A local cable provider faces demand q(p) = 100p-2, and cost function C(q) = q^3/2. Assume that this provider is the only firm offering cable in this town. (a) Find the equilibrium price, quantity, and profit for the cable provider. (b) Find the equilibrium price, quantity, and profit if the monopolist were to produce at the perfectly competitive equilibrium. (c) Can the local regulator impose a lump-sum tax on the cable provider to produce at the competitive cquilibrium? Why or why not? If so, find the value of the tax 1 (d) Can the local regulator impose a per-unit tax on the cable provider to produce at the competitive equilibrium? Why or why not? If so, find the value of the per-unit tax t.