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4 votes

Has mathematical economics contributed to the mathematics of space exploration?

In the history of dynamic programming some economic works are considered pioneering contributions to the theory of dynamic programming (and in this sense it can be said that they contributed to ...
BakerStreet's user avatar
  • 3,802
4 votes
Accepted

Approximate Pareto efficiency with ordinal preferences

Consider a game: Set of Players $= \{1,2\}$ Action Sets of the players: $\triangle_1\subseteq\mathbb{R}^n$ and $\triangle_2\subseteq\mathbb{R}^m$. For Eg: In case of Prisoner's Dilemma, $\triangle_1=\...
Amit's user avatar
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4 votes

Core in a replicated economy

In the economy provided in the question, competitive equilibrium allocations is equal to the set of efficient allocations. This along with the fact that the competitive equilibrium allocations always ...
Amit's user avatar
  • 8,811
3 votes
Accepted

When is local Pareto-efficiency equivalent to global Pareto-efficiency?

Yes. The proof is virtually the same. Let $x^*\in X$ be a Pareto dominated state. There must be some $x\in X$ such that $u_i(x)>u_i(x^*)$ for some agent $i$ and $u_j(x)\geq u_j(x^*)$ for every ...
Michael Greinecker's user avatar
3 votes

Finding Pareto efficiency with negative externalities

Set of Pareto efficient allocations is given by the following set: $\mathcal{P}=\{(m_s, m_f, d)\in\mathbb{R}^3_+|(d=50)\ \vee \ (0\leq d \leq 50 \ \wedge \ m_s=0) \ \vee \ (50\leq d \leq 100 \ \wedge \...
Amit's user avatar
  • 8,811
2 votes

Finding the set of Pareto Optimal Allocations

Interpretation 1: Given the data in the problem, I think you're interested in a pure-exchange economy with externalities i.e., $u_1(x_1,y_2) = x_1^\beta y_2^{1-\beta}$, $u_2(x_2,y_2) = \min(x_2,y_2)$,...
Amit's user avatar
  • 8,811
2 votes

Are the marginal conditions for Pareto optimality sufficient?

These are all conditions that cover local deviations. Without further assumptions, usually ones involving convexity & closedness of sets and/or concavity & continouity of functions they are ...
Giskard's user avatar
  • 29.2k
2 votes
Accepted

Lump sum transfers to implement any Pareto efficient equilibrium as the market outcome

Here is the Edgeworth box of your exercise: The green dot with the curves running through it is your equilibrium allocation. The red and blue lines are indifference curves of $A$ and $B$, while the ...
Giskard's user avatar
  • 29.2k
2 votes
Accepted

Can we define the core as the intersection of Pareto efficient allocations and upper-contour sets?

Assume there are three individuals $A, B, C$ and three goods $x, y, z$. Endowment for $A$ is $(1,0,0)$ for $B$ is $(0,1,0)$ and for $C$ is $(0,0,1)$. Assume the utility function for the individuals ...
tdm's user avatar
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2 votes
Accepted

Find the set of Pareto efficient allocations. $U_1 = -|x_1-2|$ and $U_2 = −|x_2 − 8|$

To answer your question, you can't use the Edgeworth box in this kind of setup because it is used for an economy where we have two goods and two agents. However, there exists an alternative graphical ...
mynameparv's user avatar
2 votes

Are ALL externalities inefficient?

Pareto efficiency and inefficiency, as Michael Greinecker comments, are properties of allocations of resources. An allocation is efficient if there is no alternative allocation which makes someone ...
Adam Bailey's user avatar
  • 8,519
1 vote

What precisely is bad about externalities?

In particular, why are externalities bad? This is a non-economics question. Economics cannot say if something can be good or bad. For that you need moral philosophy. For example, if some economic ...
1muflon1's user avatar
  • 56.8k
1 vote

Are ALL externalities inefficient?

There might be a bit of a misunderstanding. It is not the existence of the externality as such that is Pareto inefficient, but rather the level of the externality which is usual Pareto inefficient. ...
tdm's user avatar
  • 12.2k
1 vote

Social Welfare Function (Pareto Efficiency)

Pareto efficient compensation criterion is a criterion that allocates compensation such that it is impossible to reallocate resources such that one person can be made better off without making at ...
WilliamT's user avatar
  • 1,819
1 vote

Information asymmetry and market failure

It’s little bit more nuanced. Market failure in economics is rigorously defined as a situation where markets are not allocatively efficient (see Ledyard 2017). That is, technically speaking, market ...
1muflon1's user avatar
  • 56.8k
1 vote

Under what conditions does market failure occur?

I just wrote about this very thing. There are many misconceptions and incorrect information floating around about market failure. The 3 types of market failures I identify are: Externalities Anti-...
Governology's user avatar

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