Microeconomics CLEP question?

[MCunningham]

I just finished reading a chapter in a Microeconomics textbook that stated the following:

1. Price = Marginal Revenue (P = MR) in a perfectly competitive firm.

and

2. Price = Marginal Cost (P = MC) in a profit-maximizing firm.


My questions:

1. Why would price be equal to marginal revenue? Isn't marginal revenue widely variable, because it's the extra revenue brought in by one more unit of production? How would that be applicable to the price level of a firm's total unit of production?

2. If price was equal to the marginal cost, how would that maximize profits? In that case, wouldn't you want the price to be MORE than the marginal cost?

I'm just not at all clear on how these two statements are fact. They don't make sense to me. Is anyone able to clear these up for me?

Thanks in advance!

MC