# 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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### If the government builds a bridge, how do we know it's the best possible usage of real resources (i.e. steel, labor, etc) at the time?

I would assume the "goal" of any economic activity is to make the largest amount of people the "happiest" -- i.e. Pareto Efficiency or sum-total 'utility.' How do we know if this ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### Pareto efficiency and maximization of sum of utilities

I'm trying to understand the relation between maximizing sum of utilities and finding Pareto efficient allocations. According to https://econ.ucsb.edu/~tedb/Courses/UCSBpf/pflectures/chap2.pdf (page ...
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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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### 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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### 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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### 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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### 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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### 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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### Pareto Set with strictly convex preferences

Suppose the agents A and B have the following utility functions $x_A y_A+12x_A+3y_A$ and $x_By_B +8x_B+9y_B$ respectively with endowments (8,30) and (10,10). The contract curve's equation turns out ...
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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 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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### 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 ...
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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 ...
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### Efficiency in Auctions

Consider a finite number of bidders, each bidding for a single indivisible object, with private independent values from some probability distribution. There are 2 intuitive notions of (ex-post) ...
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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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### 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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### 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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### Pareto efficiency analysis of level of M1 growth from quantitative easing

BMO recently conducted an analysis on US monetary policy and noted that quantitative easing has had diminishing effects on M1 growth. Daniel Krieter wrote: QE has fed through to the real economy in a ...
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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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### 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 ...