (b) u(x1,x2)=x1x2,v(x1,x2)=x1 + x2 How do i go ...
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1answer
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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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2answers
52 views

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
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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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1answer
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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
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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
69 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
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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
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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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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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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...
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2answers
63 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
294 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
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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 ...
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1answer
38 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 ...
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1answer
56 views

Does Preference have a Hierarchy? A Silly Question

I have what is probably a very silly question, but I have gone down the rabbit hole and can’t get back out..... Is there is a hierarchy of preference, and within each level of choice do we reset the ...
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1answer
114 views

Marshallian demand with Leontif preferences

Consider a utility function on the form $u(q_{1},q_{2},q_{3}) = min\{\alpha ln(q_{1}) + (1 - \alpha) ln(q_{2}), ln(q_{3})\}$ I know that optimal behaviour requires $\alpha ln (q_{1}) + (1 - \alpha) ...
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3D printed educational aids for constrained optimization

Has anyone seen or heard of 3D printed plastic blocks used to explain bivariate functions and constrained optimization to students? Basically you could print in an approximately 5 inch size a ...
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1answer
78 views

Why Certainity Eqivalence in PIH only holds for quadratic utilities

In my current macro economics course, it has been stated that there is certainty equivalence in the random walk permanent income hypothesis ("which implies individuals act as if future consumption was ...
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1answer
110 views

Can a continuous preference be represented by a discountinuous function?

I can think of some examples, but what can be an outline of the proof?
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1answer
69 views

Exercise where lagrangian is needed?

I teach a general equilibrium class in my university and I want to have an exercise that is not too difficult where the Lagrangian multiplier is needed. I was under the impression that with Cobb ...
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158 views

Quasi-linear Optimal Consumption Bundle

I have a question involving optimal consumption bundles for quasi-linear preferences. Utility is given by $$U(x_1,x_2) = 16\sqrt{x_1} + 2x_2$$ and $p_1 = 8, p_2 = 4, I = 30$. What I have so far ...
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1answer
344 views

Calculating income and substitution effects

Consider a simple quasi-linear utility function of the form $U(x,y)=x +ln(y)$. For this problem, assume that you have “enough” income, so that the optimal consumption bundle is where: $x,y >> 0$....
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1answer
102 views

Prove that $u$ is a utility function for $\succsim$

If X is finite, define this function $u : X \rightarrow \mathbb{R}$ by $u(x) = |\{z\in X:z \prec x \}|$. Prove that $u$ is a utility function for $\succsim$. Is it sufficient to prove that the ...
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1answer
121 views

The relationship between indirect utility and expenditure functions

I am trying to understand the fact that $e(p, v(p,y)) = y$. There is a proof in the text Advanced Microeconomic Theory (Jehle and Reny) that states the following: Because $u(·)$ is strictly ...
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1answer
73 views

Proof that utility is nonincreasing in prices

The following is a proof that the indirect utility function is nonincreasing in prices, but I can't understand the last step. How do they conclude that $v(p_1, y) \ge$ from the previous reasoning? ...
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1answer
49 views

Existence of maximum utility with two bads

I am working with a consumption set $X = R_+^2$ and preferences that are complete, transitive, continuous and strongly monotonically decreasing. The economy is characterized by the presence of two ...
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1answer
110 views

What is the concept of ordinal utility?

I have read in many books that since utility cannot be measured - so ordinal concept or comparison concept is used. If that is so, how can one define a mathematical function for utility which gives a ...
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2answers
85 views

Ruling out boundary solutions in Utility Maximization

Solving the basic Utility Maximization Problem, i.e. \begin{align} max_{x\geq 0} u(x) \\ s.t. \,\,\, p^Tx\leq w \end{align} we get the Kuhn-Tucker first order condition \begin{gather} \frac{\...
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3answers
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A question about Lagrange multiplier(when $\lambda=0$)

I need help in a maximization problem(finding the optimal investment portfolio). where $R_s$ and $\Phi$ are $n$ by $1$, with other variables being scalars. $C^s$ is consumption (or wealth) of an ...