Amoroso–Robinson relation

The Amoroso–Robinson relation, named after economists Luigi Amoroso and Joan Robinson, describes the relation between price, marginal revenue, and price elasticity of demand. It is a mathematical consequence of the definitions of the quantities. For example, it holds true both when perfect competition holds and when a monopoly is present.

The relation states that

${\displaystyle {\frac {\partial R}{\partial x}}=p\left(1+{\frac {1}{\epsilon _{x,p}}}\right)}$

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where

• ${\displaystyle {\frac {\partial R}{\partial x}}}$ is the marginal revenue,
• ${\displaystyle x}$ is the quantity of a particular good,
• ${\displaystyle p}$ is the good's price,
• ${\displaystyle \epsilon _{x,p}}$ is the price elasticity of demand.