(50 pts) In a monopolized industry, the demand is given by
q=D(p)=p^(-\epsi )
, where
\epsi >1
. Marginal cost is constant and equal to
c
. (1) Derive, the demand elasticity. (2) Solve the monopolist's problem by finding the price that maximizes the profit. (3) Derive the socially optimal price. (4) Write the total welfare,
W^(**)
with socially optimal price in terms of
c
and
\epsi
only. (5) Compute the welfare loss under monopoly.