Formula

Calculating Consumer Surplus Using Integration

The total consumer surplus can be precisely calculated by treating the quantity (QQ) as a continuous variable, which allows for the use of integration. For any given price (P0P_0) and quantity (Q0Q_0), whether at market equilibrium or not, the consumer surplus is found by integrating the individual surpluses—the difference between the inverse demand function, f(q)f(q), and the price, P0P_0��from zero to the total quantity sold, Q0Q_0. The integral form is: 0Q0(f(q)P0),dq\int_{0}^{Q_0} (f(q) - P_0) ,dq. This can also be expressed as F(Q0)P0Q0F(Q_0) - P_0Q_0, where F(Q)F(Q) represents the integral of the inverse demand function, f(q)f(q), from 0 to QQ. This alternative method involves finding the total area under the demand curve up to the quantity (Q0Q_0) and then subtracting the total consumer expenditure (P0×Q0P_0 \times Q_0).

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Updated 2026-07-02

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