Characterize each of the following statements as true or false, and explain your answer.

A. If marginal revenue is less than average revenue, the demand curve will be downward sloping.

B. Profits will be maximized when total revenue equals total cost.

C. Given a downward-sloping demand curve and positive marginal costs, profit-maximizing firms will always sell less output at higher prices than will revenue-maximizing firms.

D. Marginal cost must be falling for average cost to decline as output expands.

E. Marginal profit is the difference between marginal revenue and marginal cost and will always equal zero at the profit-maximizing activity level.