Lecture 3- Pareto efficiency and welfare theorems In Pure Exchange Economies

Question 1

What are the 4 different definitions of Pareto efficiency?

Answer 1

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.

Question 2

What are the 2 problems associated with Pareto efficiency?

Answer 2

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.

Question 3

How do you find the Pareto set?

Answer 3

• 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.

Question 4

What is an alternative method for finding the Pareto set?

Answer 4

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

Question 5

When finding all the Pareto sets what must you always remember

Answer 5

The corner solutions

Question 6

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

Answer 6

See notes

Question 7

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

Answer 7

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

Question 8

Explain what local non satiation is?

Answer 8

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

Question 9

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

Answer 9

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

Question 10

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

Answer 10

Theorem 2 states that given the assumptions of LNS, and all agents having continuous and convex preferences Pareto efficiency implies that there is a walrasian equilibrium