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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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11 views

A problem: allocation of apartments

Setup: Trine owns an apartment in Copenhagen. She is willing to rent it out at any positive price. Peter and Simon lives together and are both students. They will like to rent the apartment for less ...
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Efficiency conditions for externalities

I have a 2 consumer 2 goods economy. Both the goods produce an externality for the other consumer, therefore, they are a part of the other's utility function. How do I show that despite the ...
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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 ...
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Why is market equilibrium pareto efficient?

Let us assume that the current price $P$ is lower than the 'equilibrium price' $P^\star$ so that $Q$ is lower than $Q^\star$. If we move from this combination towards the equilibrium one, it may be ...
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1answer
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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
72 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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1answer
53 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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2answers
173 views

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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1answer
104 views

Utility Possibility Frontier with two consumers and 3 commodities

I am trying to solve the following problem: Consider a pure exchange economy with three commodities and two households with individual endowments: $$e_1=(1,2,3), e_2=(3,2,1),$$ respectively, and ...
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1answer
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Computing the competitive equilibrium given initial allocation

Suppose that there are two agents, 1 and 2, and two goods, honey (h) and lemon (l), and that the agents' preferences over these goods are defined by the following utility functions: $$u^1(x_h^1, x_l^...
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1answer
62 views

Walrasian Equilibrium intuition given prices and some initial allocation

Suppose we have two agents who are each assigned some initial allocation of two different goods, where the prices of each good are given. Also, suppose the utility functions for each agent are weakly ...
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1answer
48 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
135 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 $𝑈_𝑖(𝑥_𝑖)=𝑥_𝑖$, for 𝑖∈1,2, and the feasibility constraint on the amount of x ...
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1answer
548 views

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
90 views

Solution to maximization not Pareto efficient

In my economics class, we saw a proof that if an allocation $ ((\hat x_h), (\hat y_f)), h\in H$ (the set of households), $f\in F$ (the set of firms) is Pareto optimal/efficient, it must necessarily be ...
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Pareto Efficiency Outcomes in Games

I have started studying the Pareto efficiency notion in Game theory. The definition I am familiar with is this: Strategy profile $\mathbf{s}$ Pareto dominates strategy $\mathbf{s}'$ if for all $i\in\...
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Why do we have to normalize the income of consumers when working with an Edgeworth Box in a simple trade model with Pareto optima?

I was studying microeconomics and I confess I am not the brightest person for maths and sorry if this is very dumb but I get that we CAN normalize the income and I get where it comes from and how it ...
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307 views

Pareto set with Cobb-Douglas and Leontief preferences

If $U_A(x_A,y_A)=x_Ay_A$ and $U_B(x_B,y_B)=min(x_B,y_B)$ and the total endowments are (8,4), is the Pareto set given by the line joining the kinks of B (black line shown in the diagram)? Shouldn't the ...
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222 views

Pareto set and Edgeworth box

General equilibrium framework; two individuals, two goods represented in an Edgeworth box. Is it true that if the preference are both strongly monotonic the Pareto set will go from the origin of an ...
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2answers
286 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}...
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133 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?
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314 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
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How does elasticity impact market efficiency?

I am wondering how the price elasticity of demand (or supply) impacts market efficiency. A more specific question - can we say that in a monopolized market elasticity will be low, and that in a ...
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1answer
37 views

Are slacks the same as mix-inefficiency?

On the diagram below it is stated that A' has input slacks as it could reduce the amount of $x_2$ and still be on the frontier (by moving to C). However I recall mix-inefficiency having a similar ...
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2answers
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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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534 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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If US capital income taxation were eliminated, which ordinary income tax brackets would be equally progressive?

This question only considers federal taxes in the United States. Also, by "capital income" I am including dividends, interest, capital gains, corporate incomes and estates. The Chamley-Judd result ...
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Do I understand the second welfare theorem correctly?

As far as I understand, the second welfare theorem says that all Pareto-optimal allocations can be reached by market equilibrium on free competitive markets. Yet it seems that this understanding is ...
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1answer
929 views

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 are ...
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217 views

Pareto efficient adverse selection

Please look at the following. Question which I posted. I did not understand the answer for the part b - Pareto efficient. I am happy if you explain it in more details. Thank you. Also please ...
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1answer
169 views

The social welfare of a unique general competitive equilibrium in an exchange economy

The first theorem of welfare economics states that "Every Walrasian Equilibrium (WE) is Pareto Efficient (PE)" - Microeconomic Theory Nicholson, Synder 11th ed. p477. But PE is quite a weak condition. ...
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1answer
307 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
795 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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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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104 views

A question regarding definition of Pareto efficiency

It says on Wikipedia: "All the points on this locus are Pareto efficient allocations, meaning that from any one of these points there is no reallocation that could make one of the people more ...
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1answer
126 views

Find Pareto-optima two good economy

There's an exercise I cannot wrap my head on. I actually have the solution to the problem, but still I don't quite understand it. Let an economy be composed of two consumers $A$ and $B$ and two goods ...
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101 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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Exercise about social planner's optimal allocation of resources

a. There are 2 cities C1 and C2. Everyone in both the cities has same concave, increasing utility function. There's only 1 good, with the social planner. How should s/he allocate it? b. Now ...
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Is there a term for economic policy design built from minimizing per-household adverse impact?

May be easiest to start with an example: let's say I'm looking to eliminate the mortgage interest deduction, but want to minimize the impact on households from doing so. I also want the change to be ...
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How does a Pareto efficient equilibrium scale for n individuals?

Say I have a starting situation with Pareto efficient allocations between 2 individuals, now a third one comes in and changes the allocations. Now a fourth one, etc. Up untill a nth individual comes ...
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$U=xy$ for all people in a small island, What are the pareto efficient allocations? [closed]

On a certain island there are only two goods, wheat and milk.The only scarce resource is land. There are 1,000 acres of land. An acre of land will produce either 16 units of milk or 37 units of ...
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634 views

Pareto Optimality and Core

I know this is a basic question. Can I get a mathematical proof for "Any allocation in the core of an economy is also Pareto optimal." I found this statement on some PPT online.
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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
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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
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Pareto optimal and Walrasian equilibrium [closed]

There are 100 units of good 1 and good 2 in a economy. Consumer 1 and consumer 2 have 50 units of each good. Consumer 1 only wants good 1 whereas consumer 2 only wants good 2. Note: Neither of these ...
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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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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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Pareto optimality with Lagrange

I understand that you find the interior solutions for the pareto efficient set with Lagrange (Maximizing the utility with the endowment constraints and holding the other player's utility fixed) How do ...
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1answer
309 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
814 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 ...