Auction Market Model

Typical exam question: 1) compare the models and state the characters of the models; 2) given a special circumstance and which model would you use.

-Walrasian Equilibrium: price that equals demand and supply--exogenous info and asymmetric info, so no need to revise my demand function since nothing can extract from the price the counterpart offer.
-REE: rational expectation equilibrium--I learn from the price (change my trading decision and demand function), equilibrium price is where every part does not want to change their trading decision when they see it, stops when I see the price the same to my expectation.

• New concept of equilibrium: if prices are vehicles of information, the equilibrium price is that price at which, once observed, agents do not want to trade again.

• GS paradox: the informed paid the price to become informed, the non-informed can free-ride the info from the price they observe, so the informed become less and less incentivized to pay the price.

• (Solution) To write this model, we introduce the noise (noise trader), that can not extract precise info from the price, so the prices are not fully revealing, i.e. the market is made up of the informed, non-informed and noise trader (they are irrational, and their welfare function is hard to write..).

• informed trader (risk averse):
  -speculate (on their signal)
  -hedge (for their endowments)
  So, for a noise trader, they can not extract the exact information from the price. (if bad, sell, long)

• traders act competitively: that is, when the trader submit their demand function, they do not take into account the price impact their net demand would cause on the equilibrium price.

• Imperfect competition: they take into account the price impact, so they would be less aggressive and trade less.

• F: future value of stock

• "A" is the degree of risk aversion

• Use the Theorem of Projection for Normal Distribution and compute
  -note: the trick is just like you do the OLS, and Cov(F,S) is sigma square s, Var(S) is also sigma sqare s, E(F) is 0, so that E(F|S)=S.