consider a monopolist, who faces the demand function Q(P)=1/128+Q^2/2

a) Is the demand curve elastic/inelastic/unit elastic?

b)Given your answer in the previous question, can p be =1/4 be the monopolist's optimal price? Explain the intuition behind your answer without solving the monopolist's problem explicitly.

c) Find out the marginal revenue also the marginal cost functions and show them graphically.

d)Find the monopolist's price, output, profit, and the price of the cost margin

e)What are the consumer surplus, producer surplus and the social welfare in the market?

f)If the monopolist's costs are given by C(Q)=F+Q^2/2, then what is the maximum value of the fixed costs F that keeps the monopolist in the market in the long-run?

g)Find the consumer surplus, producer surplus,and social welfare in the market compare them with those in the perfectly competitive market in problem 1