Calculating Consumer surplus Using Integration
The total consumer surplus can be precisely calculated by treating the quantity (Q) as a continuous variable, which allows for the use of integration. For any given price (P₀) and quantity (Q₀), 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), and the price, P₀—from zero to the total quantity sold, Q₀. The integral form is: . This can also be expressed as , where F(Q) represents the integral of the inverse demand function, f(q), from 0 to Q. This alternative method involves finding the total area under the demand curve up to the equilibrium quantity () and then subtracting the total expenditure (). For a more comprehensive understanding of integration, section 19.1 of 'Mathematics for Economists: An Introductory Textbook' by Pemberton and Rau is a recommended resource.
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Ch.8 Supply and demand: Markets with many buyers and sellers - The Economy 2.0 Microeconomics @ CORE Econ
The Economy 2.0 Microeconomics @ CORE Econ
Introduction to Microeconomics Course
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