(a) Consider a profit-maximizing monopolist with costs of C(q) = cq and an inverse demand of p(Q) = a-bQ, where {a; b; c} > 0. What is the rm's objective equation as a function of q?

(b) What are the first- and second-order conditions associated with the rm's problem?

Using these conditions, demonstrate that the optimal quantity is Q* = (a-c)/2b. 

(c) If a = 9, b = 2, and c = 3, by how much would the rm's quantity change if the firm were subjected to a per-unit tax of $2? 

(d) If a = 9, b = 2, and c = 3, by how much would the rm's quantity change if the firm were subjected to a lump-sum tax of $4?