Class 9: Area, Consumer Surplus, Integration

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Class 9 Area, Consumer Surplus, Integration
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What is Total Possible Revenue?
The total possible revenue is the money that the
producer would receive if everyone who wanted the
good, bought it at the maximum price that he or
she was willing to pay.
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Consumer Surplus
The total extra amount of money that people who
bought the good would have been willing to pay is
called the consumer surplus.
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Finding Areas

• What is the area of the region R that is
  enclosed between the x-axis and the graph of f(x)
  2?x ? x2/2, for x between 1 and 4?

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Finding Areas

• What is the area of the region R that is
  enclosed between the x-axis and the graph of f(x)
  2?x ? x2/2, for x between 1 and 4?

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For n 6 rectangles
Sum of areas called S6 f(m1)??x f(m2)??x
f(m3)??x f(m4)??x f(m5)??x f(m6)??x
4.531250.
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More rectangles Larger n
As n increases, the value of Sn increases,
getting closer and closer to the true are under
the curve.
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Integral Notation

• We write the value of the midpoint sum as n gets
  very large by an integral

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Find Revenue from Buffalo Dinners Not
SoldOptimum price and quantity are 19.19 and
2300
4014
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Find Consumer Surplus for Dinners