Suppose a monopolist has a total cost function of:

TC = 400 + 20Q + Q^2

where Q is the quantity of output produced and sold. The monopolist faces a demand curve given by:

P = 100 - Q

a) Determine the monopolist's profit-maximizing level of output and price.

b) Calculate the monopolist's profit at this level of output and price.

c) Determine the monopolist's marginal revenue and marginal cost at the profit-maximizing level of output.

d) Calculate the monopolist's price elasticity of demand at the profit-maximizing level of output.