Flashcards in Lecture 3- Pareto efficiency and welfare theorems In Pure Exchange Economies Deck (10)

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1

## What are the 4 different definitions of Pareto efficiency?

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1. You cannot make someone strictly better off without making someone else strictly worse off.

2. Set of allocations that satisfy market clearing condition. This means you can compute this on a Edgeworth box and for every good the amount demanded= the amount supplied.

3. Within a set, for any alternative feasible allocation if somebody is strictly better off under the alternative then somebody else must be strictly worse off.

4. Pareto dominate allocation. For X to be a pareto efficient allocation it must be that there is no other allocation of resource that makes everybody else weakly better off and at least one person strictly better off.

2

## What are the 2 problems associated with Pareto efficiency?

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1. Doesn't put any relevance into the strength of preferences e.g if one person strongly prefers A>B it will not take this into account.

2. Doesn't consider the notion of fairness. For example for person A and person B it is pareto efficient for A to get everything and B to get nothing.

3

## How do you find the Pareto set?

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- Find Ub or Ua in terms of the other e.g Ub1=10-Xa1 and Ub2=10-Xa2

- Then plug this into the Utility function e.g plug in Ub1 and Ub2 into the utility function in terms of A

- Set up Langrangian e.g (10-XA1)^B (10-XA2)^1-B + Lamna(XA1^Alpha XA2^1-Alpha-K) K is the constraint on the max utility of A

- Take FOC'S, and equal 1 and 2, and then divide the equation gives you all the interior points in the edgeworth box that are Pareto efficient.

4

## What is an alternative method for finding the Pareto set?

### MRS A(1 AND 2)=MRS B(1 AND 2)

5

## When finding all the Pareto sets what must you always remember

### The corner solutions

6

## Draw an edgeworth box and find the Pareto set for cases where: a>B and B>a

### See notes

7

## What is the contract curve, and how would you represent it on a edgeworth box?

### The contract curve is a set of points that Pareto dominate the initial endowment.

8

## Explain what local non satiation is?

### For any bundle of goods there is always a bundle goods arbitrarily close that is preferred to it

9

## What is the first fundamental theorem of welfare economics, and what assumptions are needed?

### If markets are complete and everyone's preferences are locally non satiated then any walrasian equilibrium is Pareto optimal

10