Questions tagged [pareto-efficiency]

An efficiency standard based on the idea that the most efficient outcomes are those where no individual can be made better-off without making at least one other worse-off.

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Can we define the core as the intersection of Pareto efficient allocations and upper-contour sets?

Suppose that an economy has $n$ agents, each with endowment $\omega_i$. Their preferences are represented by the quasiconcave and increasing function $u_i$. Let the set of Pareto efficient allocations ...
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When is local Pareto-efficiency equivalent to global Pareto-efficiency?

Given a state-space $X \subseteq \mathbb{R}^m$ and $n$ utility functions, $u_1,\ldots,u_n: X\to \mathbb{R}$, define a state $x\in X$ as Locally Pareto-efficient if it has an open neighborhood $N(x)$ ...
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Has mathematical economics contributed to the mathematics of space exploration?

We see the work of Bellman showing up in both orbital trajectory planning/optimization and, obviously DSGE modeling. Also, in a recent example, the JWST uses ideas surrounding Pareto optimization and ...
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Is this situation Pareto Optimal

"If either player is receiving his maximum payoff, then that outcome is Pareto optimal." Is this True,False or Uncertain. Solution: I guessed it false because we dont know the exact Utility ...
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Are the marginal conditions for Pareto optimality sufficient?

In introductory microeconomics textbooks, it is argued that the following three conditions are necessary for the Pareto optimality; Exchange Efficiency (MRS must be equal among all individuals) Input ...
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Social Welfare Function (Pareto Efficiency)

What is the Pareto efficiency compensation criterion? Can you give me an example?
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Information asymmetry and market failure

Markets with information asymmetry frequently result in a loss of efficiency relative to perfect information, see e.g.; moral hazard. Yet I have seen the claim Information asymmetry isn't a market ...
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Core in a replicated economy

I'm trying to solve the following problem on general equilibrium: Consider an economy with two individuals with utility functions $u^A(x^A,y^A) = \min \{ x^A, y^A \}$ and $u^B(x^B,y^B) = \min \{ x^B, ...
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Find the set of Pareto efficient allocations. $U_1 = -|x_1-2|$ and $U_2 = −|x_2 − 8|$

A professor has 20 hours to allocate between two PhD students. Let x1 and x2 be the time allocated to the two students. The utility of each student is as follows: $U_1 = −|x_1 − 2|$ and $U_2 = −|x_2 − ...
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Utility Possibility Set and Utility Possibility Frontier

Consider an Exchange economy with two individuals $a$ and $b$ and two goods $1$ and $2$. Denote consumption of good $j$ by individual $i$ as $x_{ij}$ for $i\in\{a,b\}$ and $j\in\{1,2\}$ The utility ...
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Approximate Pareto efficiency with ordinal preferences

Pareto-efficiency is a very important property, but in some cases it cannot be attained (for example, when agents play a game such as the Prisonner's Dilemma). In such cases, it can be useful to ...
Erel Segal-Halevi's user avatar
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Pareto efficient allocations for non-monotonic, quasi-linear utility function

Suppose we have an pure exchange economy with 2 consumers, and 2 goods $x_1$ and $x_2$. Fix some $\alpha_1$ and $\alpha_2$. The utility for consumer $i$ is defined by: $$u_i(x_{1i},x_{2i}) = x_{1i} - |...
Mondayisgood's user avatar
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How to find the contract curve for a funky utility involving the min operator?

Suppose a pure exchange economy where agents’ ($A$ and $B$) preferences are given by the following utility functions: $u_A = \min(3x+y,x+3y)$ $u_B = x^\frac{1}{2} y^\frac{1}{2}$ Find the contract ...
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How to find the contract curve when both agents have linear utilities?

I'm trying to solve the following excercise: Find the contract curve for an exchange economy where agents' ($A$ and $B$) preferences and endowments are given by: $u_A = x_A + y_A$ $u_B = s x_A + y_A$ $...
Nicolas Torres's user avatar
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Pareto optimal allocations with uncountably many agents

Consider an economy with some $n$ agents with continuous utility functions $u_1,\ldots,u_n$. It is easy to prove that a Pareto-optimal allocation exists: define the welfare of an allocation $x$ as: $W(...
Erel Segal-Halevi's user avatar
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Finding the Contract Curve

I was doing a problem with the following data we have two utility functions which are as follows: $$U_1(x_1,y_1)=\beta \ln(x_1y_1) \;,\; U_2(x_2,y_2)=(\frac{x_2}{y_2})^\alpha$$ along with feasibility ...
mynameparv's user avatar
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Second welfare theorem: can it be used to show there does not exist any competitive equilibrium? (exchange economies)

The one version of the Second Welfare Theorem states that: if there exists a competitive/Walrasian equilibrium and an endowment $X$ is Pareto efficient, then there is a price vector $\hat{P}$ for ...
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Edgeworth Box (Non-Convex preference)

Consider a situation that agent A's indifference curves are concave, while B’s indifference curves are convex and both sets of indifference curves have exactly the same shape. A northeast movement ...
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Question for general equilibrium

On the production economy which have 3 good $x$, $y$, $l$ and $2$ consumers(called $1$ and $2$) and two firms(called $X$ and $Y$). Firm $1$ is owned by $1$ and produces only $x$ in function $x=2l$ and ...
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Find the set of Pareto efficient allocations

There is an exchange economy with two people and two goods. Utility functions are $u_A(x_A, y_A)=\max\{x_A, y_A\}$ $u_B(x_B, y_B)=\max\{x_B, y_B\}$ Endowments are $w_A(1,\alpha)$ and $w_B(1,\alpha)$ ...
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For each Pareto efficient allocation, suggest how we might change the endowments so that the Pareto efficient allocation is a walrasian equilibrium

I have a two-person exchange economy Each agent has the following utility $u_i(x_i,y_i)=v(x_i)+y_i$ for agent $i=\{A,B\}$ Assume that $v$ is strictly concave and increasing function that has a ...
ThePooh's user avatar
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Finding the Pareto efficient allocations

Consider a 2 person 2 good economy where there is a private good $x$ and a public good $y$. Agent 1 has an endowment of 10 units of the private good and Agent 2 has an endowment of 20 units of the ...
studentp's user avatar
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Reason behind Pareto principle

Is Mathew effect or Pareto Principle are the laws of nature like Newton law of gravitation. What are the reason behind Pareto principle?
quanity's user avatar
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I know that pareto optimal does not mean equitable, but is an equitable distribution also pareto optimal?

I am wondering if an equitable distribution is also pareto optimal in nature. I know the reverse is untrue, that a pareto optimal distribution is not necessarily a fair/equitable distribution. If you ...
user41791's user avatar
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Proving Pareto-efficiency with MRS

Given three people with the same utility function: $$ u_A(x_1,x_2)=u_B(x_1,x_2)=u_C(x_1,x_2)=\sqrt{x_1x_2} $$ Prove that the following allocation is Pareto efficient: $$ x_A=(2,2),\: x_B=(3,3),\: x_C=(...
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what is the optimal allocation for this economy

A two-person two commodity economy has social endowment of x = 1 unit of food and y = 1 unit of wine. Agents preferences are increasing in own consumption but decreasing in wine consumption of the ...
petearGriffin's user avatar
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Pareto optimal solutions

Suppose $U_1(x,y) = y - 0.5x$ and $U_2(x,y) = x - 0.5y$ where $U_i$ is the pay-off function of player $P_i$. What are all the pareto optimal solutions for $x,y \in [0,1]$? I can't think of a way to do ...
not tdm's twin's user avatar
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Preference terminologies

I am reading one paper by [Maskin et al. 1979] and cannot figure out some notations. Specially, they defined some states of nature $A$, and each player in the player set $I$ has some preferences over ...
Francis's user avatar
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Laffer curve and Pareto-efficiency

Can setting the income tax rate above the revenue-maximizing tax rate (Laffer rate) lead to a Pareto-efficient allocation?
Josh3000's user avatar
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Have there been any studies exploring whether Wikipedia editing/volunteering is Pareto efficient?

Wikipedia has often been jokingly described as an idea that "could never work in theory – only in practice." The fact that Wikipedia seemingly aggregates information so well through ...
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Do non-market gift economies tend towards Pareto optimality?

A gift economy is a system of exchange characterised by delayed exchange on the basis of the principle of reciprocity. I.e. where a market seeks to exchange goods in immediate transactions without ...
Vlad's user avatar
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Solving for the efficient subsidy amount with an externality

I am dealing with a problem that is set up as follows: Actors A and B get utility from consumption ($c_i$) and disutility from safety measures ($s_i$), however their chance of getting sick is reduced ...
BDot35's user avatar
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Researching the "invisible hand" in academic literature

The idea of the invisible hand could be expressed as: in a competitive market, agents acting selfishly in their own self interests will make choices that benefit others. There are innumerable popular ...
Mick's user avatar
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Finding the set of Pareto Optimal Allocations

I am asked to find the set of Pareto Optimal Allocations in an economy where there are two agents namely $1$ and $2$, with the following utility functions and endowments. $$u_1({x_1}^1,{x_2}^2)= \beta ...
user722271's user avatar
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Are there any economic reasons why luxury goods should not be auctioned off, or at least dynamically priced, when facing shortages?

Over the last year many prominent examples come to mind, where there does not seem to be any limiting moral or ethical reasons, and are simply not available most of the time due to demand greatly ...
M. Y. Zuo's user avatar
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How does this imply that a Pareto optimum maximizes a weighted average of utility functions?

I'm reading a passage from Asset Pricing and Portfolio Choice Theory by Kerry Back, and I don't understand some of it. I would appreciate any help anyone could provide me. In the passage, Back is ...
Ben Phronesis's user avatar
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Is it always a trade off between efficiency and equity?

Is there any situations where we can achieve both equity and efficiency? I'm thinking of Covid 19 vaccine program which is run by Goverment. Although the cost for the program is paid by the money from ...
Katie's user avatar
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Theoretical models of copyright infringement and efficiency implications

I wanted to know if there are theoretical models of copyright infringement and what are their implications for efficiency in the market and also, if possible, any empirical support they have. When I ...
Ishan Kashyap Hazarika's user avatar
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Can the theory of the second best mathematically justify labor unions in some scenarios?

An EPI page says: Some economists and policymakers might express unease at the view that the downsides of one deviation from “competitive” markets (either labor market frictions or market ...
Dolphin 613 Motorboat's user avatar
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Pareto allocations and Competitive equilibrium

Consider the one-consumer one-firm economy. The consumer has preferences over leisure $l\in(0,L)$ and consumption good $x ≥ 0$ represented by utility function $u(x, l) = ax + l$, where $a > 0$ is a ...
Maybeline Lee's user avatar
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Identical aggregation

Assume the following: all firms are identical, i.e. at each time period $t$, $\forall i$, $j: F_{t}^j = F_{t}^i = F_t$ and the technology is CRS. All consumers have the same endowment of capital $\...
Maybeline Lee's user avatar
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Uncertainty and Pareto efficient policies

There are two economic agents $i\in \{1,2\}$ with state dependent utility $u_{is}=-(x-b_{is})^2$ where $x\in R$ and $b_{is}\in R$ is bliss point of $i$ in state $s\in\{1,2\}$. Assume $b_{1s}\lt b_{2s}$...
Maybeline Lee's user avatar
3 votes
1 answer
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Efficiency in a market that is both a monopoly and a monopsony

We know that market power in general leads inefficient outcomes (in terms of Pareto efficiency). This makes instinctive appeal as, for example, a powerful seller who has a lot of market power can ...
Ishan Kashyap Hazarika's user avatar
1 vote
1 answer
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Do points inside the PPF curve always mean productive inefficiency?

If a firm produces combinations of goods along the PPF curve, it has achieved its productive efficiency. And when a firm reaches productive efficiency, it means that all factors of production have ...
Underwood's user avatar
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Pareto Improvement with Monopolies

This may be one of the more 'elementary' questions on this site.. But I really can't wrap my head around it and a search on the web hasn't yielded much. Given that Pareto efficiency is defined as when ...
shine yang's user avatar
2 votes
1 answer
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Counter example for strong and weak Pareto optimality

We know that strong Pareto efficient is equivalent to weak Pareto efficient if we have continuous and strongly monotone preferences. Please give me an example which we don’t have continuous and ...
studentp's user avatar
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Finding Pareto efficiency with negative externalities

Student S has one hobby of listening to music. The noise of the speaker can produce noise up to 100 decibels (measured by D). Her money is measured by Ms . Her utility function is Us = 10D1/2 + Ms ...
alessioriccardi's user avatar
4 votes
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Adverse Selection: Positive Selection of Worker Types (Mas-Collel)

I'm reviewing some question from Mas-Collel and I am stuck on a chapter 13 question related to adverse selection. Consider a model of positive selection in which there are workers of two possible ...
CASIOfx-991EX's user avatar
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How did Pareto came up with Pareto Distribution of wealth law?

I am not an economist but a mathematics student. I heard about the Pareto law - the mathematical modelling of the distribution of wealth, how did Pareto come up with this law? technically speaking ...
A witch's user avatar
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Pareto efficiency of organ markets

Organ sale is legal in Iran. I was wondering: are organ markets Pareto efficient? Or could an argument be made for them being Pareto efficient? I have been thinking that both the buyer and the seller ...
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