Monopoly Demand and Marginal Revenue
A monopolist is the market's only seller, so it faces the market demand curve. To sell more under one uniform price, it normally must lower the price. This makes marginal revenue smaller than price.
Suppose inverse demand is
Total revenue and marginal revenue are
For linear demand, MR shares demand's vertical intercept but has twice its slope.
Marginal-revenue closing challenge
Reveal marginal revenue one sale at a time, then close before revenue falls
To sell one more seat, every earlier ticket falls to the new uniform price. You have two forecast tokens; close at revenue-maximizing Q=8 and remember that MR can become negative.
Marginal revenue is hidden. Take the risk or spend one forecast token.
The output and discount effects
Selling one more unit creates an output effect: revenue from the new unit. But lowering the common price creates a discount effect: reduced revenue on every earlier unit. Marginal revenue equals the first minus the second.
This explains why MR can become negative while price remains positive. In the inelastic portion of demand, a quantity increase lowers total revenue. A profit-maximizing monopolist with nonnegative marginal cost therefore does not choose that region: reducing quantity would raise revenue and lower cost.
Do not treat the MR curve as buyer willingness to pay. Demand records the price buyers pay at each quantity; MR records how the seller's total revenue changes. This distinction becomes essential when choosing monopoly output and price.
Build MR from an actual ticket table
If five tickets sell at 20, total revenue is 100. To sell six, the venue lowers the uniform price to 18, making total revenue 108. The sixth ticket's marginal revenue is only 8, not 18.
We can reconstruct the 8 in two ways. The new ticket adds 18, but the five old tickets each lose 2, subtracting 10. Thus . Or simply calculate the change in total revenue, . Both routes must agree.
Connect MR to total revenue
When MR is positive, adding output raises TR. When MR is zero, TR is at a peak or flat between discrete quantities. When MR is negative, extra output lowers TR. This sign relationship makes the MR curve easier to understand than memorizing its slope.
The mistake to avoid is reading price from MR. Price belongs to demand because it records buyer willingness to pay. MR is the seller's change in revenue after accounting for the lower common price.
KNOWLEDGE QUIZ
Build a monopoly revenue schedule
A venue faces inverse demand P=30−2Q for Q=0–10. It must charge one price to all visitors.
- Calculate price and total revenue for every quantity.
- Calculate discrete marginal revenue from each additional ticket.
- Graph demand and MR and identify where TR is maximized.
- For Q=5→6, separate revenue on the new ticket from lost revenue on the first five tickets.