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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8
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4answers
466 views

Fair and efficient allocation of “family goods”

Consider an exchange economy with two goods, e.g. home furniture (x) and electrical equipment (y). The interesting thing about these goods is that, when a family owns a bundle, all members of the ...
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2answers
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Lee and Saez (2012): Pareto-Improvement?

I'm interested in the following quote that came up in this earlier answer. Second, when labor supply responses are along the extensive margin only, which is the empirically relevant case, the co-...
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What is the true source of dynamic(Pareto) inefficiency in OLG models?

This question confuses me for some time. My first impression is that Pareto sub-optimality is due to feature that old generations will consume everything without any incentive to trade. But after ...
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3answers
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Quasilinear Utility: Pareto Optimality Implies Total Utility Maximization?

I read that if we have quasilinear utility for all consumers, then any pareto optimal allocation maximizes the sum of utility levels of all consumers. That is: $\textbf{What we know:}$ $$1)\quad u^i(...
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2answers
107 views

Does every allocation have a maximal Pareto-improvement?

Consider an economy with a finite number of goods and a finite quantity of each good. Each agent $i$ has a preference-relation $\succeq_i$ which is a total, reflexive and transitive relation over the ...
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2answers
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Pareto optimality with externalities

I'm reading the book "Economics of natural ressources and the environment" written by D. Pearce and R. Turner. They explain that the competitive equilibrium is not a Pareto optimum in case of (...
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2answers
12k views

Perfect complement preferences in an exchange economy

So I have an exam in a bit, I understand that to find the optimal choice you have to equate tangent of the two indifference curves. However, if the other indifference curve is a perfect complement, ...
6
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2answers
707 views

Does a General Equilibrium here require Pareto Optimality?

There are two consumers $A$ and $B$, and two producers $X$ and $Y$. he consumers are endowed with labour(L) and capital(K) $L_A,K_A$, and $L_B,K_B$ respectively. The preferences of the two consumers ...
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3answers
576 views

Is the Convex Combination of Two Pareto Optimal Allocations Also Pareto Optimal?

I am studying for my qualifiers, and I ran into this question from a previous year's exam. $\textbf{Question:}$ Consider a two-consumer two-good pure exchange economy. Both preferences are locally ...
5
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3answers
291 views

What's the opposite of a Pareto improvement called?

Wikipedia defines a Pareto Improvement, "given a certain initial allocation of goods among a set of individuals" as: a change to a different allocation that makes at least one individual or ...
5
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1answer
400 views

Converting word definitions of Pareto-Optimal into math symbols

I'd like to have a mathematical version of the following two definitions just because I remember symbols better than words. But I lack the math prowess to convert them from words to symbols. Can ...
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1answer
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Sen's Liberal Paradox

Economist and philosopher Amartya Sen posited that no social system could guarantee: A minimal sense of freedom in social choice Pareto efficiency His original article can be found here. In his ...
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1answer
70 views

Contract curve and Pareto frontier

Consider an exchange economy with two agents. Each agent $i \in \{1,2\}$ derives utility $u^i(x_1,x_2) \in \mathbb R$ by consuming $(x_1,x_2) \in \mathbb R_+^2$. Let $u_j^i(x_1,x_2) = \partial u^i(...
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955 views

Corner Solutions for Pareto Efficiency

I have been reviewing calculations to find walrasian equilibrium and pareto efficient allocations. Assume we are in an environment with two consumers, $A$ and $B$, and two goods, $x$ and $y$. From ...
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2answers
707 views

How to calculate Pareto Optimal outcome in a game with a Nash Equilibrium

I have at hand a two period game. In period 1, Union decides wage offer $w$. In period 2, firm decides on L, given wage. Union maximizes $wL$ Firm maximizes $=(L(100-L) - wL) \quad if \quad L&...
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1answer
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Definition of Pareto efficiency and prisoner's dilemma

Pareto efficiency is defined in Wikipedia as: Pareto efficiency or Pareto optimality is a state of allocation of resources from which it is impossible to reallocate so as to make any one ...
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1answer
980 views

Why do externalities lead to a Pareto-inefficient outcome?

So we know that under a Pareto-inefficient outcome, there is room for Pareto improvement, i.e. making someone better off without hurting anyone. Assume that there is a drug company which is in ...
3
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1answer
183 views

Blocking Coalitions

For $n$ individuals, can a blocking coalition only be formed by at least $n/2$ individuals? For example, if there are 6 individuals, can less than 3 individuals form blocking coalitions?
3
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1answer
145 views

Have there been any attempts to turn free-trade agreements into Pareto improvements?

The textbook economic case for free trade agreements is that they constitute a Kaldor-Hicks improvement, which that in any given country the winners win more than the losers lose, when the benefits ...
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1answer
6k views

How to find corner Pareto efficient allocations

I have some troubles in understanding how to find Pareto efficient allocation that are on the frontier of the Edgeworth box. I mean, the interior ones, can be found using the equality $MRS_A = MRS_B$, ...
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1answer
552 views

Writing the core as the intersection of pareto efficient outcomes of all coalitions

I have been reviewing general equilibrium models and was trying to find an efficient method for computing the core of a cooperative game. I was taught this topic in a very poor way so I believe I ...
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2answers
614 views

Pareto optimality and Externalities

Let's consider 5 farmers, each of them has 2 cows to put into the field. So every farmers can put 0,1 or 2 cows. I denote the three stategies by $q_i$, i=0,1,2. Now, the payoffs ( i.e. the amout of ...
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3answers
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Does Pareto-efficency take into account growth?

I'll try to state my question clearly:   For a given a "wealth" allocation Wt = (w1, w2, w3, ... ) for individuals I = (i1, i2, i3, ... ). And a distribution of D= (w1/|W|, w2/|W|, w3/|W|, ... ...
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341 views

Calculating price in a pure exchange economy

The problem is simple, I'm not really sure of my answer though. Consider an economy where there are two consumers and two goods: $$U_1(x_{11}, x_{21}) = x_{11}$$ $$U_2(x_{12}, x_{22}) = x_{22}$$ $...
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2answers
139 views

How can an outcome be Pareto efficient but not Kaldor-Hicks efficient?

An policy is a Pareto improvement if it makes some people better off and no one worse off. And a policy is a Kaldor-Hicks improvement if it can be turned into a Pareto improvement by redistributing ...
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1answer
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Are there any real world examples of potential Pareto improvements?

Professor George Fallis in his book "Housing Economics" writes when discussing the notion of a Pareto improvement (Page 123) In the real world, almost all policies recommended by economists ...
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1answer
413 views

Bertrand-equilibrium with discrete price set

Consider a market for a homogenous product with three producers, firms A, B and C. The firms have constant marginal costs which are equal to $c = 20$ for each firm. Consumers always buy from the firrm ...
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1answer
313 views

Finding Pareto Optimality

Consider an exchange economy with two individuals and 2 commodities. The endowments of the commodities are 1 each. Which one of the following are Pareto Optimum. a. {$\frac{1}{2},\frac{1}{2},(\frac{1}...
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1answer
295 views

Difference between Nash equilibrium and Pareto Efficiency

Nash Equilibrium is defined as a solution concept referring to a best outcome which players won't want to unilaterally deviate given the response of other players doesn't change. To me it seems like ...
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2answers
261 views

Inclusion of firms on the efficient frontier of a Production Possibility Set

I'm working through Cooper's Data Envelopment Analysis, and they are going over Production Possibility Sets. They present 9 firms, each with two inputs and one output: Graphically it easy to see why ...
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1answer
1k views

equilibrium, optimum, and decentralizing the optimum

I'm reading a paper on parking: Anderson & de Palma, 2003, The economics of pricing parking. The authors repeatedly refer to either 'decentralizing the optimum' or 'the optimum can be ...
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1answer
74 views

What is the difference between a power law exponent and the Pareto exponent?

I use the poweRlaw package in R to fit a power law to my data. I am trying to figure out what is the value of the Pareto exponent. Assume the probability mass function is defined by: $$ p(x) = \...
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1answer
152 views

Understanding Pareto Optimal

I am looking at an exchange economy where I have two types of goods and n consumers. Half of the consumers have a utility function given by $U(x)= 5\ln{x} +m $ and the other half of the consumers have ...
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1answer
2k views

Market equilibrium and pareto efficiency

How can I prove that the equilibrum point $D(p)=S(p)$ is pareto efficient? The definition of pareto efficient: there is no way to make any person better off without hurting anybody else $D(p)$ is ...
2
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1answer
240 views

Productive Allocative Efficiency (Competitive Equilibrium)

I am doing an Intermediate Microeconomics class... in a 2*2*2*2 economy, I know that MRS (marginal rate of substitution) is supposed to be equal to MRTS (marginal rate of technical substitution) in ...
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1answer
72 views

Is a lack of any barriers to entry a necessary condition for ensuring pareto optimality is reached?

I understand that a competitive market is necessary for a market to equilibriate to a pareto optimal state, and that things like economies of scale, network effects, government restrictions, and ...
2
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1answer
576 views

Under what conditions does market failure occur?

Edit: Is it possible to broadly categorize the ways in which market failures occur into relatively few categories? If so, what are they?
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1answer
251 views

Constraints on a symmetric pareto allocation under uncertainty

I've been trying to figure out how the author came up with the constraints for this liquidity model in a textbook I'm reading. details: http://imgur.com/TpVjg4w $U = \pi_1u(C_1) + \pi_2u(C_2)$ where ...
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0answers
730 views

An economy with no Pareto-efficient envy-free allocations

In a famous paper from 1974, Hal Varian proved (in Theorem 2.3) that: In an economy with homogeneous divisible googs, if all agents have monotonic and convex preferences, then there exists an ...
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3answers
2k views

Two quasilinear utility functions

Suppose there are two agents $\{A,B\}$ with the following utility functions: $U_A(x_A,y_A)=x_A+f(y_A)$ and $U_B(x_B,y_B)=x_B+g(y_B)$ $f$ and $g$ are strictly increasing and strictly concave. How do I ...
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2answers
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How do we find pareto optimal points in a 2 goods simple exhange economy? [closed]

Suppose there are 2 individuals in a simple exchange economy with utilities $U_{1}= ax_{1} + x_{2}$ and $U_{2}= y_{1}y_{2}$. Endowments are $(x_{1},x_{2})=(4,0)$ and $(y_{1},y_{2})=(1,5)$. We are ...
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1answer
79 views

Pareto Efficient level of Public Good

As part of self study towards an entrance exam, I am solving the following question. There are two consumers in the economy and two goods, one private and one public. The utilities of the consumers ...
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1answer
979 views

Is the convexity of production sets necessary for the welfare theorems?

I have read that the convexity of production sets (for instance non-increasing returns to scale) is not a necessary assumption for the first welfare theorem but it is for the second welfare theorem. ...
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1answer
114 views

Can one prove Pareto efficiency in an n-party system by showing all Pareto improvements between any two given parties are made?

I've made a proof of Pareto efficiency of a funding system that I've developed. There are effectively four types of actors. I've shown all Pareto improvements are made between any two given parties ...
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1answer
457 views

Why is Pareto efficiency not always equitable or equilibrium?

Just for information. I think we can agree on that a Pareto optimal allocation is where you cannot put someone in a better position without making someone else worse off. I know that any competitive ...
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1answer
318 views

Finding the Pareto optimal set with preferences for 3 individuals

Question: Let $N=\{1,2,3\}$ be a set of three people and $X=\{a,b,c,d\}$ a set of 4 political parties. The individuals have the following preferences: Individual 1: $a \succ_1 b \sim_1 c \succ_1 d$ ...
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1answer
782 views

Question on Pareto optimality problem

In an economy with two agents whose utility functions are $$ U_A(x_1,x_2) = \alpha \cdot x_1 + x_2 \hskip 20pt U_B(y_1,y_2) = y_1 \cdot y_2. $$ The given allocations are bundle (4,0) for A and bundle ...
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1answer
74 views

SPNE and Pareto Optimality

"The SPNE of a sequential game might not necessarily be Pareto Optimal" I understand the definitons of Nash Equilibria and Pareto Optimality and that these are not synonymous concepts. An example in ...
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1answer
242 views

Solving for Pareto Efficient Utility Possibility Frontier using constrained optimisation

The economy is a one-good two individual endowment economy in which individual $i’s$ preferences are given by $π‘ˆ_𝑖(π‘₯_𝑖)=π‘₯_𝑖$, for π‘–βˆˆ1,2, and the feasibility constraint on the amount of x ...
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2answers
472 views

Pareto Optimality of Endowments

Consider a $2*2$ exchange economy where individual $1$ has an endowment $(4,5)$ and individual 2 has an endowment $(6,5)$. The utility functions of individuals are represented by $U({x}_i{y}_i)$=${x}...