Lecture 8

Question 1

Prove the Only if of the following proposition.

Answer 1

The “if” proof isn’t on the exam so i doubt this’ll be on it but who knows.

Question 2

Give a proof of the first welfare theorem.

Answer 2

Question 3

State the first welfare theorem.

Answer 3

If utility is increasing in x and contiuous, then a price vector p* has a conrresponding allocation x* which is pareto efficient if x* is a walrasian equilibrium.

Question 4

State the second welfare theorem.

Answer 4

If utility is continuous, quasi-concave and increasing, then if x* is a Pareto-efficient allocation, there exists a price vector p* s.t (x, p) is a Walrasian equilibrium of the exchange economy.