Consider a Monopolist who does not know the demand curve it faces. Suppose
that
p = a − bq + e (7)
with probability p or
p = a − bq + e (8)
with probability 1 − p. The p is the prior belief.
Here e is uniformly distributed over the interval[−1, 1]. Find the profit
function,V(p), for the second period as a function of p? Set up a two period
maximization problem for the monopolist. In particular, find EV(p), where
p is the next period beliefs. Find p using the Bayesian updating method by
splitting the set of possible outcomes into three sections. Make sure you know
the probability of each of the sections occurring. Use these three sections and
their probabilities to find EV(p) the expected value of next periods profits.