Questions tagged [utility]
Utility, or usefulness, is the (perceived) ability of something to satisfy needs or wants.
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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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How to derive optimal labour supply from utility? [on hold]
I am struggling with this question:
An agent's utility is U = log(C) - 2L2 (where log(C) is the natural logarithm).
The agent produces their own output with a production function
C = Y = AL^α, where ...
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1answer
26 views
A utility function that gives a regressive tax rate
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 who rigorize these kinds of representation?
2) Were ...
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Maximum utility of 3 commodities using Lagrange Multiplier? [on hold]
Given a consumer utility function consuming commodity x, y, and z as U(x,y,z) = √x + √y + √z and the price of x, y and z are $2, $3 , & $4 respectively.
What should be the consumer's purchase of ...
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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
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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 ...
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2answers
135 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
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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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0answers
37 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...
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2answers
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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
114 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
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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
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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
109 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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0answers
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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
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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
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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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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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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
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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
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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
95 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
60 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
46 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
63 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
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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 ...
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2answers
794 views
hicksian demand of perfect complements [closed]
As the title states, I want to know how to derive the hicksian demand of perfect complements $\text{min} \, \{x1,x2\}$. Thanks in advance.
Also, no price is given, or budget. my main question is ...
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2answers
114 views
Continuous function in microeconomics
In the following picture two preference relations are defined -
Ist preference relation defines lexicographic relation. Though we know that lexicographic preferences doesn't have utility function. ...
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1answer
89 views
quasiconcave vs convex function
I have been struggling trying to understand the difference between a quasiconcave and a convex utility function. As far as I understand a function can be both at a certain point, but is not clear to ...
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1answer
81 views
separable utility function and cross price effect
Suppose that consumer's utility function for three goods is separable, that is,
$U(x_1, x_2, x_3) = f_1(x_1) + f_2(x_2) + f_3(x_3)$ ...(i)
where $f_i$ is increasing and strictly concave, i=1,2,3. ...
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1answer
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advanced mathematical treatement of revealed preference and utility theory?
I am looking for a textbook that treats revealed preference and utility theory much more thoroughly than does Mas-Collel.
What would be suggestions for this? Specifically I'm interested in conditions ...
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1answer
67 views
Interpretation of Interesting Utility Function
Solving introductory microeconomics problems I have come across the following type of utility function:
$$ f(K,L) = (\alpha K^{\frac{\sigma - 1}{\sigma}} + (1 - \alpha) L^{\frac{\sigma - 1}{\sigma}})^{...
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1answer
100 views
Lagrangian: when to discount budget constraint?
I am getting a bit confused about setting up the Lagrangian in intertemporal constrained optimization problems. The confusion is as to when is the one-period budget constraint multiplied by the ...
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2answers
83 views
What is a good way to generate realistic utility curves?
I am aiming to program a basic simulation of a simplified economy to look at the impact of various interventions.
The economy will have N groups of homogeneous consumers and M producer / employer ...
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2answers
57 views
Utility and consumption tax
If I have a model with taxes on consumption denoted $\tau$ should I write the utility function as $u(c)$ or $u((1-\tau)c)$? Thanks
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3answers
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modelling disutility from over consumption
In introductory economics courses the concept of marginal utility is illustrated through simple examples like how much benefit one gets from eating another slice of pizza (i.e first slice provides 100 ...
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3answers
134 views
Is the utility of money *actually* logarithmic?
Apologies for asking what is probably a basic question from someone that is not in the economics field.
But I was playing around with the idea of determining how a group of people could split a bill ...
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0answers
23 views
Finding savings in an Overlapping Generations model
I have not seen this question asked anywhere, so I'm posing it here in case anybody else (hopefully) can help me get to the answer. In a nutshell, my question is: how do we arrive at the saving ...
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survival probability and integration by parts
I am trying to integrate by parts by using an indicator function. However, I am not really sure if it is a correct way to change the bounds of integral with indicator functions. I am trying to deal ...
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The use of preference relations in choice theory and the $\succsim$ symbol
At least as from Edgeworth and Pareto we think about utility in mathematical terms. My question twofold
(i) about the start of the usage of binary relations to model preferences in economics, and ...
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1answer
44 views
Construct utility function for a risk-averse agent
I am trying to construct utility function for an agent who can be risk-seeking or risk-averse. We have an agent $i$ who has an ideal point $x$ in a policy space $X = [0,1]$. There is a policy (option) ...
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1answer
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Would a very cheap renewable energy source be harmful economically?
This question is not on whether these devices work or not but so much as if they did work. What if electricity can be made so cheap that everyone could afford it ti the point there was no demand for ...
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1answer
50 views
Continuation value versus utility in asset pricing
Is there a difference between continuation value ($V_t$) and utility ($U_t$) except for a possible scaling / difference in units? My question refers to the consumption-based asset pricing literature.
...
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0answers
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Utility and functions
A text I read posits that utility functions tend to be unstable, if the utility people draw out of goods depends on the consumption of the particular comparison group. Can you explain why this ...
