A monopolist faces a demand curve given by Q = RA^0.5/p^2, where p is its price, A is its level of advertising and r is a positive constant. Advertising and output both cost the monopolist 1 per unit. The monopolist chooses price and advertising in order to maximise profit.

(a) Show that the monopolist chooses a price of p^m=2 (with output of Q= RA^0.5/4), an advertising of A^m = (R/8)^2, and a level of output given by Q^m= r^2/32.

(b) Bearing in mind the way the monopolists output changes with A (found in (a), find expressions for the monopolists profit and for consumer surplus, both as functions of advertising.

(c) Hence, calculate the level of advertising preferred by society and show that it is greater than one chosen by the monopolist

(d) state two factors that might overturn the 'over advertising' result in c.