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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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Optimization of budget constraint and utility [on hold]

Alice cares about two things: how much leisure time she has ($x_1$) and what mark she gets on tomorrow’s Micro exam ($x_2$). Her preferences between these goods can be represented by the utility ...
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1answer
37 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 do I work out U max(2x,y)

My professor has given me a task and I simply don't have any clue how to work this one out. I do not understand this type of utility equation. I do not understand this at all. Umax = (2x,y) the ...
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1answer
39 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
129 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
30 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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9 views

Implications of CES on changes in demand

I have a CES utility function, in my class notes I have remark that when the CES is constant and less than one the demand in absolute terms remains unchanged when price of second commodity changes. ...
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2answers
78 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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29 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
55 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
61 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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Why is the indirect utility function quasiconvex?

Why is the indirect utility function quasiconvex? And in particular, why is it enough to show that the budget correspondence is semiconvex?
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1answer
35 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 ...
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1answer
29 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
48 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
104 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
69 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
73 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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54 views

Image of binary relation

From the book: "a binary relation $R$ associated to each element $x$ of $X$ some elements $y$ of $X$. We denote by $R(x) = \{y \in X : x R y\}$ the image of $x$ through $R$" but then is an example: ...
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1answer
48 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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77 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
151 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
61 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
66 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
52 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
45 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
47 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
55 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 ...
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2answers
647 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
102 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
61 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
68 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
64 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
86 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
66 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
88 views

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
116 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
22 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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0answers
26 views

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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0answers
34 views

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
39 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
60 views

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
45 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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65 views

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 ...
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22 views

Production choices in Hayek's theory of information-bearing prices

As I understand the work of Hayek, he asserts that prices encapsulate the true societal worth of the item being sold by integrating the compound need for all of the ingredients and work which go into ...
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1answer
71 views

Relative risk aversion, a property of period or lifetime utility

This question is to be understood in the context of consumption based asset pricing. I'm wondering whether relative risk aversion is a property of the period utility function, which is simply a ...