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.

Filter by
Sorted by
Tagged with
1
vote
2answers
143 views

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 ...
1
vote
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 ...
1
vote
1answer
1k 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. ...
1
vote
1answer
879 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.
1
vote
2answers
2k views

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 ...
1
vote
1answer
196 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 ...
1
vote
1answer
587 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 ...
1
vote
1answer
50 views

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 ...
1
vote
1answer
246 views

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 ...
1
vote
1answer
257 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 ...
1
vote
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 ...
1
vote
1answer
319 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: $a \succ_1 b \sim_1 c \succ_1 d$ ...
1
vote
1answer
805 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 ...
1
vote
1answer
128 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 ...
1
vote
1answer
341 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 ...
1
vote
2answers
712 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}...
1
vote
1answer
298 views

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 ...
1
vote
1answer
286 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 ...
1
vote
1answer
139 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 ...
1
vote
1answer
103 views

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 ...
1
vote
0answers
17 views

Price equilibria with transfers

I am pretty new to Microeconomics so please bear with me if I am missing something obvious. I am solving the following problem: The question is in the setting of pure exchange economy with two ...
1
vote
0answers
13 views

Identify the Pareto welfare weights

I am asked to identify the Pareto welfare weights from the FOC of the following problem $max_{{x_1}{x_2}} U_1(x_1)\ st\ u_2=U_2(x_2)\ and\ x_{1n}+x_{2n}=yn$ The Langrangian is: $L=U_1(x_1)+\lambda_1(...
1
vote
0answers
51 views

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 ...
1
vote
0answers
131 views

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\...
1
vote
0answers
429 views

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 assume ...
1
vote
0answers
14 views

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 ...
1
vote
0answers
430 views

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 ...
1
vote
0answers
252 views

About Lindahl equilibrium and Pareto Optimality

Let an economy with 20 consumers, one private good $x_2$ and one public good $x_1$. The public good is produced using the private good as input with the following technology $x_1=g(z)=z^{1/2}$, where $...
0
votes
2answers
167 views

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 ...
0
votes
2answers
682 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 ...
0
votes
1answer
317 views

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 ...
0
votes
1answer
101 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 ...
0
votes
1answer
2k views

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 ...
0
votes
1answer
1k views

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 ...
0
votes
1answer
47 views

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 ...
0
votes
1answer
36 views

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 ...
0
votes
1answer
31 views

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) ...
0
votes
1answer
115 views

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 ...
0
votes
2answers
243 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 ...
0
votes
1answer
132 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 ...
0
votes
1answer
47 views

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 ...
0
votes
1answer
45 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 ...
0
votes
1answer
188 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. ...
0
votes
1answer
119 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 ...
0
votes
0answers
30 views

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 ...
0
votes
0answers
27 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 ...
0
votes
1answer
347 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 ...
0
votes
0answers
33 views

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 ...
0
votes
0answers
73 views

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 ...
0
votes
1answer
100 views

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 ...