Equilibrium with Exchange

Question 1

What is the difference between Partial and General Equilibrium analysis?

Answer 1

Partial looks at a single market in isolation, general looks at multiple markets

Question 2

What are three important themes of General Equilibrium theory?

Answer 2

Decentralisation, prices as signals/messages, “invisible hand”

Question 3

What is (General) Competitive Equilibrium?

Answer 3

The equilibrium in a model where agents are price takers (perfect competition)
Also called Walrasian or Arrow-Debreu Equilibrium

Question 4

What is the outline of the CE model?

Answer 4

A large number of distinct goods each have a market and a market price, a large number of consumers each with an endowment of goods (could be labour) have preferences over consumption bundles and choose what they sell and buy at market prices, a large number of firms each have a production technology and choose a profit-maximising production plan
Knowing technology, preferences, and initial distribution of endowments is enough for a theory of the whole economic system

Question 5

What does it mean for a market to clear?

Answer 5

Total supply in the market equals total demand in that market for a given price
If the market doesn’t clear, the price would change

Question 6

What are the primitives for CE theory?

Answer 6

Scarcity of resources (initial endowments), property rights (distribution of endowments and ownership of firms), utility functions, production functions

Question 7

What is the most basic form of CE theory?

Answer 7

The Pure Exchange model (2 goods, 2 consumers, no firms)

Question 8

What are the definitions of Pareto domination, superiority, and improvement?

Answer 8

Consider 2 feasible states of affairs (allocations) X and Y where nobody strictly prefers X to Y but at least one person strictly prefers Y to X
Y is Pareto-superior to or Pareto-dominates or is a Pareto-improvement over X

Question 9

What is Pareto-efficiency?

Answer 9

A feasible allocation X is Pareto-efficient if there is no feasible allocation which is Pareto-superior to it, i.e. someone can be made better off without making anyone worse off, otherwise it is Pareto-inefficient
A Pareto-efficient state of affairs may not be normatively desirable
Two agents would be expected to negotiate until they reach a Pareto-efficient outcome (allocation)

Question 10

What is an Edgeworth Box?

Answer 10

A representation of the feasible and optimal allocations for two consumers in a pure exchange economy
One agent has one set of axes on one side of the box representing two goods and the other agent has the same, the width of the box is determined by the amount of each good available, each point in the box is a feasible allocation, the endowment would be some point W

Question 11

How would you represent the set of Pareto-efficient allocations on an Edgeworth Box?

Answer 11

A contract curve which plots the points where each agent’s IC are tangent
At any other point in the box the ICs passing through the point form an ellipse shape with the enclosed area being a Pareto-improvement so agent’s will negotiate to the contract curve

Question 12

What is the basis of CE in a pure exchange economy?

Answer 12

An “auctioneer” announces the prices and the agents act as utility maximising price takers
The two agent case is equivalent to the case of two groups of many agents with the same preferences and endowments

Question 13

How does each agent make their optimal choice in the pure exchange model?

Answer 13

Based on the price pair set by the auctioneer, there is one budget line passing through the endowment
Each agent will choose the amount of each good which places them at the tangent between an IC and the BL which results in the choice being the intersection between the BL and contract curve

Question 14

What is net demand and what is the significance for CE in the pure exchange economy?

Answer 14

Net demand denoted e = final allocation - endowment for each good
A CE is a price pair such that the market clears so the sum of net demands for each good must equal zero, otherwise there will be positive excess demand or supply (prices should adjust)

Question 15

What restriction does CE place on prices?

Answer 15

The price pair must be such that each agent chooses the same point in the Edgeworth Box

Question 16

Under what conditions does an equilibrium price pair exist?

Answer 16

As long as the optimal bundle for each agent changes in a continuous way as prices change

Question 17

What are some features of equilibria?

Answer 17

They are not necessarily unique, they can be stable or unstable (changing prices when not in equilibrium sometimes moves closer to an equilibrium and sometimes not), and they are Pareto-efficient as long as preferences satisfy non-satiation

Question 18

What is the First Fundamental Theorem of Welfare Economics?

Answer 18

As long as preferences satisfy the non-satiation property (thin ICs), a CE allocation is Pareto-efficient
Implicitly assumes there are no externalities, agents act as price takers, and an equilibrium exists

Question 19

How can an agent act as a monopolist in a pure exchange economy?

Answer 19

If one of the agents sets the prices

Question 20

What is an offer curve?

Answer 20

An agent’s offer curve traces out the optimal bundles as a price changes

Question 21

How would a monopolist in a pure exchange economy act?

Answer 21

The monopolist chooses the point on the price taking agent’s offer curve passing through the endowment which maximises their utility (tangent)
This is Pareto-inefficient as the monopolist’s IC is tangent to the offer curve, not the price taker’s IC (or the BL)

Question 22

How would you algebraically derive equilibrium prices and allocations in a pure exchange economy?

Answer 22

Solve the utility maximisation problem subject to the budget constraint to get demand in terms of prices, then use the market clearing condition on net demands to find the prices (for two goods, if one market clears so does the other) which can be normalised (multiplying prices by same number doesn’t change budget set)

Question 23

What is Walras’ Law?

Answer 23

p_xe_x + p_ye_y = 0 for both agents as each agent will choose a bundle on the BL so the value of the sale of one good must equal the value of the sale of the other good so we get Walras’ Law (above eqn added together for both agents) which is that the value of aggregate excess demands summed over all goods is zero (true for all prices, not just eqm) so if there is excess demand in one market there must be excess supply in the other

Question 24

What is the Second Fundamental Theorem of Welfare Economics?

Answer 24

As long as preferences are convex, for any Pareto-efficient allocation there is an endowment such that the allocation is a CE allocation

Question 25

What is an implication of the Second Welfare Theorem?

Answer 25

If a central planner wishes to change the allocation, they should use lump sum taxation to effectively change the endowments (assuming this is feasible)