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## Consumer Surplus

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**Consumer Surplus**Math 150: Spring 2004**Basic Idea**• Consumers have “extra cash” if the price of an item is kept artificially low • Example: The price of a bottled Coke is kept at $1.00 even though high demand might allow $1.50 to be charged. In this case you (the consumer) have a “surplus” of 50 cents.**Changing Prices**• Prices probably wouldn’t stay constant, though (at say $1.50) so the difference between the artificial price and the actual price will vary (say p(x) – 1.00) • To find the actual Consumer Surplus, we need to “add up” all these different surpluses using an integral**Consumer Surplus**• The Consumer Surplus for a product with demand curve p(x) at a fixed price B=p(A) is the area between the graphs y=p(x) and y=B from x=0 to x=A • Written as an integral, this is**Example**• EX: Suppose a product has demand curve p(x) = 50 - .6x in dollars and that the price is held artificially low at p=$20. What is the consumer surplus for this product? • Solution: The price is held at p=20 and this occurs when 50 - .6x = 20 so when x = 50 units. Then the consumer surplus is**Review for Final Exam**• Derivatives (About 25 questions total; about 15 from here) • Basic Derivatives • Polynomials • Exponential and logarithmic functions • Product rule, quotient rule • Chain rule • Slopes of tangents (evaluate at a point) • Equations of tangents • Continuity and differentiability • Applications of derivatives • Rates of change (velocity, marginal cost, marginal revenue, marginal profit) • Maxima and minima • Maximize profit, minimize cost • Maximize area, minimize perimeter • Economic Order Quantities • others • Graphing • Increasing and decreasing functions, extrema • Concavity, Points of inflection • Behavior as x!1, asympotes, behavior as f(x)\rightarrow\infty • Implicit Differentiation**More Topics for Final**• Integrals (about 10 from here) • Anti-derivatives (general and finding C) • Definite Integrals and the FTC • Riemann Sums (right and left hand sums) • Applications • Average value of a function • Future value of an income stream • Consumer surplus • Others • Distance from velocity • Total consumption/usage from rate of consumption/usage • The Method of Substitution