Questions tagged [utility]

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

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18 views

Risk seeking investors: Do they benefit from return at all?

Starring on the indifference curves for different types of risk preferences I ask myself why the risk seeking investor would be indifferent between an investment on the far left of his indifference ...
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Von Neuman-Morgenstern utility theorem apply only to linear utility functions?

Does the Von Neuman-Morgenstern utility theorem apply only to linear utility functions? If yes, what extension of this theorem of which theorem needs to be applied to use more specific utility ...
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Calculate hicksian demand with utility function (with restriction)

$U(x_1, x_2) = 1/2 * x_1 $ I am trying to calculate the Hicksian demand when when $U(x_1, x_2) = 2$ and the value of the minimum expenditure when $p_1 = 9$ and $p_2 = 16$ For the hicksian demand I ...
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61 views

Calculate income and sustitution effect from utility funcion

Utility function $U(x_1 , x_2) = x_1 + 4 * x_2 $ $ p_1 = 3, p_2 = 8, m =120 $ $p_2$ changes from $8$ to $10 $ How can I calculate the income and substitution effect. I first thought about calculating ...
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Microeconomics Slutsky [closed]

I'm trying to calculate the sustitution and income effects with slutsky method. $ U(x_1,x_2) = x_1+ 4x_2 $ $P_1 = 3, P_2 = 8, P'_2= 10 $ (my new price) and $ m = 120 $ However with $Uma(x)/Uma(y) = ...
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Calculate Marshallian demand from a utility function [closed]

I can't seem to understand where I should start with. I think these problems can be solved using Lagrange but I know nothing more. $U(x_1, x_2, x_3) = x_1 · x_2 · x_3 $ Is there any procedure that I ...
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CES utility with negative values

We know that the CES utility function approximates a Leontief utility function as in the following: $$u(x_1,x_2) = (x_1^{-r}+x_2^{-r})^{-1/r}\overset{r\rightarrow\infty}{\longrightarrow}\min\{x_1, x_2\...
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Why are utility functions typically assumed to be concave?

Why is it usually required that utility function be concave? Is it because concavity is a necessary (or sufficient?) assumption for a unique equilibrium? Can someone please spell this out for me? ...
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1answer
76 views

How do you measure the MRS for more than two goods?

For two goods, the MRS is defined as the amount of one good you would trade off for the other. Mathematically, $$\text{MRS} = \frac{dy}{dx}$$ where the amount of goods $X$ and $Y$ are denoted by $x$ ...
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Is addiction a case of increasing marginal utility?

I got to know that alcohol addiction is a case of increasing marginal utility. My professor refutes me bluntly stating that once a person starts consuming he no longer remains to be a 'rational ...
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MRS and IC : The language sounds contradictory

The MRS$_{xy}$ is defined as $\left(-\frac{dy}{dx}\right)$ and Nicholson/Snyder (NS) writes it as the amount of $x$ we can trade for $y$ while remaining equally well off. However, the analytical ...
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Question about Marginal Utility [closed]

The following statement is given as true and I cannot make sense why. It is the only information given. "The $MRS$ of flour in 1kg bags for flour in 2kg bags is negative and constant." I ...
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197 views

What is the problem with this opportunity cost example?

The "stand-up economist" Yoram Bauman used the concept of opportunity cost to make the following joke: [S]omebody offers you a choice between a Snickers bar and a package of M&Ms. ...
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1answer
38 views

How come a representative consumer with quasilinear utility need not economize?

Suppose a representative consumer has the following quasilinear utility function: U_i(x_1,x_2)=ax_1+ax_2-(1/2)*[(x_1)^2+(x_2)^2] + k where a>0 is a utility parameter, x_1 and x_2 are the goods, and ...
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1answer
54 views

King–Plosser–Rebelo Preferences and Additively Separable

The wiki of King–Plosser–Rebelo preferences says that the utility function has the multiplicatively separable form $$u(C, L)=\frac{1}{1-\sigma_{c}} C^{1-\sigma_{c}} v(L)$$ and "in the limit case ...
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2answers
54 views

Understanding utility function curve and marginal rate of substitution

This example appears in a different question, but there is something I don't understand. Maybe this question is better suitated for algebra stackexchange. John’s utility function for food (f) and ...
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1answer
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Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$

I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
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53 views

How are weak preferences different to strict preferences/indifference?

Given a utility function $u(\cdot)$ and two bundles $x$ and $y$. Assuming $u(x)=u(y)$. I am to prove or disprove that $x \succcurlyeq y$. Now I'm confused by this. We say $x$ is strictly preferred to $...
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290 views

Fundamental question on marginal utility

I was just thinking back to some introductory economics courses, but now I'm extremely confused on a fundamental concept. How is marginal utility interpreted as the additional "happiness" ...
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Demand for minimum of $4$ different goods

The consumer has the utility function with $4$ goods $$U=\min\left \{ \sqrt{x+y},z+w \right \}$$ The prices are $p=(3,2,2,1)$ with wage $m=1$. Find the demand. So far I have observed that it is ...
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Adding scaled CRRA utility

Suppose our utility function is the usual CRRA utility with $\gamma=2$ so that: $$u(C) = \frac{C^{1-\gamma}}{1-\gamma} = -\frac{1}{C}$$ Now suppose there are 2 goods, A and B, available for ...
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69 views

Derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1 + p_2\overline{x}_2)$ to derive Slutsky equation

Why is the partial derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1+p_2\overline{x}_2)$ for $p_1$ $$ \frac{\partial x_1^S(p_1, p_2, \overline{x}_1, \...
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Economic theory journals for a refinement theorem about utility function representation

I would like to ask which are the (mathematical) economics journals that publish papers about economic theory and that focus mainly on the mathematical aspects of it. Let me be more precise. If I have ...
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Unsolveable Demand/Utility Problem?

A consume has a preference relation on $\mathbb{R}^4_+$ with a utility function defined as $$ U(x_1,x_2,x_3)=(\ln(3x_1+2x_2+x_3))^3$$ Find the demand at prices $p=(1,1,1)$ and wage $4$. Attempt I ...
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1answer
38 views

Concept of Utility in demand systems

I have seen that researchers use different utility function in demand systems estimation such as Stone Geary. What is the role of these utility functions? What are utility function other than stone ...
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72 views

Utility function and homogenous of degree zero

I've a utility function which is given by ($x_i$-$b_i$)$^{c_i}$ $\sqrt{x_2}$ . What values of b and c can I input to ensure Homogenous of degree zero in prices and wealth? I think c will be positive....
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157 views

Are the goods in additively separable utility functions normal goods?

Inspired by this answer. To make it a bit more precise, by normal good I mean demand is (not necessarily strictly) increasing in income, and by additively separable utility function I mean that a ...
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116 views

Expected utility theory (Lottery notation)

A wheel of fortune has outcomes $S=\left \{ 1000,100,50,20,0 \right \}$ as money prices. A consumer has the preferences $$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$ ...
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167 views

Question about Social Welfare Function and Social Profile

What are the meanings of a social welfare function and social profile? How are they related?
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1answer
57 views

Derive demand function from utility [closed]

Never encountered such a problem as I am new. $$U(x_1,x_2)=(a\ln(x_1)+b\ln(x_2))^n$$ and $a,b,n>0$ with income $w>0$ and prices $p_1,p_2>0$. Find the demand function. Attempt I am thinking ...
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1answer
66 views

The Price and Demand Index in Homothetic Kimball Utility

Suppose with Kimball preferences, utility $Q$ from consuming $\left\{q_{\omega}\right\}_{\omega \in \Omega}$ is implicitly given by $$\int_{\omega \in \Omega} Y\left(\frac{q_{\omega}}{Q}\right) d \...
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1answer
76 views

The Intuition of CES Utility

Suppose a (symmetric) CES utility function $$U(\mathbf{x})=\left[\int_{\Omega}\left(x_{\omega}\right)^{\frac{\sigma-1}{\sigma}} d \omega\right]^{\frac{\sigma}{\sigma-1}}, \sigma>1$$ 1 The indirect ...
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134 views

Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic?

As we know that $Q*P=const.$ for Cobb-Douglas preferences, we can thus conclude that $\frac{dQ/Q}{dP/P}$ is always $-1$: $$ QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P} $$...
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How do I determine PED from price consumption curve with slope of zero?

Given a budget for two goods $x_1$ and $x_2$, a fixed price for good 2 and three prices for good 1 with the corresponding optimal amount of good 1 ($x_1$), I like to calculate the PED for good 1. By ...
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1answer
69 views

Without knowing the Slutsky equation and income/substitution effect, how can I show a certain good is inferior or Giffen?

Say I've got a function $x_1(p_1,p_2,m)$ where $p_1, p_2$ are the prices for good 1, good 2 respectively and m is the income. Now, I haven't heard of the Slutsky equation yet nor the income/...
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240 views

Relation of Engel-curve to income elasticity of demand; is the slope of the Engel-curve equal to the elasticity of income?

I learnt that $\frac{\Delta x}{\Delta m} \gt 0$ for normal goods, $\frac{\Delta x}{\Delta m} \lt 0$ for inferior goods, $\frac{\Delta x}{\Delta m} \gt 1$ for luxury goods and $0 \lt \frac{\Delta x}{\...
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1answer
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Marginal Utility vs Cost of production

I have a confusion. Marginal utility is always decreasing and people will not be happy to pay 2 times of price for 2 times of a coffe but I guess the price of producing 2 times of coffe will be the ...
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1answer
67 views

Is an income tax always more favourable for consumers compared to ad valorem/quantity tax?

I'm studying the optimal choice of consumers with regards to taxation. I read that for consumers, income tax is generally (for Cobb-Douglas preferences) preferred compared to ad valorem tax: If the ...
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41 views

Social welfare in terms of preferences

How does one define a social welfare in terms of individuals’ preferences $\succeq_i$? If we have utility functions $u_i$ then a social welfare maximizing outcome $x$ is simply one that maximizes $\...
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1answer
88 views

Why is the derivative of a monotonic transformation of a utility function assumed to always be greater than 0?

I'm looking into utility functions and their relation to indifference curves. Now, I understand a positive monotonic transformation does not change the order (it's a rank-preserving transformation). I ...
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1answer
65 views

Demand function for partially subsumable products

I am struggling with this question that should be simple for economists (I am not an economist at all): There is a market with a limited number of (heterogenous) consumers with two firms, each ...
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1answer
57 views

Utility maximization: pollution and housing prices

A factory releases a toxic pollutant which causes two types of damage to a representative area resident whose utility function is $U(S,H,x)= a \cdot \log(S) + b \cdot \log(H) + c \cdot \log (x)$ where ...
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Multi dimensional Auction in economics

I am following this paper . They have different suppliers and one buyer and They are using auction to select best suppliers Suppliers will submit. suppliers offer a multidimensional bidding on quality ...
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85 views

Ordinally Separable Utility Representation

Let $X_i$ be a separable, compact, Banach space. Definition: A weak order $\succeq$ on $X=\prod_{i=1}^NX_i$ has an ordinally separable representation if there exists $u_i: X\rightarrow \mathbb{R}$ and ...
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1answer
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Trouble Understanding the Integral Underlying Random Utility Models

Given a utility function, $U_{nj} = V_{nj} + \varepsilon_{nj}$, it makes sense that we can find the probability the decision maker $n$ chooses alternative $i$ as: $$Pr(U_{ni} > U_{nj} \forall j \...
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67 views

How are real income and utility the same thing?

The textbook I'm using, "Microeconomic Theory: Basic Principles and Extensions", treats utility and real income as the same thing in the chapters on compensated and uncompensated demand. I ...
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1answer
72 views

Modern descendants of Frank Ramsey's paper "A Mathematical Theory of Saving"?

I haven't studied economics, but I'm interested in applied ethics, and I came across Frank Ramsey's paper "A Mathematical Theory of Saving". I thought his application of calculus to a ...
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1answer
254 views

How to prove that a utility function U(x,y)=min(x,2y) is quasiconcave?

I have a question that asks: "Let there be two goods 1 and 2.Let $x$ and $y$ denote their respective quantities.$(x,y)$ represents a bundle. Suppose a consumer’s preferences over bundles in $R^2_+...
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1answer
41 views

How to Represent as a Payoff Matrix

I'm trying to represent the following as a pay-off matrix. I have 100 dollars to invest in one agricultural stocks with a choice of apples, pears or grapes. Return on investment relies on whether ...
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1answer
71 views

Can I rename a utility function based on its properties?

A big name researcher gives a name to a specific utility function 30 years ago. Now I am writing a paper and feel that a new name might be more suited because of the properties associated with the ...

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