Definition
Marginal revenue is equal to the ratio of the change in revenue for some change in quantity sold to that change in quantity sold. This can also be represented as a derivative when the change in quantity sold becomes arbitrarily small. More formally, define the revenue function to be the following
- .
By the product rule, marginal revenue is then given by
- .
For a firm facing perfectly competition, price does not change with quantity sold, so marginal revenue is equal to price. For a monopoly, the price decreases with quantity sold, so marginal revenue is less than price (for positive ).
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