We will examine the effect of a sales tax on a monopolist's profit maximizing price and rate of output. Assume that the monopolist faces a linear inverse demand curve given by p(y)=a-by, where a>0 and b>0, and a quadratic total cost function c(.) given by c(y)=(1/2)ky^2, where k>0. The monopolist is also assumed to pay a fraction s, 0

a) Set up the monopolists profit maximization problem in the presence of the sales tax, and find the profit maximizing rate of output say y=y^s(a,b,k,s)

b) Find the monopolists optimal price, say p=p^s(a,b,k,s)