Lecture 5 - Walrasian Equilibrium and Welfare theorems in Economies with production

Question 1

To be in walrasian equilibrium we need prices p such that at p:

Answer 1

• Allocation X has every agent choosing their optimal consumption bundle subject to their budget constraint.
• Production Y has every firm maximising profit subject to their production set.
• The markets clear

Question 2

What are the exogenous variables in a production economy

Answer 2

• There are a set I of consumers or agents.
• A set J of goods
• A set M of firms

Question 3

What is the budget constraint for consumers in a production economy equal to?

Answer 3

The value of goods they demand is no greater than the income they get plus the value of endowment plus any income from shares they own.

Question 4

What are the conditions needed for a walrasian equilibrium in a production economy

Answer 4

1. For each consumer i in a set of I consumers, the choice bundle Xi solves the UMP:
2. For each firm m in a set of M firms bundle Ym solves the profit maximisation problem.
3. All markets clear: Demand = Endowment + Net output

Question 5

What is the excess demand vector equal to

Answer 5

Excess Demand = Demand - Supply

Question 6

What must excess demand be equal to in order to find a walrasian equilibrium

Answer 6

0

Question 7

What is the method for finding the walrasian equilibrium in a production economy

Answer 7

• For each firm m in a set of m firms find the profit max production vectors of each firms as a function of prices Ym(p) and the profit P.Ym(p)
• For each consumer i in a set of I firms, find their optimal bundle s.t BC Xi(p) including profits from shares in the BC.
• Write down the market clearing condition Z(p)=0
• Find the price vector P that clears all markets.