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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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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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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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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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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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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228 views

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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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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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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51 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 ...
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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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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 ...
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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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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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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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247 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 ...
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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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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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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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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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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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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 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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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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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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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 ...
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Sen's Liberal Paradox

Economist and philosopher Amartya Sen posited that no social system could guarantee: A minimal sense of freedom in social choice Pareto efficiency His original article can be found here. In his ...
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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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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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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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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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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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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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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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Fair and efficient allocation of “family goods”

Consider an exchange economy with two goods, e.g. home furniture (x) and electrical equipment (y). The interesting thing about these goods is that, when a family owns a bundle, all members of the ...
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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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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 ...