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