Lent - Handout 1: Exchange, Edgeworth Box, Competitive Equilibrium, First and Second Welfare Theorems

Question 1

What is the difference between general equilibrium and partial equilibrium?

Answer 1

• partial equilibrium theory studies a single market in isolation (assume conditions in the other markets are fixed)
• general equilibrium theory studies the effect of all markets

Question 2

What are the three important theories of general equilibrium theory?

Answer 2

• decentralisation
• prices as signals (means prices are the only message that producers and consumers use to make decisions)
• the invisible hand

Question 3

What are the conditions when considering Competitive Equilibrium or General Competitive Equilibrium

Answer 3

• we consider models in which all agents are price takers
• that is: perfect competition - no monopolies or oligopolies

Question 4

What are the 4 primitives of Competitive Equilibrium theory?

Answer 4

• scarcity of resources (initial endowments)
• property rights (distribution of endowments and ownership of firms)
• needs and desires (utility functions)
• technology possibilities in production

Question 5

What is meant by a pure exchange model?

Answer 5

no production is possible

Question 6

Define Pareto efficiency in words?

Answer 6

• improving the condition of every individual as far as possible whenever this can be done without harming someone else
• OR
• a state where it is impossible to make someone better off without making someone else worse off

Question 7

Explain what it means for B to be Pareto-superior to A or B to Pareto-dominate A or B to be a Pareto-improvement over A

Answer 7

• take 2 feasible states of affairs A and B involving some group of people (e.g. A and B are different ways of sharing out a fixed bundle of goods among the group)
• if nobody strictly prefers A to B, but at least one person strictly prefers B to A then we say that B is Pareto-superior to A

Question 8

What is the relationship between a Pareto-efficient allocation and the MRS? For 2 goods and 2 people. Derive this.

Answer 8

• MRS(A) = MRS(B)
• use the Lagrange multiplier method
• start with maximising u(x1A, x2A) by choosing x1A, x2A, x1B, x2B; s.t. u(x1B, x2B) = u̅
• we also have: x1A + x1B = w1 (= w1A + w1B), where w = endowment
• and: x2A + x2B = w2 (= w2A + w2B)
• thus, L = u(x1A, x2A) - λ(u(x1B, x2B) - u̅) - µ1( x1A + x1B - w1) - µ2(x2A + x2B - w2)
• by taking FOCs, we get that MRS(A) = MRS(B) = µ1/µ2

Question 9

What is meant by the contract curve?

Answer 9

the set of Pareto-efficient allocations where A’s indifference curve is tangent to B’s indifference curve, so A’s MRS equals B’s MRS

Question 10

Each point in the Edgeworth Box is a…?

Answer 10

is a feasible allocation

Question 11

A Competitive Equilibrium is a price pair (p1, p2) such that…?

Answer 11

a Competitive Equilibrium is a price pair (p1, p2) such that, when each agents acts as a price taker and chooses their best bundle at those prices, both markets clear (i.e. supply = demand for both markets)

Question 12

At an equilibrium, the price pair must be such that each agent chooses the same point in the Edgeworth Box. Will an equilibrium price pair necessarily exist?

Answer 12

• yes, if the optimal bundle for each agent changes in a continuous way as prices change
• when p is very low, there will be positive excess demand for the good, as long as the good is desirable
• when p is very high, the price of the other good is very low relative to p, so there will be excess demand for the other good, and hence negative excess demand for the good considered
• hence, there must be at least one price at which aggregate excess demand for the good is zero (from the Edgeworth box, if one market clears, the other must also clear)