Consider a situation where a monopolist faces the following inverse market demand curve:

p = 100 0.5q

and the following cost function:

T C = 8q + q^2

a) Derive the marginal revenue and marginal cost functions.

b) What are the equilibrium price and quantity if this market behaved as if it were perfectly competitive?

c) What are the equilibrium price and quantity when the monopolist produces as a monopolist?