Equillibrium Theory Flashcards
What is the requirement for a Walrasian equillibrium
All agents optimize, market clear and budget constrains are overheld
How many budget constraints do agents face in a Arrow-Debreu economy?
Consumers only face 1 budget constraint
How many markets are then in an Arrow-Debreu economy?
L*S, where L is number of commodities, S is number of states
What is a contingent commodity?
A contract that promises the delivery of one unit of a commodity in a certain state
When does trade occur in an Arrow-Debreu model?
Only at t=0, trade occurs in contingent commodities that are consumed in period 1
what are the endowments of the agents in an Arrow-Debreu economy?
In an AD economy, agents are endowed with contingents commodities. Defined by commodity type and state of the world
How many markets are then in an Asset Market model economy?
2L + S. Where L is number of commodities, S is number of states
Describe the Financial Market model
It is special case of the Asset market model with only one good in the economy, i.e. L=1
Why can’t arbitrage exist in a Financial equilibrium?
If an arbitrage opportunity existed, the agent could increase utility without affecting the budget constraint in a negative way. This contradicts the optimality condition of equilibrium
Why won’t redundant asset be traded in equillibrium?
Since assets are traded to obtain new payoff profiles and then payoff profile of a redundant asset can be replicated by other assets, there is no reason to trade a redundant asset Redundant assets can still be priced in terms of other assets
What are the conditions for MRS in a FE?
The marginal rates of substitution across states of the world are equal for all agents
What are the welfare implication of FE?
When markets are complete, FE is Pareto Optimal. When markets are incomplete, FE is constrained Pareto Optimal. Issuing a new good outside of the existing asset span may not always complete markets
What is the relationship between the FE and the AD equillibrium?
When markets are complete, the FE collapses to the AD equilibrium. Allocations will be the same. As long as agents can transfer wealth between any states, the optimum can be achieved
Will agents ever trade securities in a Lucas model?
No, since agents are assumed to be similar, agents will either all want to sell, buy or keep. An agent can never find someone to take the other side of the trade, since agents are identical. Therefore, prices will be such that no trade will occur, i.e. no agents wants to sell or buy
What is the general euler equation for the price of a security in terms of any payoff?
Derive Breeden’s formula
Derive the Consumptions CAPM
