1. Consider the sequential trading model of Glosten and Milgrom (1985). Let us assume that:

• The future value of the asset, V, can take the value of 42 or 36 with equal probability. That is, =0.5.
• Half the traders are informed and half are uninformed. That is =0.5.
• Further, assume that the uninformed traders are equally likely to buy or sell.
• The dealer earns zero expected profits, such that:

at=E(V|Bt)

bt=E(V|St)

where at is the ask price, bt is the bid price, Bt indicates a buy order and St indicates a sell order all at time t.

• Given Bayes theorem:

PYZ=P(Z|Y)P(Y)P(Z)

solve for the bid price, ask price and bid-ask spread at time t.

b) Following from part (a), assume that the dealer receives a buy order at time t. Would the dealers quotes increase or decrease from t to t+1? Would the bid-ask spread increase or decrease from t to t+1? Explain the economic intuition of these predictions.