7
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Is the Convex Combination of Two Pareto Optimal Allocations Also Pareto Optimal?
To complement densep's answer, here is a schematic Edgeworth box illustration of what can go wrong. The points on the dashed line are convex combinations of the Pareto optimal points $(x_1,x_2)$ and $(...
- 16.6k
6
votes
Accepted
Lee and Saez (2012): Pareto-Improvement?
(Note that this answer implicitly makes reference to the specific model in Lee and Saez.)
Short answer: the increased taxes on high-skilled workers exactly offset the higher real wages they obtain ...
- 3,682
6
votes
What is the true source of dynamic(Pareto) inefficiency in OLG models?
Shell 1971 argues (in a ten page paper, so read it!) that the dynamic inefficiency stems from the double infinity of traders and goods, and not the dynamics. This allows us to do the Hilbert hotel ...
- 164
6
votes
Accepted
What's the opposite of a Pareto improvement called?
I usually use the phrase "Pareto worsening". It is not really widespread, in fact I am not sure I have ever heard anyone else use it. However now I googled it and people seem to use it in connection ...
- 26k
6
votes
Accepted
Can the theory of the second best mathematically justify labor unions in some scenarios?
Quoting your quote, emphasis altered by me:
The “theory of the second best” clearly argues that once markets depart at all from perfect competition, efficiency may well be increased by further ...
- 26k
5
votes
Does a General Equilibrium here require Pareto Optimality?
Competitive equilibrium is the price vector $(p_x, p_y, w =1, r)$ such that it solves the following system of equations:
Demand for $X$ = Supply of $X$
Demand for $Y$ = Supply of $Y$
Demand for $L$ =...
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5
votes
Lee and Saez (2012): Pareto-Improvement?
The reason is that at the same time the wage of the high-skilled increases.
By reducing the minimum wage, the number of people working in the low-skilled sector increases (involuntary unemployment ...
- 5,157
5
votes
Accepted
Converting word definitions of Pareto-Optimal into math symbols
Let $\Omega$ be the set of all feasible allocations with an element $\omega \in \Omega$. Consider $I$ agents such that the utility of agent $i$ is described by $u_i(\omega)$.
Definition 1: $\omega \...
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5
votes
Perfect complement preferences in an exchange economy
Set of Pareto Efficient Allocations consists of feasible allocations $((x_J, y_J), (x_D, y_D))$ satisfying $y_J=\displaystyle\frac{x_J}{2}$.
Competitive Equilibrium is the price $(p_x, p_y=1)$ ...
- 4,417
5
votes
Accepted
Pareto optimality with externalities
I feel like I do not understand the exact meaning behind the notion of
the Pareto optimality.
It's not you. There are different senses of the phrase "Pareto Optimal," and you have to figure out ...
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5
votes
Pareto Optimality and Core
An allocation is defined as being a part of the "core" of an economy if there's no coalition of people that blocks the allocation. A coalition will block an allocation if all of its members could be ...
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5
votes
Accepted
Does every allocation have a maximal Pareto-improvement?
I think there is a short proof if you also assume that the number of agents $n$ is finite and that the preferences are continuous.
Given the second assumption Debreu's theorem (1954, "Representation ...
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5
votes
Accepted
Definition of Pareto efficiency and prisoner's dilemma
(A, B) and (B, A) are in fact Pareto efficient.
I believe that your confusion may be because when discussing the Pareto inefficiency of the Prisoner's dilemma equilibrium, we always discuss (B,B) as ...
- 5,394
5
votes
Adverse Selection: Positive Selection of Worker Types (Mas-Collel)
In PO, you want all types with opportunity cost $r(\theta)\leq \theta$ to trade, because the firm gets more productivity than the worker has to give up on home productivity ("opportunity cost&...
- 5,090
4
votes
Two quasilinear utility functions
The statement is not true.
Let $x_A + x_B = 1$, $y_A + y_B = 1$.
Let $U_A(x_A,y_A) = x_A + \ln(y_A)$, $U_B(x_B,y_B) = x_B + \ln(y_B + 1)$.
$f \neq g$ are both strictly increasing & concave. For ...
- 26k
4
votes
Accepted
Finding Pareto Optimality
To be a Pareto optimum, there must not exist another feasible allocation that makes every agent at least as well off and one or more agents strictly better off.
So, let us consider the options here. ...
- 2,871
4
votes
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In modern economics, what are the least restrictive conditions shown to theoretically achieve Pareto Efficiency?
Well, when considering the minimal conditions necessary for an allocation to be Pareto optimal we must go to the primitives. First, we need the fact that all agents have rational preferences. What ...
- 1,548
4
votes
What is the true source of dynamic(Pareto) inefficiency in OLG models?
There is an unpublished 1982 working paper by Donald Brown and John Geanakoplos, called “Understanding Overlapping Generations Economies as a Lack of Market Clearing at Infinity” (a scan used to be ...
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4
votes
Accepted
Is the Convex Combination of Two Pareto Optimal Allocations Also Pareto Optimal?
Here
$$\not\exists\;x_i^\star\; s.t.\; u_i(\alpha x_i)\geq u_i(\alpha x_i^\star)\;\forall i\;\text{and}\;u_i((1-\alpha)\hat{x}_i)\geq u_i((1-\alpha)x_i^\star)$$
$$\implies\not\exists\;x_i^\star\;s.t.\...
- 26k
4
votes
Accepted
Why do externalities lead to a Pareto-inefficient outcome?
If you allow side payments then the issue you identify goes away in a Coase sense.
The citizens being polluted could pay for production to be reduced by one unit. This amount would have to be ...
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4
votes
How do we find pareto optimal points in a 2 goods simple exhange economy?
The following plot has the answer to your question, observe it carefully:
- 4,417
4
votes
Accepted
Is the convexity of production sets necessary for the welfare theorems?
Convexity of the production set is indeed not needed for the proof of the first welfare theorem but for the proof of the second welfare theorem. It is not a necessary condition though.
It is ...
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4
votes
Bertrand-equilibrium with discrete price set
The key is the definition of the Nash equilibrium solution concept that you are applying to solve your game. In non-formal terms, a Nash equilibrium is a set of strategies such that no player can ...
- 16.6k
4
votes
How to calculate Pareto Optimal outcome in a game with a Nash Equilibrium
For Pareto optimality, you can ignore the timing. Also, anything you know about Nash equilibria in this game is irrelevant.
Let $v_F(w, L)$ be the payoff of the firm and $v_U(w, L)$ be the payoff of ...
- 9,330
4
votes
What's the opposite of a Pareto improvement called?
The strict logic opposite of course is simply any change where at least one person is worse off but not sure we need a name for that. The conceptual opposite to Pareto improvement can as you say be a ...
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4
votes
Accepted
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?
A short answer is that in case of provision of public goods in real-life we can never be completely sure if they are provided in optimal quantity due sheer difficulty of quantifying all costs and ...
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4
votes
Accepted
How did Pareto came up with Pareto Distribution of wealth law?
The Pareto distribution was derived based on the observation of Vilfredo Pareto that in Italy $80\%$ share of land belonged to $20\%$ of the country’s population, and he showed this held for many ...
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3
votes
Quasilinear Utility: Pareto Optimality Implies Total Utility Maximization?
I don't think it is true in a standard pure exchange economy the question is referring to. Consider the following counterexample:
Suppose
$I = \{1,2\}$ and $u_1(x_1, m_1) = \sqrt{x_1} + m_1$ and $...
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