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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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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1answer
43 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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2answers
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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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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 ...
0
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1answer
73 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 ...
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3answers
107 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 ...
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1answer
43 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 ...
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1answer
63 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:
$$
p(x) = \...
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1answer
147 views
Difference between Nash equilibrium and Pareto Efficiency
Nash Equilibrium is defined as a solution concept referring to a best outcome which players won't want to unilaterally deviate given the response of other players doesn't change. To me it seems like ...
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1answer
56 views
Pareto Efficient level of Public Good
As part of self study towards an entrance exam, I am solving the following question.
There are two consumers in the economy and two goods, one private and one public. The utilities of the consumers ...
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2answers
184 views
robinson economy with production
Facing a little bit of a problem with this questions, did a similar one BUT the utility function was not linear and got MRS dependent on goods (was not just a number) - here I am at a loss.
The ...
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1answer
120 views
Utility Possibility Frontier with two consumers and 3 commodities
I am trying to solve the following problem:
Consider a pure exchange economy with three commodities and two households with individual endowments:
$$e_1=(1,2,3), e_2=(3,2,1),$$
respectively, and ...
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1answer
59 views
Computing the competitive equilibrium given initial allocation
Suppose that there are two agents, 1 and 2, and two goods, honey (h) and lemon (l), and that the agents' preferences over these goods are defined by the following utility functions:
$$u^1(x_h^1, x_l^...
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1answer
67 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
57 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
182 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
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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
95 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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0answers
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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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1answer
38 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 ...
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2answers
400 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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1answer
249 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
359 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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1answer
163 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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1answer
350 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
78 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 ...
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1answer
40 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
238 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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2answers
606 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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0answers
31 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 ...
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59 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 ...
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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 are ...
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1answer
229 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
171 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
356 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
859 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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2answers
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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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1answer
111 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
127 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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1answer
112 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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413 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 ...
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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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1answer
91 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 ...
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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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1answer
712 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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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
134 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
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 ...
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1answer
150 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 ...
