Questions tagged [utility]

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

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59 views

How do I derive the aggregate demand function given two utilities functions?

Assume that we have two people with the same utility function of $U_i = x^{1/2} + y^{1/2}$ where $i=1,2$ and $I_i$ is the income. Let $P_x$ denote price of good $x$ and $P_y$ denote price of good $y$. ...
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How do I solve the Envelope Theorem condition in Microeconomics?

I am preparing myself for a MSc in Economics and don't understand why, according to the Envelope Theorem, when deriving a utility function $ u(θ, q(θ), r(θ)) = B(q-r) - C(\frac{q}{θ})$, its derivative ...
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When the global optimal is outside of the constraint set, what will be the demand?

$u:\mathbb R^n\to\mathbb R$ is a quasi-concave utility function so the indifference curves are convex. $a,b\in\mathbb R^n$ are two points. Our budget set is the (one-dimensional) segment $[a,b]$ that ...
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What can be said about $(p − q)x_0=C$ from the information given?

A consumer consumes only two goods $x$ and $y$. The price of good $x$ in the local market is $p$ and that in a distant market is $q$, where $p > q$. However, to go to the distant market, the ...
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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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104 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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What are the correct utility functions?

It is common to talk about utility functions. For example in a universe with only two goods, we might assume each person (or group of people) carries a function $u(x,y)$ in their heads. When offered ...
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Indifference curve - Does $dU = 0$ hold in higher dimensions? / Problem of integrability

In two dimensions, we have on an indifference curve that $dU=0$. Does this apply to indifference objects in higher dimensions? I was thinking that if $dU > 0$, then one is moving to a higher ...
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55 views

How do I figure out whether the ICs are convex or concave?

Question: Randy Ratpack hates studying both economics and history. The more time he spends studying either subject, the less happy he is. But Randy has strictly convex preferences. (a) Sketch an ...
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Effect of a productivity shock on the real exchange rate within a two period model

So if we have a two period model, tradable goods and nontradable goods, where consumers tend to maximize utility, then we have the following Euler equation: $$\frac{ u' (c_1) }{P_1} = (1+r)\beta \frac{...
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Relation between demands of $x, y$ and $z$

Question: Consider a consumer with utility function $U(x,y,z)=y\min\{x,z\}$. The prices of all three goods are the same. The consumer has $100 to spend on these three goods.The demands will be such ...
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Is there any evidence for consumer utility-maximising behaviour, at individual or market level?

Even though utility maximisation is ubiquitous in economic textbooks to model consumer behaviour, its usefulness is rarely demonstrated by evidence. Is there any evidence that some consumers do ...
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Is the Cobb-Douglas Utility Function Locally Non-Satiated at (0,0)?

My understanding of local non-satiation is that increasing your allocation of one good by a marginal amount increases utility. Suppose your utility takes the following form: $$U(x,y)=x^\alpha y^\beta$$...
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Calculating risk interest rate within a two period model

I am trying to calculate how to determine the interest rate ( = risk free rate + premium) within the following model where a consumer decides to invest in a safe asset or in a risky asset. The utility ...
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327 views

Why do many papers not write the actual utility function?

Why do many papers write the intertemporal maximisation problem for the household as \begin{equation}E_{0} \sum_{t=0}^{\infty} \beta^{t} U\left(C_{t}, N_{t}\right)\end{equation} and then do not write ...
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How is the defintion of the mean preserving spread (MPS) not too general?

The mean preserving spread is defined as follows: Consider two lotteries g and h. Let $x_g$ und $x_h$ denote the corresponding random variables. Then h is a mean preserving spread (MPS) of g, if: $...
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Does the duality of utility maximization and cost minimization hold in practice?

I recently learned about the relationship between utilization maximization and cost minimization. Are there studies on whether this duality holds in real life? Any information on this topic for a ...
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Study whether $\succsim$ represented by $u(x)=\lfloor x \rfloor$ is continuous [closed]

Using the following definition of continuity: $\succsim$ is continuous if for any bundles $x,y,z$ such that x$\succ$y$\succ$z, there exists $\alpha \in (0,1)$ such that $\alpha x + (1-\alpha)z \sim y$....
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Expenditure function. Prove that this set is bounded

I need to prove that the following set is bounded in order to derive the expenditure function: $e(p,v)=min_x px$ ST $\{x \in R^n_+$ such that $U(x)\geq v\}$. Knowing that $U(x):R^n \longrightarrow R$ ...
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Is it considered acceptable or unacceptable to use currency as a measure of utility?

There will always exist at least one economist who condones measuring utility in US dollars and another who does not. However, I am wondering which way the majority of contemporary economists lean. ...
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Prove that budget constraint is Lower Hemi Continuos (LHC)

I need to prove that the following constraint is LHC. $B=\{x \in R^n : px\leqslant pw)$ But Im not capable of finding and sequence $\{x_n\}$ such that $x_n \in B(p_n,w_n) \forall n$ and that $x_n\...
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Why doesnt Law of Diminishing Marginal Utility not affect price effect?

Ok so in my textbook, it is given that the downward slope of the demand-price curve is justified by three factors: Law of Diminishing Marginal Utility Income Effect(Real income) Substitution effect ...
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Remove Linear Good From Quasi-linear Utility Function

Given a quasi-linear utility function: $u(x_1, x_2) = f(x_1) + \beta x_2$, $\beta > 0 $ What would happen if good 2 ($x_2$) is removed from the market? Would the new utility function be: $u(x_1) =...
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Gross substitutes vs. net substitutes

Wikipedia explains the difference between products that are "gross substitutes" and products that are "net substitutes". However, the mathematical explanation doesn't give much intuition about these ...
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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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Why couldn't the Karush-Kuhn-Tucker optimization find the solution?

I have the following utility maximization problem: $$\max (xy)$$ $$(x+y-2)^2 \leq 0$$ Conditions: $$y-2\lambda (x+y-2) =0$$ $$x-2\lambda (x+y-2) =0$$ $$\lambda(x+y-2)^2=0$$ When I set $\lambda>0$, ...
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Two interpretations of the Lagrange Multiplier

A question about the second answer on this thread: Help understanding Lagrangian multipliers? If we have a standard utility maximizing problem $$ \max_{x,y} U(x,y) $$ with the constraint $p_{x}x + ...
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Differentiability of the utility function and indifference curves

Comment on the following affirmative: In the traditional consumer model, the hypothesis of differentiability of the utility function and of convexity of preferences, assure the indifference curves ...
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Mathematics of the income and substitution effects

I have recently been learning about the concept of utility and the indifference curve. I am having some problems understanding the effects on consumption of two goods $X$ and $Y$ of a change in the ...
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Does decreasing marginal utility imply risk aversion?

Unless I misunderstood something, seems like risk aversion and decreasing marginal utility is the same thing in the utility model, but intuitively, it seems entirely possible that an individual with ...
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Additional components in utility functions (behavioral economics)

I am looking for a term describing the second part of a utility function in behavioral economics and related disciplines. For example, Thaler (1983) describes a utility function that could be ...
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What would we say on the utility of risk and its consequences?

Anything has its risks and anything has its utility or desutility. The risk aversion causes a looking for safer alternatives in the market which maximizes utility in a trading off between risk and ...
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Demand functions homogeneous of degree zero in prices and income - how this relates to budget exhaustion (solving a consumer's problem)

I have the following demand system: It appears to me that each demand function is homogeneous of degree zero in prices and income as: Why would this demand system not satisfy the following budget ...
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214 views

Price-consumption curve

Suppose a consumer whose income is $b$ has a utility function given by $U(x,y) = 2xy+y^2$ with the price of $x$ being $p_x$ and the price of $y$ being $p_y$. Draw the price-consumption curve assuming ...
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making a utility model for CO2 compensating travel demand

I'm trying to make a model which is build around the idea of carbon offsetting fuel (the consumer pays an extra fee per litre fuel for the compensation of the emitted CO2). The goal here is to make a ...
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How to find the Utility Possibility Frontier when there are Perfect Substitutes?

I am trying to derive the Utility Possibility Frontier (UPF) when both utility functions display perfect substitutes (in an Edgeworth economy with to consumers and two goods). The specific problem: $...
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Equivalent Variation of Price Change

If Bernice (whose utility function is min {x; y} where x is her consumption of earrings and y is money left for other stuff ) had an income of \$12 and was paying a price of \$3 for earrings when the ...
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Name of this $u\left(x_{1}, x_{2}\right)=x_{1}+\alpha x_{2}+\beta \sqrt{x_{1} x_{2}}$ utility function?

I have seen this $u\left(x_{1}, x_{2}\right)=x_{1}+\alpha x_{2}+\beta \sqrt{x_{1} x_{2}}$ a numbers of time now. I wonder whether it is somehow special and therefore has it's own name? Kind regards,
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How to derive utility possibility frontier?

I'm trying to derive the utility possibility frontier of a economy whose consumption contract curve is $$y_A = \frac {y} {x} x_A$$ and $$y_B = \frac {y} {x} x_B$$where $x_A + x_B = x$ and $y_A + y_B= ...
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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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Specification of the parameters of this utility function [Behavioral Economics]

This is from page 274 of "Advances in Behavioural Economics" by Camerer, Rabin, Loewenstein. This chapter of the book is entitled "A theory about fairness, competition, and cooperation". I have ...
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Aggregate CES Cobb-Douglas utility over different individuals

Suppose I have a CES Cobb-Douglas Utility function: $$U_i=X^{\alpha_i} Y^{1-\alpha_i}$$ Can I add utilities of different individuals meaningfully? I.e, where people have different $\alpha_i$. $$\...
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Monotonic transformation of utility functions [duplicate]

Why taking monotonic transformation of a utility function does not change marginal rate of substitution?
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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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How to calculate CRRA bounds from Holt and Laury (2002) type lottery?

Lottery is between: Option A: a certain choice of £5 Option B: £10 with probability 0.1 and £1 with probability 0.9 The probability of receiving £10 increases in each subsequent choice. How do I ...
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Difference between direct and indirect utility

What is the difference between direct and indirect utility? Following the advanced microeconomics textbook Jehle and Reny I can not understand either the intuition or the math definition. It confuses ...
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Why is the marginal utility of money assumed to be constant in Marshallian Theory of Consumer Behaviour

While studying the Marshallian Theory of Consumer Behaviour, I came across the assumption that the marginal utility of money is assumed to be constant. Can someone please explain why is this so?
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Utility Theory/Marginal Rate of Substitution: Can the marginal rate of substitution be calculated for a point of the budget line?

This a person's budget line with various points, and their consumption, C*, and their endowment e, which is worth $5000 (unimportant). Also shows is their initial indifference curve. The difference ...
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Concavity of Cobb-Douglass Utility Function on Non-Open set

My textbook argues that the Cobb-Douglass utility function $u=(x1)^a(x2)^b$ with $a,b>0$ and $a+b<1$ is concave on $R2+$ by computing the Hessian and showing it to be negative semidefinite for ...
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How to describe a utility function in words?

Suppose I have a utility function of Cobb-Douglas form $$U(x, y) =x^{0.2}*y^{0.8}$$ I want to describe it in words. I would say like: The utility of consumer is captured by number of good x and ...

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