# Tag Info

• 1,553

### 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
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 ...
• 231

### 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 ...
• 571
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 ...
• 26k
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

### 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

### 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
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
Accepted

### 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

### 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 ...
• 9,330
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
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 ...
• 4,694

### 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
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 ...
• 9,330

### 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

### 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

### 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 ...
• 186
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 ...
• 41.5k
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 ...
• 41.5k
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 \$...