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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Proving Pareto-efficiency with MRS

Given three people with the same utility function: $$ u_A(x_1,x_2)=u_B(x_1,x_2)=u_C(x_1,x_2)=\sqrt{x_1x_2} $$ Prove that the following allocation is Pareto efficient: $$ x_A=(2,2),\: x_B=(3,3),\: x_C=(...
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what is the optimal allocation for this economy

A two-person two commodity economy has social endowment of x = 1 unit of food and y = 1 unit of wine. Agents preferences are increasing in own consumption but decreasing in wine consumption of the ...
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Pareto optimal solutions

Suppose $U_1(x,y) = y - 0.5x$ and $U_2(x,y) = x - 0.5y$ where $U_i$ is the pay-off function of player $P_i$. What are all the pareto optimal solutions for $x,y \in [0,1]$? I can't think of a way to do ...
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Preference terminologies

I am reading one paper by [Maskin et al. 1979] and cannot figure out some notations. Specially, they defined some states of nature $A$, and each player in the player set $I$ has some preferences over ...
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Laffer curve and Pareto-efficiency

Can setting the income tax rate above the revenue-maximizing tax rate (Laffer rate) lead to a Pareto-efficient allocation?
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Have there been any studies exploring whether Wikipedia editing/volunteering is Pareto efficient?

Wikipedia has often been jokingly described as an idea that "could never work in theory – only in practice." The fact that Wikipedia seemingly aggregates information so well through ...
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Do non-market gift economies tend towards Pareto optimality?

A gift economy is a system of exchange characterised by delayed exchange on the basis of the principle of reciprocity. I.e. where a market seeks to exchange goods in immediate transactions without ...
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Solving for the efficient subsidy amount with an externality

I am dealing with a problem that is set up as follows: Actors A and B get utility from consumption ($c_i$) and disutility from safety measures ($s_i$), however their chance of getting sick is reduced ...
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Researching the "invisible hand" in academic literature

The idea of the invisible hand could be expressed as: in a competitive market, agents acting selfishly in their own self interests will make choices that benefit others. There are innumerable popular ...
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Finding the set of Pareto Optimal Allocations

I am asked to find the set of Pareto Optimal Allocations in an economy where there are two agents namely $1$ and $2$, with the following utility functions and endowments. $$u_1({x_1}^1,{x_2}^2)= \beta ...
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Are there any economic reasons why luxury goods should not be auctioned off, or at least dynamically priced, when facing shortages?

Over the last year many prominent examples come to mind, where there does not seem to be any limiting moral or ethical reasons, and are simply not available most of the time due to demand greatly ...
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How does this imply that a Pareto optimum maximizes a weighted average of utility functions?

I'm reading a passage from Asset Pricing and Portfolio Choice Theory by Kerry Back, and I don't understand some of it. I would appreciate any help anyone could provide me. In the passage, Back is ...
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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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Theoretical models of copyright infringement and efficiency implications

I wanted to know if there are theoretical models of copyright infringement and what are their implications for efficiency in the market and also, if possible, any empirical support they have. When I ...
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Can the theory of the second best mathematically justify labor unions in some scenarios?

An EPI page says: Some economists and policymakers might express unease at the view that the downsides of one deviation from “competitive” markets (either labor market frictions or market ...
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Pareto allocations and Competitive equilibrium

Consider the one-consumer one-firm economy. The consumer has preferences over leisure $l\in(0,L)$ and consumption good $x ≥ 0$ represented by utility function $u(x, l) = ax + l$, where $a > 0$ is a ...
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Identical aggregation

Assume the following: all firms are identical, i.e. at each time period $t$, $\forall i$, $j: F_{t}^j = F_{t}^i = F_t$ and the technology is CRS. All consumers have the same endowment of capital $\...
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Uncertainty and Pareto efficient policies

There are two economic agents $i\in \{1,2\}$ with state dependent utility $u_{is}=-(x-b_{is})^2$ where $x\in R$ and $b_{is}\in R$ is bliss point of $i$ in state $s\in\{1,2\}$. Assume $b_{1s}\lt b_{2s}$...
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Efficiency in a market that is both a monopoly and a monopsony

We know that market power in general leads inefficient outcomes (in terms of Pareto efficiency). This makes instinctive appeal as, for example, a powerful seller who has a lot of market power can ...
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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 Improvement with Monopolies

This may be one of the more 'elementary' questions on this site.. But I really can't wrap my head around it and a search on the web hasn't yielded much. Given that Pareto efficiency is defined as when ...
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Counter example for strong and weak Pareto optimality

We know that strong Pareto efficient is equivalent to weak Pareto efficient if we have continuous and strongly monotone preferences. Please give me an example which we don’t have continuous and ...
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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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Adverse Selection: Positive Selection of Worker Types (Mas-Collel)

I'm reviewing some question from Mas-Collel and I am stuck on a chapter 13 question related to adverse selection. Consider a model of positive selection in which there are workers of two possible ...
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How did Pareto came up with Pareto Distribution of wealth law?

I am not an economist but a mathematics student. I heard about the Pareto law - the mathematical modelling of the distribution of wealth, how did Pareto come up with this law? technically speaking ...
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Pareto efficiency of organ markets

Organ sale is legal in Iran. I was wondering: are organ markets Pareto efficient? Or could an argument be made for them being Pareto efficient? I have been thinking that both the buyer and the seller ...
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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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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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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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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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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(...
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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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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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3 votes
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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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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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3 answers
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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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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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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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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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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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2 votes
1 answer
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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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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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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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1 answer
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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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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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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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