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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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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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### 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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### 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 when the allocations are restricted

This question is about Pareto optimality (PO) in cake-cutting. The basic definition is: an allocation is PO if there does not exist another allocation in which all players are weakly better off and ...
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### In modern economics, what are the least restrictive conditions shown to theoretically achieve Pareto Efficiency?

In researching this question, I've come across plenty of sources that regurgitate intro econ textbooks that say markets equilibrate to Pareto efficiency in conditions of perfect competition (where ...
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### 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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### 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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### 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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### 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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### 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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### Competitive equilibrium in an exchange economy with lexicographic preferences [closed]

I am really stuck with this problem and not able to approach it. Any help will be much appreciated. I tried to draw edgeworth box with initial endowment point. I do know that for competitive ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### Kaldor-Hicks optimum allocation with externality

Suppose there are two individuals. Level of good h can be determined only by individual 1 and it has a positive externality on individual 2. To find Pareto efficient allocation, we add the utilities ...
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### 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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### 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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### 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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### 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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### 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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### How does Joseph Stiglitz and Greenwald explain why markets with imperfect information fail to have a pareto efficient equilibrium?

How does Joseph Stiglitz and Greenwald explain why markets with imperfect information fail to have a pareto efficient equilibrium? What premises do they use to come to that conclusion? For example, ...
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^...