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Marginal profit is the derivative of the profit function with respect to quantity. It measures the rate at which profit changes as the quantity produced changes.
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Derivative: A measure of how a function changes as its input changes. In calculus, it represents an instantaneous rate of change.
Marginal Cost: $\frac{dC}{dq}$, where $C$ is total cost and $q$ is quantity; it measures the cost of producing one more unit.
Marginal Revenue: $\frac{dR}{dq}$, where $R$ is total revenue and $q$ is quantity; it measures the revenue gained from selling one more unit.