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For example, I may be able to sell 10 guitars at 100each, butinordertosell11guitars, Iwillhavetoofferapriceof95. Unfortunately, it's very difficult to sell 10 guitars at 100andthensellthelastoneat95. In our model of a monopoly, there can only be one price for a good. If I choose to sell 11 units, I make 95revenueonthe11thguitar, butIlose5 revenue on each of the first 10 guitars. If it costs me 50toproduceaguitar, mymarginalrevenueisthen95 - 50 =45.

Let's generalize. Assume that a monopolistic firm faces a linear, downward- sloping market demand curve, described as follows:

Q = 100 - P
Let's further assume its marginal cost curve is constant at a value of 10.
MC = 10

Our firm naturally wants to maximize profits and will therefore aim to satisfy the profit maximizing condition, MC = MR. Marginal costs are constant at ten, so half of our equation is easy. To find our marginal revenue, we first look at the total revenue. Total revenue is simply:

R = P * Q

Because the monopolist faces the entire market demand curve, price and quantity have a one-to-one relationship. That is, P = 100 - Q. We can rewrite our total revenue as:

R = (100 - Q) * Q = 100 * Q - Q^2

The marginal revenue is simply the first derivative of the total revenue with respect to Q.

MR = 100 - 2 * Q

If you don't feel comfortable with derivatives, you can convince yourself this MR is correct by analyzing its components.

MR = (100 - Q) - Q

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