In this question you 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)=1/2ky^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 maximing rate of outuput say y=y^s(a,b,k,s)
b)Find the monopolists optimal price, say p=p^s(a,b,k,s).
c) Find the comparative statics for an increase in the sales tax, namely y^s/s and p^s/s , and provide an economic interpretation of them.
d)What is the economic interpretation of an increase in the parameter a? You might want to plot the demand function to help with your interpretation.