Analysis of Market Power as Market Imperfection

First, some definitions and reminders:

Marginal Revenue - MR - Additional revenue resulting from producing and selling one more unit of the good or service.

Marginal Cost - MC - Additional cost incurred when one more unit of the good or service is produced.

By the time you get to this simple example you should already know the definitions of consumer surplus, producer surplus and deadweight loss.

When markets are competitively organized the marginal benefit accruing to consumers from the last unit consumed is equal to society's opportunity cost of producing that last unit.  What does it mean to say that the market is competitively organized?

For the sake of the argument we will suppose that there is just one firm in the market, pictured as above.  The demand curve and marginal cost curve are given by P = 100 - 1/2 Q and MC = 10 + 1/4 Q.

Derive the marginal revenue curve equation.

Label the intercepts with the appropriate numbers.

What are the profit maximizing price and quantity for this firm?

Suppose that the firm could be compelled to operate as though it had no market power.  That is, it must mimic the competitive outcome.  What would be the market price and quantity?

What is the deadweight loss associated with market power in this example?